Dept. of Physics, University of Rome, Tor Vergata
Via della Ricerca Scientifica 1, 00133, Roma, Italy
ph +39 067259.4595, fax +39 062023507, cell +39 3496494879
biferale at roma2 dot infn dot it
Cascades and transitions in turbulent flows
Physics Reports, 2018 PreprintA Alexakis, L Biferale
Turbulent flows are characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal three and two dimensional homogeneous and isotropic cases characterized by the presence of a strictly direct and inverse energy cascade, respectively. New phenomena appear that alter the global and local transfer properties. In this review, we provide a critical summary of historical and recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse energy cascades, the different scenarios include: split cascades for which an invariant flows both to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a large scale condensate is formed. We classify all possible transitions from one scenario to another as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, magnetohydrodynamics (MHD) turbulence, and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as, e.g., the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We briefly discuss the presence of anomalous scaling laws in 3D hydrodynamics and in other configurations, in connection with the intermittent nature of the energy dissipation in configuration space. A quick overview is also provided concerning the importance of cascades in other applications such as bounded flows, quantum fluids, relativistic and compressible turbulence, and active matter, together with a discussion of the implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address
Smart Inertial Particle
Physical Review Fluids 3 (8), 084301, 2018 PreprintS Colabrese, K Gustavsson, A Celani, L Biferale
We performed a numerical study to train smart inertial particles to target specific flow regions with high vorticity through the use of reinforcement learning algorithms. The particles are able to actively change their size to modify their inertia and density. In short, using local measurements of the flow vorticity, the smart particle explores the interplay between its choices of size and its dynamical behavior in the flow environment. This allows it to accumulate experience and learn approximately optimal strategies of how to modulate its size in order to reach the target high-vorticity regions. We consider flows with different complexities: a two-dimensional stationary Taylor-Green-like configuration, a two-dimensional time-dependent flow, and finally a three-dimensional flow given by the stationary Arnold-Beltrami-Childress (ABC) helical flow. We show that smart particles are able to learn how to reach extremely intense vortical structures in all the tackled cases
Unraveling turbulence via physics-informed data-assimilation and spectral nudging
preprint arXiv:1804.07680P Clark Di Leoni, A Mazzino, L Biferale
Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. Up to now, spectral nudging was applied for empirical data-assimilation as a mean to improve deterministic and statistical predictability in the presence of a restricted set of field measurements only. Here, we explore under which conditions a nudging protocol can be used for two novel objectives: to unravel the value of the physical flow parameters and to reconstruct large-scale turbulent properties starting from a sparse set of information in space and in time. First, we apply nudging to quantitatively infer the unknown rotation rate and the shear mechanism for turbulent flows. Second, we show that a suitable spectral nudging is able to reconstruct the energy containing scales in rotating turbulence by using a blind set-up, ie without any input about the external forcing mechanisms acting on the flow. Finally, we discuss the broad potentialities of nudging to other key applications for physics-informed data-assimilation in environmental or applied flow configurations
Energy transfer in turbulence under rotation
Physical Review Fluids 3, 034802, 2018 PreprintM Buzzicotti, H Aluie, L Biferale, and M Linkmann
It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C)/slow manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high-Reynolds-number direct numerical simulations (DNS) within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where kz≠0. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices
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
Journal of Turbulence 19 (2), 167-197, 2018 PreprintM Buzzicotti, M Linkmann, H Aluie, L Biferale, J Brasseur and C Meneveau
The effects of different filtering strategies on the statistical properties of the resolved-to-subfilter scale (SFS) energy transfer are analysed in forced homogeneous and isotropic turbulence. We carry out a-priori analyses of the statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations with up to 20483 grid points as a function of the filter cutoff scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors with non-sharp spectral filter profiles. Of interest is the importance of Galilean invariance and we confirm that local SFS energy transfer displays intermittency scaling in both skewness and flatness as a function of the cutoff scale. Furthermore, we quantify the robustness of scaling as a function of the filtering type
Multiscale anisotropic fluctuations in sheared turbulence with multiple states
Physical Review Fluids 2 (5), 052602, 2017 PreprintK P Iyer, F Bonaccorso, L Biferale, F Toschi
