A priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes

GP Offermans, L Biferale, M Buzzicotti, M Linkmann

Physics of Plasmas 25 (12), 122307, 2018

DOI: https://doi.org/10.1063/1.5046842 preprint arXiv:1807.00759

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

M Linkmann, M Buzzicotti, L Biferale

Journal of Turbulence 19 (6), 493-527, 2018

DOI: https://doi.org/10.1080/14685248.2018.1462497 preprint arXiv:1805.02413

A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method

G Tauzin, L Biferale, M Sbragaglia, A Gupta, F Toschi, A Bartel, M Ehrhardt

Computers & Fluids, Volume 172, 241-250, 2018

DOI: https://doi.org/10.1016/j.compfluid.2018.05.031 preprint arXiv:1809.06735

Time irreversibility in reversible shell models of turbulence

M De Pietro, L Biferale, G Boffetta, M Cencini

The European Physical Journal E 41 (4), 48, 2018

DOI: https://doi.org/10.1140/epje/i2018-11655-2 preprint arXiv:1801.00944v2

Nonuniversal behaviour of helical two-dimensional three-component turbulence

M Linkmann, M Buzzicotti, L Biferale

The European Physical Journal E 41 (1), 4, 2018

DOI: https://doi.org/10.1140/epje/i2018-11612-1

Rayleigh-Taylor turbulence with singular non-uniform initial conditions

L Biferale, G Boffetta, AA Mailybaev, A Scagliarini

Physical Review Fluids 3, 092601, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.092601

Equivalence of Non-Equilibrium Ensembles in Turbulence Models

L Biferale, M Cencini, M De Pietro, G Gallavotti, V Lucarini

Phys. Rev. E 98, 012202, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.012202

On the effects of thermal fluctuations in the fragmentation of a nano-ligament

X Xue, M Sbragaglia, L Biferale, F Toschi

Phys. Rev. E 98, 012802, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.012802

Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions

J Friedrich, G Margazoglou, L Biferale and R Grauer

Phys. Rev. E 98, 023104, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.023104

Cascades and transitions in turbulent flows

Alexakis, L Biferale

Physics Reports, 2018

DOI: https://doi.org/10.1016/j.physrep.2018.08.001 preprint arXiv:1808.06186

Inferring flow parameters and turbulent configuration with physics-informed data-assimilation and spectral nudging

P Clark Di Leoni, A Mazzino, L Biferale

Phys. Rev. Fluids 3, 104604, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.104604 preprint arXiv:1804.07680v2

Turbulent statistics and intermittency enhancement in coflowing superfluid 4 He

L Biferale, D Khomenko, V L'vov, A Pomyalov, I Procaccia, G Sahoo

Physical Review Fluids 3 (2), 024605, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024605 preprint arXiv:1711.08246

Energy transfer in turbulence under rotation

M Buzzicotti, H Aluie, L Biferale, M Linkmann

Physical Review Fluids 3, 034802, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.034802 preprint arXiv:1711.07054

Smart Inertial Particles

S Colabrese, K Gustavsson, A Celani, L Biferale

Physical Review Fluids 3 (8), 084301, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.084301 preprint arXiv:1711.05853

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

F Milan, M Sbragaglia, L Biferale, F Toschi

The European Physical Journal E 41 (1), 6, 2018

DOI: https://doi.org/10.1140/epje/i2018-11613-0 preprint arXiv:1711.05498

Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence

M Buzzicotti, M Linkmann, H Aluie, L Biferale, J Brasseur, C Meneveau

Journal of Turbulence 19 (2), 167-197, 2018

DOI: https://doi.org/10.1080/14685248.2017.141759

Energy cascade and intermittency in helically decomposed Navier-Stokes equations

G Sahoo, L Biferale

Fluid Dynamics Research 50 (1), 011420, 2018

DOI: https://doi.org/10.1088/1873-7005/aa839a

Time irreversibility and multifractality of power along single particle trajectories in turbulence

M Cencini, L Biferale, G Boffetta, M De Pietro

Physical Review Fluids 2 (10), 104604, 2017

DOI https://doi.org/10.1103/PhysRevFluids.2.104604

Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

A Briard, L Biferale, T Gomez

Physical Review Fluids 2 (10), 102602, 2017

DOI https://doi.org/10.1103/PhysRevFluids.2.102602

TurBase: a software platform for research in experimental and numerical fluid dynamics

R Benzi, L Biferale, F Bonaccorso, HJH Clercx, A Corbetta, W MÃ¶biu , F Toschi, F Salvadore, C Cacciari, G Erbacci

2017 International Conference on High Performance Computing Simulation (HPCS), p51-57, 2017

DOI https://doi.org/10.1109/HPCS.2017.18

From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows

L Biferale, M Buzzicotti, M Linkmann

Physics of Fluids 29 (11), 111101, 2017

DOI: https://doi.org/10.1063/1.4990082 preprint arXiv:1706.02371

Multiscale anisotropic fluctuations in sheared turbulence with multiple states

KP Iyer, F Bonaccorso, L Biferale, F Toschi

Physical Review Fluids 2 (5), 052602, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.052602

Local and nonlocal energy spectra of superfluid He 3 turbulence

L Biferale, D Khomenko, V L'vov, A Pomyalov, I Procaccia, G Sahoo

Physical Review B 95 (18), 184510, 2017

DOI: https://doi.org/10.1103/PhysRevB.95.184510

Optimal subgrid scheme for shell models of turbulence

L Biferale, AA Mailybaev, G Parisi

Physical Review E 95 (4), 043108, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.043108

Discontinuous Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

G Sahoo, A Alexakis, L Biferale

Physical Review Letters 118 (16), 164501, 2017

DOI: https://doi.org/10.1103/PhysRevLett.118.164501

Flow navigation by smart microswimmers via reinforcement learning

S Colabrese, K Gustavsson, A Celani, L Biferale

Physical Review Letters 118 (15), 158004, 2017

DOI https://doi.org/10.1103/PhysRevLett.118.158004

Finding efficient swimming strategies in a three-dimensional chaotic flow by reinforcement learning

K Gustavsson, L Biferale, A Celani, S Colabrese

The European Physical Journal E 40 (12), 110, 2017

DOI: https://doi.org/10.1140/epje/i2017-11602-9 preprint arXiv:1711.05826

Chaotic and regular instantons in helical shell models of turbulence

M De Pietro, AA Mailybaev, L Biferale

Physical Review Fluids 2 (3), 034606, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.034606

Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Ganapati Sahoo, Massimo De Pietro, Luca Biferale

Physical Review Fluids, vol. 2, 024601, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.024601

Lagrangian statistics for Navier–Stokes turbulence under Fourier-mode reduction: fractal and homogeneous decimations

Michele Buzzicotti, Akshay Bhatnagar, Luca Biferale, Alessandra S Lanotte and Samriddhi Sankar Ray

New Journal of Physics 18 (11), 113047 (2017)

DOI: :10.1088/1367-2630/18/11/113047

Abstract: We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under

Fourier-mode reduction. The Navier–Stokes equations are evolved on a restricted set of modes,

obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity

(reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of

mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a

tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and

frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex

stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still

connected by a dimensional bridge-relationwhich is independent of the degree of Fourier-mode

decimation.

Coherent structures and extreme events in rotating multiphase turbulent flows

Luca Biferale, Fabio Bonaccorso, Irene M Mazzitelli, Michel AT van Hinsberg, Alessandra S Lanotte, Stefano Musacchio, Prasad Perlekar, Federico Toschi

Physical Review X 6 (4), 041036 (2017)

DOI: 10.1103/PhysRevX.6.041036

Abstract: By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence under

rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale

leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By

seeding the flow with millions ofinertial particles, we quantify—for the first time—the effects of those coherent

vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively

show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the

entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever

measurement of the relative importance between Stokes drag, Coriolis force, and centripetal force along the

trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion

properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.

Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition

Moritz Linkmann, Ganapati Sahoo, Mairi McKay, Arjun Berera, Luca Biferale

Astrophys. Journal 836, 26 (2017)

DOI: 10.3847/1538-4357/836/1/26

Abstract We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

Chaotic and regular instantons in helical shell models of turbulence

Massimo De Pietro, Alexei A. Mailybaev, Luca Biferale

to be puslidhe on PRF arXiv:1608.00742v1

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

J. D. Gibbon, A. Gupta, G. Krstulovic, R. Pandit, H. Politano, Y. Ponty, A. Pouquet, G. Sahoo, and J. Stawarz

DOI:10.1103/PhysRevE.93.043104

Abstract: It is shown how suitably scaled, order-m moments, D m , of the Els¨asser vorticity ﬁelds in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P M = 1. These vorticity ﬁelds are deﬁned by ω ± = curl z ± = ω ± j, where z ± are Els¨asser variables, and where ω and j are, respectively, the ﬂuid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes ﬂuid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q ± that characterize the inertial range power-law dependencies of the z ± energy spectra, E ± (k), are then examined, and bounds are obtained. Comments are also ± made on (a) the generalization of our results to the case P M = 1 and (b) the relation between D m and the order-m moments of gradients of magnetohydrodynamic ﬁelds, which are used to characterize intermittency in turbulent ﬂows.

Reﬁned similarity hypothesis using three-dimensional local averages

K. Iyer, KR Sreenivasan and PK Yeung

Phys. Rev. E, 92, 063024 (2015)

DOI: 10.1103/PhysRevE.92.063024

Abstract: The reﬁned similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermit- tent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number R λ ∼ 650, on a periodic box of 4096 3 grid points to test the hypotheses using 3D averages. In particular, we study the small-scale properties of the stochastic variable V = ∆u(r)/(rǫ r ) 1/3 , where ∆u(r) is the longitudinal velocity increment and ǫ r is the dissipation rate averaged over a three-dimensional volume of linear size r. We show that V is universal in the inertial subrange. In the dissipation range, the statistics of V are shown to depend solely on a local Reynolds number.

Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Ganapati Sahoo, Massimo De Pietro, Luca Biferale

Phys. Rev. Fluids 2, 024601 (2017)

DOI: 10.1103/PhysRevFluids.2.024601

Abstract: We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.

Preferential sampling of helicity by isotropic helicoids

Kristian Gustavsson and Luca Biferale

Physical Review Fluids , vol. 1, 054201 (2016) arXiv:1609.05109

DOI: 10.1103/PhysRevFluids.1.054201}

Abstract: We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows.

These are particles whose motion is invariant under rotations but not under mirror reflections of the

particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical

particles. We show that heavy isotropic helicoids, due to the coupling between translational and

rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic

advecting flows. This opens the way to control and engineer particles able to track complex flow

structures with potential applications to microfluidics and turbulence.

Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence

K. Gustavsson, F. Berglund, P.R. Jonsson and B. Mehlig

Phys. Rev. Lett. 116, 108104 (2016) arXiv: 1501.02386

doi: 10.1103/PhysRevLett.116.108104

Abstract: Recent studies show that spherical motile micro-organisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent ﬂow. By analysing a statistical model we analytically compute how shape aﬀects the dynamics, preferential sampling, and small-scale spatial clustering. We ﬁnd that oblong organisms may spend more time in up-welling regions of the ﬂow, and that all organisms are biased to regions of positive ﬂuid-velocity gradients in the upward direction. We analyse small-scale spatial clustering and ﬁnd that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

X. I. A. Yang, C. Meneveau, I. Marusic and L. Biferale

Phys. Review Fluids 1, 044405 (2016) arXiv:1609.00743

DOI: 10.1103/PhysRevFluids.1.044405

Abstract: In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity ﬂuctuations exp(qu + ) develop power-law scaling as a function of the wall normal z distance z/δ. Here u is the streamwise velocity ﬂuctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and δ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3Re τ 0.5 z + , z 0.15δ where Re τ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30 < z + , z < δ, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, q o . ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at Re τ ranging from 2700 to 13 000 from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the ﬁltered, large-scale velocity ﬂuctuations u z L and of the remaining small-scale component, u z S = u z − u z L . The scaling of u z L falls within the conventionally deﬁned log region and depends on a scale that is proportional to 1/2 l + ∼ Re τ ; the scaling of u z S extends over a much wider range from z + ≈ 30 to z ≈ 0.5δ. Last, we present a theoretical construction of two multiplicative processes for u z L and u z S that reproduce the empirical ﬁndings concerning the scalings properties as functions of z + and in the ESS sense.

Statistical model for collisions and recollisions of inertial particles in mixing ﬂows

K. Gustavsson and B. Mehlig

The European Physical Journal E 39, 55 (2016) arXiv:1309.3834v2

doi: 10.1140/epje/i2016-16055-0

Abstract: Finding a quantitative description of the rate of collisions between small particles suspended in mixing ﬂows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles subject to Stokes force, based on results for relative velocities of heavy particles that were recently obtained within a statistical model for the dynamics of turbulent aerosols. This model represents the turbulent velocity ﬂuctuations by Gaussian random functions. We ﬁnd that the parameterisation gives quantitatively good results in the limit where the ‘ghost-particle approximation’ applies. The collision rate is a sum of two contributions due to ‘caustics’ and to ‘clustering’. Within the statistical model we compare the relative importance of these two collision mechanisms. The caustic formation rate is high when the particle inertia becomes large, and we ﬁnd that caustics dominate the collision rate as soon as they form frequently. We compare the magnitude of the caustic contribution to the collision rate to the formation rate of caustics.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

J. D. Gibbon, A. Gupta, G. Krstulovic, R. Pandit, H. Politano, Y. Ponty, A. Pouquet, G. Sahoo and J. Stawarz

Phys. Rev. E 93, 043104 (2016)

DOI: 10.1103/PhysRevE.93.043104 arXiv:1508.03756

Abstract: It is shown how suitably scaled, order-m moments, D m , of the Els¨asser vorticity ﬁelds in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P M = 1. These vorticity ﬁelds are deﬁned by ω ± = curl z ± = ω ± j, where z ± are Els¨asser variables, and where ω and j are, respectively, the ﬂuid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes ﬂuid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q ± that characterize the inertial range power-law dependencies of the z ± energy spectra, E ± (k), are then examined, and bounds are obtained. Comments are also ± made on (a) the generalization of our results to the case P M = 1 and (b) the relation between D m and the order-m moments of gradients of magnetohydrodynamic ﬁelds, which are used to characterize intermittency in turbulent ﬂows.

On the Vortex Dynamics in Fractal Fourier Turbulence

Alessandra S. Lanotte, Shiva Kumar Malapaka and Luca Biferale

The European Physical Journal E 39:49 (2016) arXiv: 1605.01527

DOI 10.1140/epje/i2016-16049-x

Abstract: Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension D. By tuning the fractal dimension parameter, we study the dynamical eﬀects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In partic- ular, we show that as we move from D = 3 to D ∼ 2.8, the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretch- ing properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous ﬂuctuations.

Inertial-particle accelerations in turbulence: a Lagrangian closure

S. Vajedi, K. Gustavsson, B. Mehlig and L. Biferale

Jour. Fluid Mech. 798,187 (2016) arXiv:1607.01888

doi:10.1017/jfm.2016.305

Abstract: The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite diﬀerent for light and heavy particles. In this article we analyse a closure scheme for the acceleration ﬂuctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of ﬂuid tracers. We compute the variance and the ﬂatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates eﬀects induced by the Lagrangian correlations along the trajectories of ﬂuid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the eﬀects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct func- tional behaviour of the acceleration variance, as a function of St, as well as the presence of a minimum/maximum for the ﬂatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity ﬁeld. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.

Reﬁned similarity hypothesis using three-dimensional local averages

K. Iyer, K.R. Sreenivasan and P.K. Yeung

Phys. Rev. E, 92, 063024 (2015) arXiv:1510.00628v2

doi:10.1103/PhysRevE.92.063024

Abstract: The reﬁned similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermit- tent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number R λ ∼ 650, on a periodic box of 4096 3 grid points to test the hypotheses using 3D averages. In particular, we study the small-scale properties of the stochastic variable V = ∆u(r)/(rǫ r ) 1/3 , where ∆u(r) is the longitudinal velocity increment and ǫ r is the dissipation rate averaged over a three-dimensional volume of linear size r. We show that V is universal in the inertial subrange. In the dissipation range, the statistics of V are shown to depend solely on a local Reynolds number.

Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers Equation

Michele Buzzicotti, Luca Biferale, Uriel Frisch, Samriddhi Sankar Ray

Phys. Rev. E 93, 033109 (2016). arXiv:1601.03697

doi: 10.1103/PhysRevE.93.033109

Abstract: We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension D. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical ﬂuctuations by changing D. We ﬁnd that a very small percentage of mode-reduction (D . 1) is enough to destroy most of the characteristics of the original non-decimated equation. In particular, we observe a suppression of intermittent ﬂuctuations for D < 1 and a quasi-singular transition from the fully intermittent (D = 1) to the non-intermittent case for D . 1. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.

Rotating turbulence under “precession-like” perturbation

Kartik P. Iyer, Irene Mazzitelli, Fabio Bonaccorso, Annick Pouquet and Luca Biferale

Eur. Phys. J. E, 38 12 (2015) 128 arXiv:1511.06159

DOI: 10.1140/epje/i2015-15128-x

Abstract: The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered.

We perform direct numerical simulations on a periodic box of 10243 grid points, where the orientation

of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate

with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas

in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in

a strong forward energy transfer and large scale structures that resemble those of isotropic turbulence.

Phase and precession evolution in the Burgers equation

Michele Buzzicotti, Brendan P. Murray, Luca Biferale, Miguel D. Bustamante.

Eur. Phys. J. E, 39 3 (2016) 34. arXiv:1509.04450

DOI: 10.1140/epje/i2016-16034-5

Abstract: We present a phenomenological study of the phase dynamics of the one-dimensional stochasti- cally forced Burgers equation, and of the same equation under a Fourier mode reduction on a fractal set. We study the connection between coherent structures in real space and the evolution of triads in Fourier space. Concerning the one-dimensional case, we ﬁnd that triad phases show alignments and synchroni- sations that favour energy ﬂuxes towards small scales –a direct cascade. In addition, strongly dissipative real-space structures are associated with entangled correlations amongst the phase precession frequencies and the amplitude evolution of Fourier triads. As a result, triad precession frequencies show a non-Gaussian distribution with multiple peaks and fat tails, and there is a signiﬁcant correlation between triad precession frequencies and amplitude growth. Links with dynamical systems approach are brieﬂy discussed, such as the role of unstable critical points in state space. On the other hand, by reducing the fractal dimension D of the underlying Fourier set, we observe: i) a tendency toward a more Gaussian statistics, ii) a loss of alignment of triad phases leading to a depletion of the energy ﬂux, and iii) the simultaneous reduction of the correlation between the growth of Fourier mode amplitudes and the precession frequencies of triad phases.

Disentangling the triadic interactions in Navier-Stokes equations

Ganapati Sahoo, Luca Biferale

The European Physical Journal E 38 (10), 114 arXiv:1510.09006

DOI: 10.1140/epje/i2015-15114-4

Abstract: We study the role of helicity in the dynamics of energy transfer in a modiﬁed version of the Navier- Stokes equations with explicit breaking of the mirror symmetry. We select diﬀerent set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wavenumbers except for those falling on a localized shell of wavenumber, |k| ∼ k m . Changing k m to be above or below the forcing scale, k f , we are able to assess the energy transfer of triads belonging to diﬀerent interaction classes. We observe that when the negative helical modes are present only at wavenumber smaller than the forced wavenumbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at wavenumber larger than the forced wavenumbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.

Eulerian and Lagrangian statistics in fully developed rotating turbulent flows.

L. Biferale, F. Bonaccorso, I. Mazzitelli, A. Lanotte, P. Perlekar, S. Musacchio, M. Hinsberg, F. Toschi,

Abstract DFD15-2015-000509 APS. We present results concerning both Eulerian and Lagrangian statistics for turbulent under rotation at small and large Rossby numbers. Concerning the Eulerian statistics we discuss the effects of the presence of strong coherent large-scale vortical structures on the small-scale statistics. Concerning Lagrangian prop- erties, we discuss the effects of preferential sampling at changing the inertial properties of the particles also due to the centrifugal and Coriolis forces.

Turbulence structure subjected to precession-like rotation.

Kartik Iyer, Irene Mazzitelli, Fabio Bonaccorso, Luca Biferale

Abstract DFD15-?