We use high-resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation functions on different sectors of the three-dimensional group of rotations, SO(3), using a high-precision quadrature. Scaling properties of anisotropic components of longitudinal and transverse velocity fluctuations are accurately measured at changing Reynolds numbers. We show that independently of the anisotropic content of the energy containing eddies, small-scale turbulent fluctuations recover isotropy and universality faster than previously reported in experimental and numerical studies. The discrepancies are ascribed to the presence of highly anisotropic contributions that have either been neglected or measured with less accuracy in the foregoing works. Furthermore, the anomalous anisotropic scaling exponents are devoid of any sign of saturation with increasing order. Our study paves the way to systematically assess persistence of anisotropy in high-Reynolds-number flows
Optimal subgrid scheme for shell models of turbulence
Physical Review E 95 (4), 043108, 2017 PreprintL Biferale, AA Mailybaev, G Parisi
We discuss a theoretical framework to define an optimal subgrid closure for shell models of turbulence. The closure is based on the ansatz that consecutive shell multipliers are short-range correlated, following the third hypothesis of Kolmogorov formulated for similar quantities for the original three-dimensional Navier-Stokes turbulence. We also propose a series of systematic approximations to the optimal model by assuming different degrees of correlations across scales among amplitudes and phases of consecutive multipliers. We show numerically that such low-order closures work well, reproducing all known properties of the large-scale dynamics including anomalous scaling. We found small but systematic discrepancies only for a range of scales close to the subgrid threshold, which do not tend to disappear by increasing the order of the approximation. We speculate that the lack of convergence might be due to a structural instability, at least for the evolution of very fast degrees of freedom at small scales. Connections with similar problems for large eddy simulations of the three-dimensional Navier-Stokes equations are also discussed
Discontinuous transition from direct to inverse cascade in three-dimensional turbulence
Physical Review Letters 118 (16), 164501, 2017 PreprintG Sahoo, A Alexakis, L Biferale
Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three-dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflections, and scale transforms) as the original equations. It is demonstrated that the examined system displays a change in the direction of the energy cascade when varying the value of a free parameter which controls the relative weights of the triadic interactions between different helical Fourier modes. The transition from a forward to inverse cascade is shown to occur at a critical point in a discontinuous manner with diverging fluctuations close to criticality. Our work thus supports the observation that purely isotropic and three-dimensional flow configurations can support inverse energy transfer when interactions are altered and that inside all turbulent flows there is a competition among forward and backward transfer mechanisms which might lead to multiple energy-containing turbulent states
Flow navigation by smart microswimmers via reinforcement learning
Physical Review Letters 118 (15), 158004, 2017 PreprintS Colabrese, K Gustavsson, A Celani, L Biferale
Smart active particles can acquire some limited knowledge of the fluid environment from simple mechanical cues and exert a control on their preferred steering direction. Their goal is to learn the best way to navigate by exploiting the underlying flow whenever possible. As an example, we focus our attention on smart gravitactic swimmers. These are active particles whose task is to reach the highest altitude within some time horizon, given the constraints enforced by fluid mechanics. By means of numerical experiments, we show that swimmers indeed learn nearly optimal strategies just by experience. A reinforcement learning algorithm allows particles to learn effective strategies even in difficult situations when, in the absence of control, they would end up being trapped by flow structures. These strategies are highly nontrivial and cannot be easily guessed in advance. This Letter illustrates the potential of reinforcement learning algorithms to model adaptive behavior in complex flows and paves the way towards the engineering of smart microswimmers that solve difficult navigation problems
Coherent structures and extreme events in rotating multiphase turbulent flows
Physical Review X 6 (4), 041036, 2016L Biferale, F Bonaccorso, I M Mazzitelli, M AT van Hinsberg, A S Lanotte, S Musacchio, P Perlekar, F Toschi
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 of inertial 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
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Scientific Activity (key words): Complex fluids. Turbulence. Intermittency and Anomalous Scaling laws. Anisotropic Flows. Turbulent Transport. Microfluidics and Biofluidic. Lattice Boltzmann equations, theory and applications. Multiphase flows. Multicomponent flows. Transport in Porous Media. Emulsions. Colloids. Fractals and Multifractals. Deterministic chaos. Dynamical Systems. Information Theory. Stochastic Processes. Critical Phenomena. Renormalization Group. Monte Carlo methods. Machine-Learning.