Inverse energy cascade in non-local helical shell-models of turbulence

M. De Pietro, L. Biferale, G. Sahoo, A. Mailybaev

Abstract: DFD15-2015-000648 APS. Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space we introduce a modified version of helical shell-models for turbulence with non-local triadic interactions. By using both analytical argument and numerical simulation we show that there exists a sub-class of mod- els with elongated shell interactions that exhibits a statistically stable inverse energy cascade. Using also data from direct numerical simula- tions of helical Navier-Stokes equations we further support the idea that energy transfer mechanism in fully developed turbulence is the result of a strong entanglement among different triadic interactions possessing different transfer mechanisms.

Inverse energy cascade in nonlocal helical shellmodels of turbulence

Massimo De Pietro, Luca Biferale, Alexei A. Mailybaev

Phys. Rev. E 92, 043021 (2015) arXiv:1508.06390

doi:10.1103/PhysRevE.92.043021

Abstract: Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations

in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of

helical shell models for turbulence with non-local triadic interactions. By using both an analytical

argument and numerical simulation, we show that there exists a class of models, with a specific

helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with

that predicted for the Navier-Stokes equations restricted to the same helical interactions. We

further support the idea that turbulent energy transfer is the result of a strong entanglement

among triads possessing different transfer properties.

Analysis of the Correlation Dimension For Inertial Particles

K. Gustavsson, B. Mehlig and M. Wilkinson

Phys. Fluids, 27 073305 (2015). arXiv:1502.05694

doi:10.1063/1.4927220

Abstract: We obtain an implicit equation for the correlation dimension which describes clustering of

inertial particles in a complex flow onto a fractal measure. Our general equation involves

a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid

appears as additive noise. When the long-time limit of the propagator is considered our

equation reduces to an existing large-deviation formalism, from which it is difficult to

extract concrete results. In the short-time limit, however, our equation reduces to a solvability

condition on a partial differential equation. In the case where the inertial particles

are much denser than the fluid, we show how this approach leads to a perturbative expansion

of the correlation dimension, for which the coefficients can be obtained exactly and

in principle to any order. We derive the perturbation series for the correlation dimension

of inertial particles suspended in three-dimensional spatially smooth random flows with

white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.

Role of helicity for large- and small-scales turbulent fluctuations

G. Sahoo, F. Bonaccorso and L. Biferale

Phys. Rev. E 92 (5), 051002 (2015) arXiv:1506.04906

doi:10.1103/PhysRevE.92.051002

Abstract: Eﬀects of the helicity on the dynamics of turbulent ﬂows are investigated. The aim is to disentangle the role of helicity in ﬁxing the direction, the intensity, and the ﬂuctuations of the energy transfer across the inertial range of scales. We introduce an external parameter α that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, α = 0, to the fully asymmetrical case, α = 1, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on α, measuring a positive forward ﬂux as soon as only a few modes with diﬀerent helical polarities are present. Small-scale ﬂuctuations are also strongly sensitive to the degree of mode-reduction, leading to a vanishing intermittency already for values of α ∼ 0.1. If the analysis is restricted to sets of modes with the same helicity sign, intermittency is vanishing for the modes belonging to the minority set, and it is close to that measured on the original Navier-Stokes equations for the other set.

Turbulence on a Fractal Fourier set

A.S. Lanotte, R. Benzi, S.K. Malapaka, F.Toschi and L. Biferale

Phys. Rev. Lett. 115 (26), 264502 (2015); arXiv:1505.07984;

doi:10.1103/PhysRevLett.115.264502

Abstract: A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension, D, from the original three dimensional case to a strongly decimated system with D = 2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set, E(k) ∼ k −5/3+3−D , explains the results. At small scales, the intermittency of the vorticity ﬁeld is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D ∼ 2.98. These eﬀects must be connected to a genuine modiﬁcation in the triad-to-triad nonlinear energy transfer mechanism.

On the evolution of particle-puffs in turbulence

S. Bianchi, L. Biferale, A. Celani and M. Cencini

Europ. Journ. Mech. B/Fluids published online August 25, 2015. arXiv:1509.08106

doi:10.1016/j.euromechflu.2015.06.009;

Abstract: We study the evolution of turbulent puffs by means of high-resolution numerical simulations. Puffs are bunches of passive particles released from an initially spherical distribution at regular time intervals of the order of the Kolmogorov time. The instantaneous shapes of particle puffs, in particular their asphericity and prolateness, are characterized by measuring the gyration tensor. Analysis has been performed by following, up to one large scale eddy-turn-over time, more than 10^4 different puffs, each made of 2000 particle tracers, emitted from different places in a homogeneous and isotropic turbulent fluid with Taylor-scale Reynolds number Re∼300. We also analyze the probability of hitting a given target placed downstream with respect to the local wind at the time of emission, presenting data for three different cases: (i) without any reconstruction of the shape, i.e. considering the bunch of point tracers, and approximating the particle-puff as a (ii) sphere or as an (iii) ellipsoid. The results show a strong dependence on the fluctuations of the instantaneous wind at the moment of the emission and appear to be robust with respect to the approximations (i)-(iii).

Rate of breakup of small inertial aggregates in homogeneous turbulence

M. U. Babler, L. Biferale and A. S. Lanotte

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Lagrangian and Eulerian rotating turbulence.

L. Biferale, I. Mazzitelli, F. Bonaccorso, M.A.T.V. Hinsberg, A.S. Lanotte, S. Musacchio, P. Perlekar and F. Toschi

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract State-of-the-art direct numerical simulations of rotating turbulence at changing Reynolds and Rossby numbers are

presented. Flow is also seeded with millions of particles, with and without inertia, light and heavy. We study two regimes, at high

and low rotation. Heavy and light particles are injected along different axis of rotations, allowing to study the combined effects of

preferential concentration in presence of Coriolis and Centripetal forces.

Clustering of particles in flows with broken parity invariance

K. Gustavsson and L. Biferale

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract The dynamics of small particles suspended in turbulent flows is an important problem in Nature and in Science. Previous

work has mainly focused on the motion of spherical particles, while less is known about particles with asymmetric shapes. We study

particles which break parity invariance (chiral particles). Particles of different chirality may respond differently to the structures of

the flow. Helicoidal-like structures in the flow affect the particles differently depending on the parity of the helicoid as well as on

the chirality of the particle. For flows where one of the two parities of the helicoidal-like structures is more common suspended

chiral particles experience different levels on clustering depending on their chirality. Using analytical methods and direct numerical

simulations we investigate the mechanisms of preferential sampling and clustering of chiral particles in flows with local or global

breaking of parity invariance.

On the role of helicity in the energy transfer in three-dimensional turbulence.

G. Sahoo and L. Biferale

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract: Behavior of the turbulent flows could be changed by changing the nature of the external force or the confining geometry which essentially results in breaking some of the symmetries of the ideal homogeneous and isotropic flows. In a numerical simulation, however, it

is possible to selectively break symmetries of the Navier-Stokes equations with other constraints like helicity. In a recent [1] simulation

of a decimated version of the incompressible three dimensional Navier-Stokes equations, where helicity was maintained sign-definite

using a helical projection, a reversal of energy cascade similar to two-dimensional Navier-Stokes equations was observed. The signdefinite

helicity breaks the parity symmetry of the flow. It is one of the important symmetries of the flow that contributes to the forward

energy cascade in three dimensional Navier-Stokes equations. In our study we measure the degree to which the parity symmetry controls

the direction of the cascade. We introduce a mechanism in which the parity is broken stochastically but in a time frozen manner with

helical constraints. We keep triadic interactions in Fourier space involving modes with definite sign of helicity and decimate the triads

of other modes with opposite sign of helicity with a fixed probability. We studied the cascade of energy in three dimensional turbulence

by changing the relative weight between positive and negative helicity modes. We present the results from our recent simulations.

Hydrodynamical turbulence by fractal fourier decimation

A. S. Lanotte, L. Biferale, S. K. Malapaka and F. Toschi

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract: We present a systematic numerical investigation of high-resolution 3D isotropic and homogeneous turbulence resolved on

a decimated set of Fourier modes. Fractal decimation acts to decrease the effective dimensionality of the flow by allowing triadic

interactions only in a set of Fourier modes N(k) proportional to kDF for large k. While keeping the symmetries of the original 3D

Navier-Stokes equations unchanged, a dramatic change in small-scale statistics is detected at decreasing the fractal dimension DF .

Already at fractal dimension DF = 2.8, a global self-similar behaviour is observed in the inertial range of scales, the consequence of

such transition are the restoration of the scaling symmetry and vorticity distribution that becomes close to Gaussian.

We relate the results to the different roles of local vs non-local interactions in the energy transfer range.

On clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

M. De Pietro, M.A.T. van Hinsberg, L. Biferale, H.J.H. Clercx, P. Perlekar and F. Toschi

Phys. Rev. E 91, 053002 (2015) arXiv:1411.1950

doi:10.1103/PhysRevE.91.053002

Abstract:We analyze the dynamics of small particles vertically conned, by means of a linear restoring

force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic

turbulent velocity field. The model that we introduce and study is possibly the simplest description

for the dynamics of small aquatic organisms that, due to swimming, active regulation of their

buoyancy or any other mechanism, maintain themselves in a shallow horizontal layer below the

free surface of oceans or lakes. By varying the strength of the restoring force, we are able to

control the thickness of the fluid slab in which the particles can move. This allows us to analyze the

statistical features of the system over a wide range of conditions going from a fully 3D incompressible

fl ow (corresponding to the case of no confinement) to the extremely confined case corresponding

to a 2D slice. The background 3D turbulent velocity field is evolved by means of fully resolved

direct numerical simulations. Whenever some level of vertical confinement is present, the particle

trajectories deviate from that of fluid tracers and the particles experience an effectively compressible

velocity field. Here, we have quantified the compressibility, the preferential concentration of the

particles and the correlation dimension by changing the strength of the restoring force. The main

result is that it exists a particular value of the force constant, corresponding to a mean slab depth

approximately equal to a few times the Kolmogorov length scale

that maximizes the clustering

of the particles.

Clustering of vertically constrained passive particles in homogeneous and isotropic turbulence

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

M. V. Hinsberg, M. De Pietro, L. Biferale, H. Clercx, F. Toschi

Abstract: We analyze the dynamics of small particles confined within a

horizontal fluid slab in a three-dimensional (3D) homogenous isotropic turbulent velocity

field. Particles can freely move horizontally as fluid tracers but are vertically

confined around a given horizontal plane via a simple linear restoring force. The

present model may be considered as the simplest description for the dynamics of

small aquatic organisms that, due to swimming, active regulation of their buoyancy

or other mechanisms, are capable to maintain themselves in a shallow horizontal

layer somewhere below the free surface of oceans or lakes. In the model varying the

strength of the restoring force can control the thickness of the fluid slab in which

the particles can move. Whenever some confinement is present, particle trajectories

deviate from fluid tracers and experience an effectively compressible velocity field.

We report a quantification of this effective compressibility as well as a quantification

of preferential concentration of tracer particles in terms of the correlation dimension.

We found that there exists a particular value of the force constant, corresponding to

a mean slab depth approximately equal to a few times the Kolmogorov length scale,

that maximizes the clustering of the particles.

On the direct and inverse energy transfer in 2-dimensional and 3-dimensional turbulent flows and in turbulent models

G. Sahoo, L. Biferale and M. De Pietro

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

Abstract: In this seminar, I will discuss a few important open problems in "Fully Developed Turbulence" concerning its most idealized

realization, i.e. the case of statistically homogeneous and isotropic fows. I will discuss

the importance of inviscid conserved quantities in relation to the most striking sta-

tistical properties shown by all turbulent fows: the growth of small-scales, strongly

non-Gaussian fuctuations, including the presence of anomalous scaling laws. By

using unconventional numerical methodology, based on a Galerkin decimation of

helical Fourier modes [1-3], I will argue that some phenomena characterizing

homogeneous and isotropic fows might be important also for a much larger spectrum of

applications, including fows with geophysical and astrophysical relevance as for the

case of rotating turbulence and/or conducting fuids. Results about both real 3D

decimated Navier-Stokes equations and dynamical models of it will be presented.

Burgers Turbulence on a Fractal Fourier set

M. Buzzicotti, L. Biferale, U. Frisch, S. Ray

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

Abstract:We present a systematic investigation of the effects

introduced by a fractal decimation in Fourier space on stochastically forced onedimensional

Burgers equations. The aim is to understand the statistical robustness

of the shock singularity under different reductions of the number of the degrees of

freedom. We perform a series of direct numerical simulations by using a pseudospectral

code with resolution up to 16384 points and for various dimensions of the

fractal set of Fourier modes DF <1. We present results concerning the scaling properties

of statistical measures in real space and the probability distribution functions

of local and non-local triads in Fourier space.

Homogeneous and Isotropic Turbulence: a short survey on recent developments

R. Benzi and L. Biferale

J. Stat. Phys. 161, Issue 6, pp 1351-1365 (2015) arXiv.1501.00695

DOI 10.1007/s10955-015-1323-9

Abstract: We present a detailed review of some of the most recent developments on Eulerian

and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review

phenomenological and numerical results concerning the issue of universality with respect to

the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of

numerical versus experimental comparisons and we discuss the dicotomy between phenomenology

based on coherent structures or on statistical approaches. A detailed discussion of

finite Reynolds effects is also presented.

Turbulence under Fractal Fourier Decimation

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

L. Biferale, A. Lanotte, Shiva Malapaka, F. Toschi

Abstract: We present a systematic investigation of 3D turbulent

fows evolved on a highly decimated set of Fourier modes. In particular, we in-

vestigate the change in small-scales intermittency when the flow is constrained to

excite only a fractal set of modes but keeping the symmetries of the original 3D

Navier-Stokes equations.

Numerical simulations of aggregate breakup in bounded and unbounded turbulent fows

M. U. Babler, L. Biferale, L. Brandt, U. Feudel, K. Guseva, A.S. Lanotte, C. Marchioli, F. Picano, G. Sardina, A. Soldati and F. Toschi

Journ. Fluid Mech. 766, 104-128 (2015). arXiv:1406.2842

doi:10.1017/jfm.2015.13

Abstract: Breakup of small aggregates in fully developed turbulence is studied by means of

direct numerical simulations in a series of typical bounded and unbounded flow

configurations, such as a turbulent channel flow, a developing boundary layer and

homogeneous isotropic turbulence. The simplest criterion for breakup is adopted,

whereby aggregate breakup occurs when the local hydrodynamic stress is proportional to the square root of

the energy dissipation at the position of the aggregate, overcomes a given

threshold which is characteristic for a given type of aggregate. Results show that

the breakup rate decreases with increasing threshold. For small thresholds, it develops

a scaling behaviour among the different flows. For high thresholds, the breakup rates

show strong differences between the different flow configurations, highlighting the

importance of non-universal mean-flow properties. To further assess the effects of

flow inhomogeneity and turbulent fluctuations, the results are compared with those

obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and

applicability of a set of independent proxies.

Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets

Z. Pouransari, L. Biferale and A. V. Johanssson

Phys. Fluids 27, 025102 (2015). arXiv:1502.06113

doi:10.1063/1.4906370

Abstract: The concept of local isotropy in a chemically reacting turbulent wall-jet flow is

addressed using direct numerical simulation (DNS) data. Different DNS databases

with isothermal and exothermic reactions are examined. The chemical reaction and

heat release effects on the turbulent velocity, passive scalar, and reactive species

fields are studied using their probability density functions (PDFs) and higher order

moments for velocities and scalar fields, as well as their gradients. With the aid of

the anisotropy invariant maps for the Reynolds stress tensor, the heat release effects

on the anisotropy level at different wall-normal locations are evaluated and found

to be most accentuated in the near-wall region. It is observed that the small-scale

anisotropies are persistent both in the near-wall region and inside the jet flame.

Two exothermic cases with different Damköhler numbers are examined and the

comparison revealed that the Damköhler number effects are most dominant in the

near-wall region, where the wall cooling effects are influential. In addition, with the

aid of PDFs conditioned on the mixture fraction, the significance of the reactive scalar

characteristics in the reaction zone is illustrated. We argue that the combined effects

of strong intermittency and strong persistency of anisotropy at the small scales in the

entire domain can affect mixing and ultimately the combustion characteristics of the

reacting flow

Intermittency in the relative separations of tracers and of heavy particles in turbulent flows

L. Biferale, A.S. Lanotte, R. Scatamacchia and F. Toschi

Journ. Fluid Mech 757, 550 (2014) arXiv:1411.3985

doi:10.1017/jfm.2014.515

Abstract: Results from direct numerical simulations (DNS) of particle relative dispersion

in three-dimensional homogeneous and isotropic turbulence at Reynolds number

Re 300 a re presented. We study point-like passive tracers and heavy particles,

at Stokes number St 0.6, 1.0 and 5. Particles are emitted from localised sources,

in bunches of thousands, periodically in time, allowing an unprecedented statistical

accuracy to be reached, with a total number of events for two-point observables

of the order of 10^11. The right tail of the probability density function (PDF) for

tracers develops a clear deviation from Richardson’s self-similar prediction, pointing

to the intermittent nature of the dispersion process. In our numerical experiment,

such deviations are manifest once the probability to measure an event becomes of the

order of – or rarer than – one part over one million, hence the crucial importance of

a large dataset. The role of finite-Reynolds-number effects and the related fluctuations

when pair separations cross the boundary between viscous and inertial range scales are

discussed. An asymptotic prediction based on the multifractal theory for inertial range

intermittency and valid for large Reynolds numbers is found to agree with the data

better than the Richardson theory. The agreement is improved when considering heavy

particles, whose inertia filters out viscous scale fluctuations. By using the exit-time

statistics we also show that events associated with pairs experiencing unusually slow

inertial range separations have a non-self-similar PDF.

Pair separation of magnetic elements in the quiet Sun

F. Giannattasio, F. Berrilli, L. Biferale, D. Del Moro, M. Sbragaglia, L. Bellot Rubio, M. Go˘si´c, D. Orozco

Suárez

Astronomy & Astrophysics 569, A121 (2014) arXiv:1409.1010

doi:10.1051/0004-6361/201424380

Abstract: The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields (i.e.,magnetic elements). By using 25 h-long Hinode magnetograms at high spatial resolution (0. 3), we tracked 68 490 magnetic element pairs within a supergranular cell near the disk center. The computed pair separation spectrum, calculated on the whole set of particle pairs independently of their initial separation, points out what is known as a super-diffusive regime with spectral index

γ = 1.55 ± 0.05, in agreement with the most recent literature, but extended to unprecedented spatial and temporal scales (from

granular to supergranular). Furthermore, for the first time, we investigated here the spectrum of the mean square displacement of pairs

of magnetic elements, depending on their initial separation r0.We found that there is a typical initial distance above (below) which the

pair separation is faster (slower) than the average. A possible physical interpretation of such a typical spatial scale is also provided.

Deformation statistics of sub-Kolmogorov-scale ellipsoidal drops in isotropic turbulence

L. Biferale, C. Meneveau and R. Verzicco

J. Fluid Mech. 754 184-207 (2014). arXiv:1409.0918

doi:10.1017/jfm.2014.366

Abstract:Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects

from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from direct numerical simulations (DNS) of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number is identified associated with unbounded growth of one or two of the droplet’s semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the critical capillary number can be predicted based on the large deviation theory for the largest finite-time Lyapunov exponent quantifying the chaotic separation of particle trajectories. Also, for subcritical capillary numbers near the critical value, the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows. The results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

Evolution of a double-front Rayleigh-Taylor system using a GPU-based high resolution thermal Lattice-Boltzmann model

P. Ripesi, L. Biferale, S.F. Schifano and R. Tripiccione

Phys. Rev. E 89 043022 (2014). arXiv:1405.1253

doi:10.1103/PhysRevE.89.043022

Abstract: We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs

GP Offermans, L Biferale, M Buzzicotti, M Linkmann

Physics of Plasmas 25 (12), 122307, 2018

DOI: https://doi.org/10.1063/1.5046842 preprint arXiv:1807.00759

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

M Linkmann, M Buzzicotti, L Biferale

Journal of Turbulence 19 (6), 493-527, 2018

DOI: https://doi.org/10.1080/14685248.2018.1462497 preprint arXiv:1805.02413

A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method

G Tauzin, L Biferale, M Sbragaglia, A Gupta, F Toschi, A Bartel, M Ehrhardt

Computers & Fluids, Volume 172, 241-250, 2018

DOI: https://doi.org/10.1016/j.compfluid.2018.05.031 preprint arXiv:1809.06735

Time irreversibility in reversible shell models of turbulence

M De Pietro, L Biferale, G Boffetta, M Cencini

The European Physical Journal E 41 (4), 48, 2018

DOI: https://doi.org/10.1140/epje/i2018-11655-2 preprint arXiv:1801.00944v2

Nonuniversal behaviour of helical two-dimensional three-component turbulence

M Linkmann, M Buzzicotti, L Biferale

The European Physical Journal E 41 (1), 4, 2018

DOI: https://doi.org/10.1140/epje/i2018-11612-1

Rayleigh-Taylor turbulence with singular non-uniform initial conditions

L Biferale, G Boffetta, AA Mailybaev, A Scagliarini

Physical Review Fluids 3, 092601, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.092601

Equivalence of Non-Equilibrium Ensembles in Turbulence Models

L Biferale, M Cencini, M De Pietro, G Gallavotti, V Lucarini

Phys. Rev. E 98, 012202, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.012202

On the effects of thermal fluctuations in the fragmentation of a nano-ligament

X Xue, M Sbragaglia, L Biferale, F Toschi

Phys. Rev. E 98, 012802, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.012802

Multiscale velocity correlations in turbulence and Burgers turbulence: Fusion rules, Markov processes in scale, and multifractal predictions

J Friedrich, G Margazoglou, L Biferale and R Grauer

Phys. Rev. E 98, 023104, 2018

DOI: https://doi.org/10.1103/PhysRevE.98.023104

Cascades and transitions in turbulent flows

Alexakis, L Biferale

Physics Reports, 2018

DOI: https://doi.org/10.1016/j.physrep.2018.08.001 preprint arXiv:1808.06186

Inferring flow parameters and turbulent configuration with physics-informed data-assimilation and spectral nudging

P Clark Di Leoni, A Mazzino, L Biferale

Phys. Rev. Fluids 3, 104604, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.104604 preprint arXiv:1804.07680v2

Turbulent statistics and intermittency enhancement in coflowing superfluid 4 He

L Biferale, D Khomenko, V L'vov, A Pomyalov, I Procaccia, G Sahoo

Physical Review Fluids 3 (2), 024605, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024605 preprint arXiv:1711.08246

Energy transfer in turbulence under rotation

M Buzzicotti, H Aluie, L Biferale, M Linkmann

Physical Review Fluids 3, 034802, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.034802 preprint arXiv:1711.07054

Smart Inertial Particles

S Colabrese, K Gustavsson, A Celani, L Biferale

Physical Review Fluids 3 (8), 084301, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.084301 preprint arXiv:1711.05853

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

F Milan, M Sbragaglia, L Biferale, F Toschi

The European Physical Journal E 41 (1), 6, 2018

DOI: https://doi.org/10.1140/epje/i2018-11613-0 preprint arXiv:1711.05498

Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence

M Buzzicotti, M Linkmann, H Aluie, L Biferale, J Brasseur, C Meneveau

Journal of Turbulence 19 (2), 167-197, 2018

DOI: https://doi.org/10.1080/14685248.2017.141759

Energy cascade and intermittency in helically decomposed Navier-Stokes equations

G Sahoo, L Biferale

Fluid Dynamics Research 50 (1), 011420, 2018

DOI: https://doi.org/10.1088/1873-7005/aa839a

Time irreversibility and multifractality of power along single particle trajectories in turbulence

M Cencini, L Biferale, G Boffetta, M De Pietro

Physical Review Fluids 2 (10), 104604, 2017

DOI https://doi.org/10.1103/PhysRevFluids.2.104604

Closure theory for the split energy-helicity cascades in homogeneous isotropic homochiral turbulence

A Briard, L Biferale, T Gomez

Physical Review Fluids 2 (10), 102602, 2017

DOI https://doi.org/10.1103/PhysRevFluids.2.102602

TurBase: a software platform for research in experimental and numerical fluid dynamics

R Benzi, L Biferale, F Bonaccorso, HJH Clercx, A Corbetta, W MÃ¶biu , F Toschi, F Salvadore, C Cacciari, G Erbacci

2017 International Conference on High Performance Computing Simulation (HPCS), p51-57, 2017

DOI https://doi.org/10.1109/HPCS.2017.18

From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows

L Biferale, M Buzzicotti, M Linkmann

Physics of Fluids 29 (11), 111101, 2017

DOI: https://doi.org/10.1063/1.4990082 preprint arXiv:1706.02371

Multiscale anisotropic fluctuations in sheared turbulence with multiple states

KP Iyer, F Bonaccorso, L Biferale, F Toschi

Physical Review Fluids 2 (5), 052602, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.052602

Local and nonlocal energy spectra of superfluid He 3 turbulence

L Biferale, D Khomenko, V L'vov, A Pomyalov, I Procaccia, G Sahoo

Physical Review B 95 (18), 184510, 2017

DOI: https://doi.org/10.1103/PhysRevB.95.184510

Optimal subgrid scheme for shell models of turbulence

L Biferale, AA Mailybaev, G Parisi

Physical Review E 95 (4), 043108, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.043108

Discontinuous Transition from Direct to Inverse Cascade in Three-Dimensional Turbulence

G Sahoo, A Alexakis, L Biferale

Physical Review Letters 118 (16), 164501, 2017

DOI: https://doi.org/10.1103/PhysRevLett.118.164501

Flow navigation by smart microswimmers via reinforcement learning

S Colabrese, K Gustavsson, A Celani, L Biferale

Physical Review Letters 118 (15), 158004, 2017

DOI https://doi.org/10.1103/PhysRevLett.118.158004

Finding efficient swimming strategies in a three-dimensional chaotic flow by reinforcement learning

K Gustavsson, L Biferale, A Celani, S Colabrese

The European Physical Journal E 40 (12), 110, 2017

DOI: https://doi.org/10.1140/epje/i2017-11602-9 preprint arXiv:1711.05826

Chaotic and regular instantons in helical shell models of turbulence

M De Pietro, AA Mailybaev, L Biferale

Physical Review Fluids 2 (3), 034606, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.034606

Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Ganapati Sahoo, Massimo De Pietro, Luca Biferale

Physical Review Fluids, vol. 2, 024601, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.024601

Lagrangian statistics for Navier–Stokes turbulence under Fourier-mode reduction: fractal and homogeneous decimations

Michele Buzzicotti, Akshay Bhatnagar, Luca Biferale, Alessandra S Lanotte and Samriddhi Sankar Ray

New Journal of Physics 18 (11), 113047 (2017)

DOI: :10.1088/1367-2630/18/11/113047

Abstract: We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under

Fourier-mode reduction. The Navier–Stokes equations are evolved on a restricted set of modes,

obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity

(reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of

mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a

tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and

frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex

stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still

connected by a dimensional bridge-relationwhich is independent of the degree of Fourier-mode

decimation.

Coherent structures and extreme events in rotating multiphase turbulent flows

Luca Biferale, Fabio Bonaccorso, Irene M Mazzitelli, Michel AT van Hinsberg, Alessandra S Lanotte, Stefano Musacchio, Prasad Perlekar, Federico Toschi

Physical Review X 6 (4), 041036 (2017)

DOI: 10.1103/PhysRevX.6.041036

Abstract: By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence under

rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale

leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By

seeding the flow with millions ofinertial particles, we quantify—for the first time—the effects of those coherent

vertical structures on the preferential concentration of light and heavy particles. Furthermore, we quantitatively

show that extreme fluctuations, leading to deviations from a normal-distributed statistics, result from the

entangled interaction of the vertical structures with the turbulent background. Finally, we present the first-ever

measurement of the relative importance between Stokes drag, Coriolis force, and centripetal force along the

trajectories of inertial particles. We discover that vortical coherent structures lead to unexpected diffusion

properties for heavy and light particles in the directions parallel and perpendicular to the rotation axis.

Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical-Fourier decomposition

Moritz Linkmann, Ganapati Sahoo, Mairi McKay, Arjun Berera, Luca Biferale

Astrophys. Journal 836, 26 (2017)

DOI: 10.3847/1538-4357/836/1/26

Abstract We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

Chaotic and regular instantons in helical shell models of turbulence

Massimo De Pietro, Alexei A. Mailybaev, Luca Biferale

to be puslidhe on PRF arXiv:1608.00742v1

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

J. D. Gibbon, A. Gupta, G. Krstulovic, R. Pandit, H. Politano, Y. Ponty, A. Pouquet, G. Sahoo, and J. Stawarz

DOI:10.1103/PhysRevE.93.043104

Abstract: It is shown how suitably scaled, order-m moments, D m , of the Els¨asser vorticity ﬁelds in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P M = 1. These vorticity ﬁelds are deﬁned by ω ± = curl z ± = ω ± j, where z ± are Els¨asser variables, and where ω and j are, respectively, the ﬂuid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes ﬂuid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q ± that characterize the inertial range power-law dependencies of the z ± energy spectra, E ± (k), are then examined, and bounds are obtained. Comments are also ± made on (a) the generalization of our results to the case P M = 1 and (b) the relation between D m and the order-m moments of gradients of magnetohydrodynamic ﬁelds, which are used to characterize intermittency in turbulent ﬂows.

Reﬁned similarity hypothesis using three-dimensional local averages

K. Iyer, KR Sreenivasan and PK Yeung

Phys. Rev. E, 92, 063024 (2015)

DOI: 10.1103/PhysRevE.92.063024

Abstract: The reﬁned similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermit- tent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number R λ ∼ 650, on a periodic box of 4096 3 grid points to test the hypotheses using 3D averages. In particular, we study the small-scale properties of the stochastic variable V = ∆u(r)/(rǫ r ) 1/3 , where ∆u(r) is the longitudinal velocity increment and ǫ r is the dissipation rate averaged over a three-dimensional volume of linear size r. We show that V is universal in the inertial subrange. In the dissipation range, the statistics of V are shown to depend solely on a local Reynolds number.

Helicity statistics in homogeneous and isotropic turbulence and turbulence models

Ganapati Sahoo, Massimo De Pietro, Luca Biferale

Phys. Rev. Fluids 2, 024601 (2017)

DOI: 10.1103/PhysRevFluids.2.024601

Abstract: We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.

Preferential sampling of helicity by isotropic helicoids

Kristian Gustavsson and Luca Biferale

Physical Review Fluids , vol. 1, 054201 (2016) arXiv:1609.05109

DOI: 10.1103/PhysRevFluids.1.054201}

Abstract: We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows.

These are particles whose motion is invariant under rotations but not under mirror reflections of the

particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical

particles. We show that heavy isotropic helicoids, due to the coupling between translational and

rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic

advecting flows. This opens the way to control and engineer particles able to track complex flow

structures with potential applications to microfluidics and turbulence.

Preferential sampling and small-scale clustering of gyrotactic microswimmers in turbulence

K. Gustavsson, F. Berglund, P.R. Jonsson and B. Mehlig

Phys. Rev. Lett. 116, 108104 (2016) arXiv: 1501.02386

doi: 10.1103/PhysRevLett.116.108104

Abstract: Recent studies show that spherical motile micro-organisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent ﬂow. By analysing a statistical model we analytically compute how shape aﬀects the dynamics, preferential sampling, and small-scale spatial clustering. We ﬁnd that oblong organisms may spend more time in up-welling regions of the ﬂow, and that all organisms are biased to regions of positive ﬂuid-velocity gradients in the upward direction. We analyse small-scale spatial clustering and ﬁnd that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

X. I. A. Yang, C. Meneveau, I. Marusic and L. Biferale

Phys. Review Fluids 1, 044405 (2016) arXiv:1609.00743

DOI: 10.1103/PhysRevFluids.1.044405

Abstract: In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity ﬂuctuations exp(qu + ) develop power-law scaling as a function of the wall normal z distance z/δ. Here u is the streamwise velocity ﬂuctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and δ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3Re τ 0.5 z + , z 0.15δ where Re τ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30 < z + , z < δ, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, q o . ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at Re τ ranging from 2700 to 13 000 from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the ﬁltered, large-scale velocity ﬂuctuations u z L and of the remaining small-scale component, u z S = u z − u z L . The scaling of u z L falls within the conventionally deﬁned log region and depends on a scale that is proportional to 1/2 l + ∼ Re τ ; the scaling of u z S extends over a much wider range from z + ≈ 30 to z ≈ 0.5δ. Last, we present a theoretical construction of two multiplicative processes for u z L and u z S that reproduce the empirical ﬁndings concerning the scalings properties as functions of z + and in the ESS sense.

Statistical model for collisions and recollisions of inertial particles in mixing ﬂows

K. Gustavsson and B. Mehlig

The European Physical Journal E 39, 55 (2016) arXiv:1309.3834v2

doi: 10.1140/epje/i2016-16055-0

Abstract: Finding a quantitative description of the rate of collisions between small particles suspended in mixing ﬂows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles subject to Stokes force, based on results for relative velocities of heavy particles that were recently obtained within a statistical model for the dynamics of turbulent aerosols. This model represents the turbulent velocity ﬂuctuations by Gaussian random functions. We ﬁnd that the parameterisation gives quantitatively good results in the limit where the ‘ghost-particle approximation’ applies. The collision rate is a sum of two contributions due to ‘caustics’ and to ‘clustering’. Within the statistical model we compare the relative importance of these two collision mechanisms. The caustic formation rate is high when the particle inertia becomes large, and we ﬁnd that caustics dominate the collision rate as soon as they form frequently. We compare the magnitude of the caustic contribution to the collision rate to the formation rate of caustics.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

J. D. Gibbon, A. Gupta, G. Krstulovic, R. Pandit, H. Politano, Y. Ponty, A. Pouquet, G. Sahoo and J. Stawarz

Phys. Rev. E 93, 043104 (2016)

DOI: 10.1103/PhysRevE.93.043104 arXiv:1508.03756

Abstract: It is shown how suitably scaled, order-m moments, D m , of the Els¨asser vorticity ﬁelds in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P M = 1. These vorticity ﬁelds are deﬁned by ω ± = curl z ± = ω ± j, where z ± are Els¨asser variables, and where ω and j are, respectively, the ﬂuid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes ﬂuid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q ± that characterize the inertial range power-law dependencies of the z ± energy spectra, E ± (k), are then examined, and bounds are obtained. Comments are also ± made on (a) the generalization of our results to the case P M = 1 and (b) the relation between D m and the order-m moments of gradients of magnetohydrodynamic ﬁelds, which are used to characterize intermittency in turbulent ﬂows.

On the Vortex Dynamics in Fractal Fourier Turbulence

Alessandra S. Lanotte, Shiva Kumar Malapaka and Luca Biferale

The European Physical Journal E 39:49 (2016) arXiv: 1605.01527

DOI 10.1140/epje/i2016-16049-x

Abstract: Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension D. By tuning the fractal dimension parameter, we study the dynamical eﬀects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In partic- ular, we show that as we move from D = 3 to D ∼ 2.8, the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretch- ing properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous ﬂuctuations.

Inertial-particle accelerations in turbulence: a Lagrangian closure

S. Vajedi, K. Gustavsson, B. Mehlig and L. Biferale

Jour. Fluid Mech. 798,187 (2016) arXiv:1607.01888

doi:10.1017/jfm.2016.305

Abstract: The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite diﬀerent for light and heavy particles. In this article we analyse a closure scheme for the acceleration ﬂuctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of ﬂuid tracers. We compute the variance and the ﬂatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates eﬀects induced by the Lagrangian correlations along the trajectories of ﬂuid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the eﬀects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct func- tional behaviour of the acceleration variance, as a function of St, as well as the presence of a minimum/maximum for the ﬂatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity ﬁeld. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.

Reﬁned similarity hypothesis using three-dimensional local averages

K. Iyer, K.R. Sreenivasan and P.K. Yeung

Phys. Rev. E, 92, 063024 (2015) arXiv:1510.00628v2

doi:10.1103/PhysRevE.92.063024

Abstract: The reﬁned similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermit- tent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number R λ ∼ 650, on a periodic box of 4096 3 grid points to test the hypotheses using 3D averages. In particular, we study the small-scale properties of the stochastic variable V = ∆u(r)/(rǫ r ) 1/3 , where ∆u(r) is the longitudinal velocity increment and ǫ r is the dissipation rate averaged over a three-dimensional volume of linear size r. We show that V is universal in the inertial subrange. In the dissipation range, the statistics of V are shown to depend solely on a local Reynolds number.

Intermittency in fractal Fourier hydrodynamics: Lessons from the Burgers Equation

Michele Buzzicotti, Luca Biferale, Uriel Frisch, Samriddhi Sankar Ray

Phys. Rev. E 93, 033109 (2016). arXiv:1601.03697

doi: 10.1103/PhysRevE.93.033109

Abstract: We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension D. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical ﬂuctuations by changing D. We ﬁnd that a very small percentage of mode-reduction (D . 1) is enough to destroy most of the characteristics of the original non-decimated equation. In particular, we observe a suppression of intermittent ﬂuctuations for D < 1 and a quasi-singular transition from the fully intermittent (D = 1) to the non-intermittent case for D . 1. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.

Rotating turbulence under “precession-like” perturbation

Kartik P. Iyer, Irene Mazzitelli, Fabio Bonaccorso, Annick Pouquet and Luca Biferale

Eur. Phys. J. E, 38 12 (2015) 128 arXiv:1511.06159

DOI: 10.1140/epje/i2015-15128-x

Abstract: The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered.

We perform direct numerical simulations on a periodic box of 10243 grid points, where the orientation

of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate

with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas

in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in

a strong forward energy transfer and large scale structures that resemble those of isotropic turbulence.

Phase and precession evolution in the Burgers equation

Michele Buzzicotti, Brendan P. Murray, Luca Biferale, Miguel D. Bustamante.

Eur. Phys. J. E, 39 3 (2016) 34. arXiv:1509.04450

DOI: 10.1140/epje/i2016-16034-5

Abstract: We present a phenomenological study of the phase dynamics of the one-dimensional stochasti- cally forced Burgers equation, and of the same equation under a Fourier mode reduction on a fractal set. We study the connection between coherent structures in real space and the evolution of triads in Fourier space. Concerning the one-dimensional case, we ﬁnd that triad phases show alignments and synchroni- sations that favour energy ﬂuxes towards small scales –a direct cascade. In addition, strongly dissipative real-space structures are associated with entangled correlations amongst the phase precession frequencies and the amplitude evolution of Fourier triads. As a result, triad precession frequencies show a non-Gaussian distribution with multiple peaks and fat tails, and there is a signiﬁcant correlation between triad precession frequencies and amplitude growth. Links with dynamical systems approach are brieﬂy discussed, such as the role of unstable critical points in state space. On the other hand, by reducing the fractal dimension D of the underlying Fourier set, we observe: i) a tendency toward a more Gaussian statistics, ii) a loss of alignment of triad phases leading to a depletion of the energy ﬂux, and iii) the simultaneous reduction of the correlation between the growth of Fourier mode amplitudes and the precession frequencies of triad phases.

Disentangling the triadic interactions in Navier-Stokes equations

Ganapati Sahoo, Luca Biferale

The European Physical Journal E 38 (10), 114 arXiv:1510.09006

DOI: 10.1140/epje/i2015-15114-4

Abstract: We study the role of helicity in the dynamics of energy transfer in a modiﬁed version of the Navier- Stokes equations with explicit breaking of the mirror symmetry. We select diﬀerent set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wavenumbers except for those falling on a localized shell of wavenumber, |k| ∼ k m . Changing k m to be above or below the forcing scale, k f , we are able to assess the energy transfer of triads belonging to diﬀerent interaction classes. We observe that when the negative helical modes are present only at wavenumber smaller than the forced wavenumbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at wavenumber larger than the forced wavenumbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.

Eulerian and Lagrangian statistics in fully developed rotating turbulent flows.

L. Biferale, F. Bonaccorso, I. Mazzitelli, A. Lanotte, P. Perlekar, S. Musacchio, M. Hinsberg, F. Toschi,

Abstract DFD15-2015-000509 APS. We present results concerning both Eulerian and Lagrangian statistics for turbulent under rotation at small and large Rossby numbers. Concerning the Eulerian statistics we discuss the effects of the presence of strong coherent large-scale vortical structures on the small-scale statistics. Concerning Lagrangian prop- erties, we discuss the effects of preferential sampling at changing the inertial properties of the particles also due to the centrifugal and Coriolis forces.

Turbulence structure subjected to precession-like rotation.

Kartik Iyer, Irene Mazzitelli, Fabio Bonaccorso, Luca Biferale

Abstract DFD15-?

Inverse energy cascade in non-local helical shell-models of turbulence

M. De Pietro, L. Biferale, G. Sahoo, A. Mailybaev

Abstract: DFD15-2015-000648 APS. Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space we introduce a modified version of helical shell-models for turbulence with non-local triadic interactions. By using both analytical argument and numerical simulation we show that there exists a sub-class of mod- els with elongated shell interactions that exhibits a statistically stable inverse energy cascade. Using also data from direct numerical simula- tions of helical Navier-Stokes equations we further support the idea that energy transfer mechanism in fully developed turbulence is the result of a strong entanglement among different triadic interactions possessing different transfer mechanisms.

Inverse energy cascade in nonlocal helical shellmodels of turbulence

Massimo De Pietro, Luca Biferale, Alexei A. Mailybaev

Phys. Rev. E 92, 043021 (2015) arXiv:1508.06390

doi:10.1103/PhysRevE.92.043021

Abstract: Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations

in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of

helical shell models for turbulence with non-local triadic interactions. By using both an analytical

argument and numerical simulation, we show that there exists a class of models, with a specific

helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with

that predicted for the Navier-Stokes equations restricted to the same helical interactions. We

further support the idea that turbulent energy transfer is the result of a strong entanglement

among triads possessing different transfer properties.

Analysis of the Correlation Dimension For Inertial Particles

K. Gustavsson, B. Mehlig and M. Wilkinson

Phys. Fluids, 27 073305 (2015). arXiv:1502.05694

doi:10.1063/1.4927220

Abstract: We obtain an implicit equation for the correlation dimension which describes clustering of

inertial particles in a complex flow onto a fractal measure. Our general equation involves

a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid

appears as additive noise. When the long-time limit of the propagator is considered our

equation reduces to an existing large-deviation formalism, from which it is difficult to

extract concrete results. In the short-time limit, however, our equation reduces to a solvability

condition on a partial differential equation. In the case where the inertial particles

are much denser than the fluid, we show how this approach leads to a perturbative expansion

of the correlation dimension, for which the coefficients can be obtained exactly and

in principle to any order. We derive the perturbation series for the correlation dimension

of inertial particles suspended in three-dimensional spatially smooth random flows with

white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.

Role of helicity for large- and small-scales turbulent fluctuations

G. Sahoo, F. Bonaccorso and L. Biferale

Phys. Rev. E 92 (5), 051002 (2015) arXiv:1506.04906

doi:10.1103/PhysRevE.92.051002

Abstract: Eﬀects of the helicity on the dynamics of turbulent ﬂows are investigated. The aim is to disentangle the role of helicity in ﬁxing the direction, the intensity, and the ﬂuctuations of the energy transfer across the inertial range of scales. We introduce an external parameter α that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, α = 0, to the fully asymmetrical case, α = 1, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on α, measuring a positive forward ﬂux as soon as only a few modes with diﬀerent helical polarities are present. Small-scale ﬂuctuations are also strongly sensitive to the degree of mode-reduction, leading to a vanishing intermittency already for values of α ∼ 0.1. If the analysis is restricted to sets of modes with the same helicity sign, intermittency is vanishing for the modes belonging to the minority set, and it is close to that measured on the original Navier-Stokes equations for the other set.

Turbulence on a Fractal Fourier set

A.S. Lanotte, R. Benzi, S.K. Malapaka, F.Toschi and L. Biferale

Phys. Rev. Lett. 115 (26), 264502 (2015); arXiv:1505.07984;

doi:10.1103/PhysRevLett.115.264502

Abstract: A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension, D, from the original three dimensional case to a strongly decimated system with D = 2.5, where only about 3% of the Fourier modes interact. This is a unique methodology to probe the statistical properties of the turbulent energy cascade, without breaking any of the original symmetries of the equations. While the direct energy cascade persists, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the codimension of the fractal set, E(k) ∼ k −5/3+3−D , explains the results. At small scales, the intermittency of the vorticity ﬁeld is observed to be quasisingular as a function of the fractal mode reduction, leading to an almost Gaussian statistics already at D ∼ 2.98. These eﬀects must be connected to a genuine modiﬁcation in the triad-to-triad nonlinear energy transfer mechanism.

On the evolution of particle-puffs in turbulence

S. Bianchi, L. Biferale, A. Celani and M. Cencini

Europ. Journ. Mech. B/Fluids published online August 25, 2015. arXiv:1509.08106

doi:10.1016/j.euromechflu.2015.06.009;

Abstract: We study the evolution of turbulent puffs by means of high-resolution numerical simulations. Puffs are bunches of passive particles released from an initially spherical distribution at regular time intervals of the order of the Kolmogorov time. The instantaneous shapes of particle puffs, in particular their asphericity and prolateness, are characterized by measuring the gyration tensor. Analysis has been performed by following, up to one large scale eddy-turn-over time, more than 10^4 different puffs, each made of 2000 particle tracers, emitted from different places in a homogeneous and isotropic turbulent fluid with Taylor-scale Reynolds number Re∼300. We also analyze the probability of hitting a given target placed downstream with respect to the local wind at the time of emission, presenting data for three different cases: (i) without any reconstruction of the shape, i.e. considering the bunch of point tracers, and approximating the particle-puff as a (ii) sphere or as an (iii) ellipsoid. The results show a strong dependence on the fluctuations of the instantaneous wind at the moment of the emission and appear to be robust with respect to the approximations (i)-(iii).

Rate of breakup of small inertial aggregates in homogeneous turbulence

M. U. Babler, L. Biferale and A. S. Lanotte

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Lagrangian and Eulerian rotating turbulence.

L. Biferale, I. Mazzitelli, F. Bonaccorso, M.A.T.V. Hinsberg, A.S. Lanotte, S. Musacchio, P. Perlekar and F. Toschi

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract State-of-the-art direct numerical simulations of rotating turbulence at changing Reynolds and Rossby numbers are

presented. Flow is also seeded with millions of particles, with and without inertia, light and heavy. We study two regimes, at high

and low rotation. Heavy and light particles are injected along different axis of rotations, allowing to study the combined effects of

preferential concentration in presence of Coriolis and Centripetal forces.

Clustering of particles in flows with broken parity invariance

K. Gustavsson and L. Biferale

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract The dynamics of small particles suspended in turbulent flows is an important problem in Nature and in Science. Previous

work has mainly focused on the motion of spherical particles, while less is known about particles with asymmetric shapes. We study

particles which break parity invariance (chiral particles). Particles of different chirality may respond differently to the structures of

the flow. Helicoidal-like structures in the flow affect the particles differently depending on the parity of the helicoid as well as on

the chirality of the particle. For flows where one of the two parities of the helicoidal-like structures is more common suspended

chiral particles experience different levels on clustering depending on their chirality. Using analytical methods and direct numerical

simulations we investigate the mechanisms of preferential sampling and clustering of chiral particles in flows with local or global

breaking of parity invariance.

On the role of helicity in the energy transfer in three-dimensional turbulence.

G. Sahoo and L. Biferale

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract: Behavior of the turbulent flows could be changed by changing the nature of the external force or the confining geometry which essentially results in breaking some of the symmetries of the ideal homogeneous and isotropic flows. In a numerical simulation, however, it

is possible to selectively break symmetries of the Navier-Stokes equations with other constraints like helicity. In a recent [1] simulation

of a decimated version of the incompressible three dimensional Navier-Stokes equations, where helicity was maintained sign-definite

using a helical projection, a reversal of energy cascade similar to two-dimensional Navier-Stokes equations was observed. The signdefinite

helicity breaks the parity symmetry of the flow. It is one of the important symmetries of the flow that contributes to the forward

energy cascade in three dimensional Navier-Stokes equations. In our study we measure the degree to which the parity symmetry controls

the direction of the cascade. We introduce a mechanism in which the parity is broken stochastically but in a time frozen manner with

helical constraints. We keep triadic interactions in Fourier space involving modes with definite sign of helicity and decimate the triads

of other modes with opposite sign of helicity with a fixed probability. We studied the cascade of energy in three dimensional turbulence

by changing the relative weight between positive and negative helicity modes. We present the results from our recent simulations.

Hydrodynamical turbulence by fractal fourier decimation

A. S. Lanotte, L. Biferale, S. K. Malapaka and F. Toschi

Abstract presented at ETC15, 15th European Turbulence Conference, 25-28 Auust, Delft, The Netherlands

Abstract: We present a systematic numerical investigation of high-resolution 3D isotropic and homogeneous turbulence resolved on

a decimated set of Fourier modes. Fractal decimation acts to decrease the effective dimensionality of the flow by allowing triadic

interactions only in a set of Fourier modes N(k) proportional to kDF for large k. While keeping the symmetries of the original 3D

Navier-Stokes equations unchanged, a dramatic change in small-scale statistics is detected at decreasing the fractal dimension DF .

Already at fractal dimension DF = 2.8, a global self-similar behaviour is observed in the inertial range of scales, the consequence of

such transition are the restoration of the scaling symmetry and vorticity distribution that becomes close to Gaussian.

We relate the results to the different roles of local vs non-local interactions in the energy transfer range.

On clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

M. De Pietro, M.A.T. van Hinsberg, L. Biferale, H.J.H. Clercx, P. Perlekar and F. Toschi

Phys. Rev. E 91, 053002 (2015) arXiv:1411.1950

doi:10.1103/PhysRevE.91.053002

Abstract:We analyze the dynamics of small particles vertically conned, by means of a linear restoring

force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic

turbulent velocity field. The model that we introduce and study is possibly the simplest description

for the dynamics of small aquatic organisms that, due to swimming, active regulation of their

buoyancy or any other mechanism, maintain themselves in a shallow horizontal layer below the

free surface of oceans or lakes. By varying the strength of the restoring force, we are able to

control the thickness of the fluid slab in which the particles can move. This allows us to analyze the

statistical features of the system over a wide range of conditions going from a fully 3D incompressible

fl ow (corresponding to the case of no confinement) to the extremely confined case corresponding

to a 2D slice. The background 3D turbulent velocity field is evolved by means of fully resolved

direct numerical simulations. Whenever some level of vertical confinement is present, the particle

trajectories deviate from that of fluid tracers and the particles experience an effectively compressible

velocity field. Here, we have quantified the compressibility, the preferential concentration of the

particles and the correlation dimension by changing the strength of the restoring force. The main

result is that it exists a particular value of the force constant, corresponding to a mean slab depth

approximately equal to a few times the Kolmogorov length scale

that maximizes the clustering

of the particles.

Clustering of vertically constrained passive particles in homogeneous and isotropic turbulence

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

M. V. Hinsberg, M. De Pietro, L. Biferale, H. Clercx, F. Toschi

Abstract: We analyze the dynamics of small particles confined within a

horizontal fluid slab in a three-dimensional (3D) homogenous isotropic turbulent velocity

field. Particles can freely move horizontally as fluid tracers but are vertically

confined around a given horizontal plane via a simple linear restoring force. The

present model may be considered as the simplest description for the dynamics of

small aquatic organisms that, due to swimming, active regulation of their buoyancy

or other mechanisms, are capable to maintain themselves in a shallow horizontal

layer somewhere below the free surface of oceans or lakes. In the model varying the

strength of the restoring force can control the thickness of the fluid slab in which

the particles can move. Whenever some confinement is present, particle trajectories

deviate from fluid tracers and experience an effectively compressible velocity field.

We report a quantification of this effective compressibility as well as a quantification

of preferential concentration of tracer particles in terms of the correlation dimension.

We found that there exists a particular value of the force constant, corresponding to

a mean slab depth approximately equal to a few times the Kolmogorov length scale,

that maximizes the clustering of the particles.

On the direct and inverse energy transfer in 2-dimensional and 3-dimensional turbulent flows and in turbulent models

G. Sahoo, L. Biferale and M. De Pietro

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

Abstract: In this seminar, I will discuss a few important open problems in "Fully Developed Turbulence" concerning its most idealized

realization, i.e. the case of statistically homogeneous and isotropic fows. I will discuss

the importance of inviscid conserved quantities in relation to the most striking sta-

tistical properties shown by all turbulent fows: the growth of small-scales, strongly

non-Gaussian fuctuations, including the presence of anomalous scaling laws. By

using unconventional numerical methodology, based on a Galerkin decimation of

helical Fourier modes [1-3], I will argue that some phenomena characterizing

homogeneous and isotropic fows might be important also for a much larger spectrum of

applications, including fows with geophysical and astrophysical relevance as for the

case of rotating turbulence and/or conducting fuids. Results about both real 3D

decimated Navier-Stokes equations and dynamical models of it will be presented.

Burgers Turbulence on a Fractal Fourier set

M. Buzzicotti, L. Biferale, U. Frisch, S. Ray

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

Abstract:We present a systematic investigation of the effects

introduced by a fractal decimation in Fourier space on stochastically forced onedimensional

Burgers equations. The aim is to understand the statistical robustness

of the shock singularity under different reductions of the number of the degrees of

freedom. We perform a series of direct numerical simulations by using a pseudospectral

code with resolution up to 16384 points and for various dimensions of the

fractal set of Fourier modes DF <1. We present results concerning the scaling properties

of statistical measures in real space and the probability distribution functions

of local and non-local triads in Fourier space.

Homogeneous and Isotropic Turbulence: a short survey on recent developments

R. Benzi and L. Biferale

J. Stat. Phys. 161, Issue 6, pp 1351-1365 (2015) arXiv.1501.00695

DOI 10.1007/s10955-015-1323-9

Abstract: We present a detailed review of some of the most recent developments on Eulerian

and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review

phenomenological and numerical results concerning the issue of universality with respect to

the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of

numerical versus experimental comparisons and we discuss the dicotomy between phenomenology

based on coherent structures or on statistical approaches. A detailed discussion of

finite Reynolds effects is also presented.

Turbulence under Fractal Fourier Decimation

Abstract Submitted for the DFD14 Meeting of The American Physical Society. 67th Annual Meeting 23-25 nov. 2015

L. Biferale, A. Lanotte, Shiva Malapaka, F. Toschi

Abstract: We present a systematic investigation of 3D turbulent

fows evolved on a highly decimated set of Fourier modes. In particular, we in-

vestigate the change in small-scales intermittency when the flow is constrained to

excite only a fractal set of modes but keeping the symmetries of the original 3D

Navier-Stokes equations.

Numerical simulations of aggregate breakup in bounded and unbounded turbulent fows

M. U. Babler, L. Biferale, L. Brandt, U. Feudel, K. Guseva, A.S. Lanotte, C. Marchioli, F. Picano, G. Sardina, A. Soldati and F. Toschi

Journ. Fluid Mech. 766, 104-128 (2015). arXiv:1406.2842

doi:10.1017/jfm.2015.13

Abstract: Breakup of small aggregates in fully developed turbulence is studied by means of

direct numerical simulations in a series of typical bounded and unbounded flow

configurations, such as a turbulent channel flow, a developing boundary layer and

homogeneous isotropic turbulence. The simplest criterion for breakup is adopted,

whereby aggregate breakup occurs when the local hydrodynamic stress is proportional to the square root of

the energy dissipation at the position of the aggregate, overcomes a given

threshold which is characteristic for a given type of aggregate. Results show that

the breakup rate decreases with increasing threshold. For small thresholds, it develops

a scaling behaviour among the different flows. For high thresholds, the breakup rates

show strong differences between the different flow configurations, highlighting the

importance of non-universal mean-flow properties. To further assess the effects of

flow inhomogeneity and turbulent fluctuations, the results are compared with those

obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and

applicability of a set of independent proxies.

Statistical analysis of the velocity and scalar fields in reacting turbulent wall-jets

Z. Pouransari, L. Biferale and A. V. Johanssson

Phys. Fluids 27, 025102 (2015). arXiv:1502.06113

doi:10.1063/1.4906370

Abstract: The concept of local isotropy in a chemically reacting turbulent wall-jet flow is

addressed using direct numerical simulation (DNS) data. Different DNS databases

with isothermal and exothermic reactions are examined. The chemical reaction and

heat release effects on the turbulent velocity, passive scalar, and reactive species

fields are studied using their probability density functions (PDFs) and higher order

moments for velocities and scalar fields, as well as their gradients. With the aid of

the anisotropy invariant maps for the Reynolds stress tensor, the heat release effects

on the anisotropy level at different wall-normal locations are evaluated and found

to be most accentuated in the near-wall region. It is observed that the small-scale

anisotropies are persistent both in the near-wall region and inside the jet flame.

Two exothermic cases with different Damköhler numbers are examined and the

comparison revealed that the Damköhler number effects are most dominant in the

near-wall region, where the wall cooling effects are influential. In addition, with the

aid of PDFs conditioned on the mixture fraction, the significance of the reactive scalar

characteristics in the reaction zone is illustrated. We argue that the combined effects

of strong intermittency and strong persistency of anisotropy at the small scales in the

entire domain can affect mixing and ultimately the combustion characteristics of the

reacting flow

Intermittency in the relative separations of tracers and of heavy particles in turbulent flows

L. Biferale, A.S. Lanotte, R. Scatamacchia and F. Toschi

Journ. Fluid Mech 757, 550 (2014) arXiv:1411.3985

doi:10.1017/jfm.2014.515

Abstract: Results from direct numerical simulations (DNS) of particle relative dispersion

in three-dimensional homogeneous and isotropic turbulence at Reynolds number

Re 300 a re presented. We study point-like passive tracers and heavy particles,

at Stokes number St 0.6, 1.0 and 5. Particles are emitted from localised sources,

in bunches of thousands, periodically in time, allowing an unprecedented statistical

accuracy to be reached, with a total number of events for two-point observables

of the order of 10^11. The right tail of the probability density function (PDF) for

tracers develops a clear deviation from Richardson’s self-similar prediction, pointing

to the intermittent nature of the dispersion process. In our numerical experiment,

such deviations are manifest once the probability to measure an event becomes of the

order of – or rarer than – one part over one million, hence the crucial importance of

a large dataset. The role of finite-Reynolds-number effects and the related fluctuations

when pair separations cross the boundary between viscous and inertial range scales are

discussed. An asymptotic prediction based on the multifractal theory for inertial range

intermittency and valid for large Reynolds numbers is found to agree with the data

better than the Richardson theory. The agreement is improved when considering heavy

particles, whose inertia filters out viscous scale fluctuations. By using the exit-time

statistics we also show that events associated with pairs experiencing unusually slow

inertial range separations have a non-self-similar PDF.

Pair separation of magnetic elements in the quiet Sun

F. Giannattasio, F. Berrilli, L. Biferale, D. Del Moro, M. Sbragaglia, L. Bellot Rubio, M. Go˘si´c, D. Orozco

Suárez

Astronomy & Astrophysics 569, A121 (2014) arXiv:1409.1010

doi:10.1051/0004-6361/201424380

Abstract: The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields (i.e.,magnetic elements). By using 25 h-long Hinode magnetograms at high spatial resolution (0. 3), we tracked 68 490 magnetic element pairs within a supergranular cell near the disk center. The computed pair separation spectrum, calculated on the whole set of particle pairs independently of their initial separation, points out what is known as a super-diffusive regime with spectral index

γ = 1.55 ± 0.05, in agreement with the most recent literature, but extended to unprecedented spatial and temporal scales (from

granular to supergranular). Furthermore, for the first time, we investigated here the spectrum of the mean square displacement of pairs

of magnetic elements, depending on their initial separation r0.We found that there is a typical initial distance above (below) which the

pair separation is faster (slower) than the average. A possible physical interpretation of such a typical spatial scale is also provided.

Deformation statistics of sub-Kolmogorov-scale ellipsoidal drops in isotropic turbulence

L. Biferale, C. Meneveau and R. Verzicco

J. Fluid Mech. 754 184-207 (2014). arXiv:1409.0918

doi:10.1017/jfm.2014.366

Abstract:Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects

from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from direct numerical simulations (DNS) of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number is identified associated with unbounded growth of one or two of the droplet’s semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the critical capillary number can be predicted based on the large deviation theory for the largest finite-time Lyapunov exponent quantifying the chaotic separation of particle trajectories. Also, for subcritical capillary numbers near the critical value, the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows. The results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

Evolution of a double-front Rayleigh-Taylor system using a GPU-based high resolution thermal Lattice-Boltzmann model

P. Ripesi, L. Biferale, S.F. Schifano and R. Tripiccione

Phys. Rev. E 89 043022 (2014). arXiv:1405.1253

doi:10.1103/PhysRevE.89.043022

Abstract: We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs