A Mesoscale Perspective on the Tolman Length
M. Lulli, L. Biferale, G. Falcucci, M. Sbragaglia, and X. Shan
Phys. Rev. E 105, 015301 - Published 3 January 2022
Abstract: We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension σ as computed from three-dimensional hydrostatic droplets and bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called Tolman length δ. LBM allows one to precisely compute σ at the surface of tension Rs and determine the Tolman length from the coefficient of the first order correction. The corresponding values of δ display universality for different equations of state, following a power-law scaling near the critical emperature. The Tolman length has been studied so far mainly via computationally demanding Molecular Dynamics simulations or by means of Density Functional Theory approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.
Structure and isotropy of lattice pressure tensors for multirange potentials
Matteo Lulli, Luca Biferale, Giacomo Falcucci, Mauro Sbragaglia, and Xiaowen Shan
Phys. Rev. E 103, 063309 - Published 30 June 2021
Abstract: We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multiphase lattice Boltzmann models (LBM) with multirange interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multirange potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of nonideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of nonideal interfaces.
λ-Navier-Stokes turbulence
A. Alexakis and L. Biferale
Phylosofical Transactions A
Abstract: We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the Navier–Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value λc∼0.3. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number Re. We show that for a fixed injection rate, as λ→λc, the kinetic energy diverges with a scaling law ε∝(λ-λc)-2/3. The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as λc is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to λc a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as λc is approached is reduced. The possibility of obtaining a statistical description of regular Navier–Stokes turbulence as an expansion around this newly found critical point is discussed.
Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database
M. Buzzicotti, F. Bonaccorso, P. Clark Di Leoni, and L. Biferale
Phys. Rev. Fluids 6, 050503 - Published 12 May 2021
Abstract: We study the applicability of tools developed by the computer vision community for feature learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis the capability of convolutional neural networks embedded in a deep generative adversarial model (deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configurations of three-dimensional turbulence in the presence of rotation, a case with multiscale random features where both large-scale organized structures and small-scale highly intermittent and non-Gaussian fluctuations are present. Second, following a reverse engineering approach, we aim to rank the input flow properties (features) in terms of their qualitative and quantitative importance to obtain a better set of reconstructed fields. We present two approaches both based on context encoders. The first one infers the missing data via a minimization of the L2 pixel-wise reconstruction loss, plus a small adversarial penalization. The second, searches for the closest encoding of the corrupted flow configuration from a previously trained generator. Finally, we present a comparison with a different data assimilation tool, based on Nudging, an equation-informed unbiased protocol, well known in the numerical weather prediction community. The TURB-Rot database of roughly 300 K two-dimensional turbulent images is released and details on how to download it are given.
Acceleration statistics of tracer and light particles in compressible homogeneous isotropic turbulence
X. Wang, M. Wan and L. Biferale
Journal Fluid Mechanics, February 2022
Abstract: The accelerations of tracer and light particles (bubbles) in compressible homogeneous isotropic turbulence are investigated by using data from direct numerical simulations up to turbulent Mach number Mt=1. For tracer particles, the flatness factor of acceleration components, Fa, increases gradually for Mt∈[0.3,1]. On the contrary, Fa for bubbles develops a maximum around Mt∼0.6. The probability density function of longitudinal acceleration of tracers is increasingly skewed towards the negative value as Mt increases. By contrast, for light particles, the skewness factor of longitudinal acceleration, Sa, first becomes more negative with the increase of Mt, and then goes back to 0 when Mt is larger than 0.6. Similarly, differences among tracers and bubbles appear also in the zero-crossing time of acceleration correlation. It is argued that all these phenomena are intimately linked to the flow structures in the compression regions close to shocklets.
Reinforcement learning for pursuit and evasion of microswimmers at low Reynolds number
F. Borra, L. Biferale, M. Cencini, A. Celani
Phys. Rev. Fluids 7, 023103 (2022)
Abstract: We consider a model of two competing microswimming agents engaged in a pursue-evasion task within a low-Reynolds-number environment. Agents can only perform simple maneuvers and sense hydrodynamic disturbances, which provide ambiguous (partial) information about the opponent's position and motion. We frame the problem as a zero-sum game: The pursuer has to capture the evader in the shortest time, while the evader aims at deferring capture as long as possible. We show that the agents, trained via adversarial reinforcement learning, are able to overcome partial observability by discovering increasingly complex sequences of moves and countermoves that outperform known heuristic strategies and exploit the hydrodynamic environment.
Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using nudging
L. Agasthya, P. Clark Di Leoni, L. Biferale
Physics of Fluids 34, 015128 (2022)
Abstract: Nudging is a data assimilation technique that has proved to be capable of reconstructing several highly turbulent flows from a set of partial spatiotemporal measurements. In this study, we apply the nudging protocol on the temperature field in a Rayleigh-Bénard convection system at varying levels of turbulence. We assess the global, as well as scale by scale, success in reconstructing the flow and the transition to full synchronization while varying both the quantity and quality of the information provided by sparse measurements either on the Eulerian or Lagrangian domain. We assess the statistical reproduction of the dynamic behavior of the system by studying the spectra of the nudged fields as well as the correct prediction of heat transfer properties as measured by the Nusselt number. Furthermore, we analyze the results in terms of the complexity of solutions at various Rayleigh numbers and discuss the more general problem of predicting all state variables of a system given partial or full measurements of only one subset of the fields, in particular, temperature. This study sheds new light on the correlation between the velocity and temperature in thermally driven flows and on the possibility to control them by acting on the temperature only.
Magnetic ground states of a model for MNb3S6(M=Co,Fe,Ni)
O. Heinonen, R. A. Heinonen, and H. Park
Phys. Rev. Materials 6, 024405 - Published 14 February 2022
Abstract: The transition-metal-intercalated dichalcogenide CoNb3S6 is a triangular antiferromagnet (AFM) that has recently been shown to exhibit a large anomalous Hall effect (AHE) below the Néel temperature, even though the response to an external field is very small. This suggests that there is an interesting magnetic structure that interacts with the electronic structure to yield the AHE, as collinear AFMs cannot exhibit a nonzero AHE. We propose a model for magnetic transition-metal-intercalated dichalcogenides and examine its ground state as a function of interaction parameters. The model exhibits transitions between planar spin spirals, nonplanar spin spirals, and a particular noncoplanar so-called 3q state. This latter state must exhibit a nonzero AHE, while the spin spirals do not.
Oscillations Modulating Power Law Exponents in Isotropic Turbulence: Comparison of Experiments with Simulations
K. P. Iyer, G. P. Bewley, L. Biferale, K. R. Sreenivasan, and P. K. Yeung
Phys. Rev. Lett. 126, 254501 - Published 22 June 2021
Abstract: Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds number Rλ~1000. In particular, oscillations modulating the power-law scaling in the inertial range are examined for structure functions up to sixth-order moments. The oscillations in exponent ratios decrease with increasing sample size in simulations, although in experiments they survive at a low value of 4 parts in 1000 even after massive averaging. The two datasets are consistent in their intermittent character but differ in small but observable respects. Neither the scaling exponents themselves nor all the viscous effects are consistently reproduced by existing models of intermittency.
Inertial range statistics of the entropic lattice Boltzmann method in three-dimensional turbulence
M. Buzzicotti and G. Tauzin
Phys. Rev. E 104, 015302 - Published 6 July 2021
Abstract: We present a quantitative analysis of the inertial range statistics produced by entropic lattice Boltzmann method (ELBM) in the context of three-dimensional homogeneous and isotropic turbulence. ELBM is a promising mesoscopic model particularly interesting for the study of fully developed turbulent flows because of its intrinsic scalability and its unconditional stability. In the hydrodynamic limit, the ELBM is equivalent to the Navier-Stokes equations with an extra eddy viscosity term. From this macroscopic formulation, we have derived a new hydrodynamical model that can be implemented as a large-eddy simulation closure. This model is not positive definite, hence, able to reproduce backscatter events of energy transferred from the subgrid to the resolved scales. A statistical comparison of both mesoscopic and macroscopic entropic models based on the ELBM approach is presented and validated against fully resolved direct numerical simulations. Besides, we provide a second comparison of the ELBM with respect to the well-known Smagorinsky closure. We found that ELBM is able to extend the energy spectrum scaling range preserving at the same time the simulation stability. Concerning the statistics of higher order, inertial range observables, ELBM accuracy is shown to be comparable with other approaches such as Smagorinsky model.
Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms
H. S. Tavares, L. Biferale, M. Sbragaglia, and A. A. Mailybaev
Phys. Rev. Fluids 6, 054606 – Published 13 May 2021
Abstract: We studied turbulence induced by the Rayleigh-Taylor (RT) instability for two-dimensional (2D) immiscible two-component flows by using a multicomponent lattice Boltzmann method with a Shan-Chen pseudopotential implemented on graphics processing units. We compare our results with the extension to the 2D case of the phenomenological theory for immiscible 3D RT turbulence studied by Chertkov and collaborators [Phys. Rev. E 71, 055301 (2005)]. Furthermore, we compared the growth of the mixing layer, typical velocity, average density profiles, and enstrophy with the equivalent case but for miscible two-component fluid. In both the miscible and immiscible cases, the expected quadratic growth of the mixing layer and the linear growth of the typical velocity are observed with close long-time asymptotic prefactors but different initial transients. In the immiscible case, the enstrophy shows a tendency to grow like ∝t3/2, with the highest values of vorticity concentrated close to the interface. In addition, we investigate the evolution of the typical drop size and the behavior of the total length of the interface in the emulsionlike state, showing the existence of a power-law behavior compatible with our phenomenological predictions. Our results can also be considered as a validation step to extend the application of the lattice Boltzmann tool to study the 3D immiscible case.
Nonequilibrium ensembles for the three-dimensional Navier-Stokes equations
G. Margazoglou, L. Biferale, M. Cencini, G. Gallavotti, and V. Lucarini
Phys. Rev. E 105, 065110 - Published 21 June 2022
Abstract: At the molecular level fluid motions are, by first principles, described by time reversible laws. On the other hand, the coarse grained macroscopic evolution is suitably described by the Navier-Stokes equations, which are inherently irreversible, due to the dissipation term. Here, a reversible version of three-dimensional Navier-Stokes is studied, by introducing a fluctuating viscosity constructed in such a way that enstrophy is conserved, along the lines of the paradigm of microcanonical versus canonical treatment in equilibrium statistical mechanics. Through systematic simulations we attack two important questions: (a) What are the conditions that must be satisfied in order to have a statistical equivalence between the two nonequilibrium ensembles? (b) What is the empirical distribution of the fluctuating viscosity observed by changing the Reynolds number and the number of modes used in the discretization of the evolution equation? The latter point is important also to establish regularity conditions for the reversible equations. We find that the probability to observe negative values of the fluctuating viscosity becomes very quickly extremely small when increasing the effective Reynolds number of the flow in the fully resolved hydrodynamical regime, at difference from what was observed previously.
Stress Overshoots in Simple Yield Stress Fluids
R. Benzi, T. Divoux, C. Barentin, S. Manneville, M. Sbragaglia, and F. Toschi
Phys. Rev. Lett. 127, 148003 - Published 27 September 2021
Abstract: Soft glassy materials such as mayonnaise, wet clays, or dense microgels display a solid-to-liquid transition under external shear. Such a shear-induced transition is often associated with a nonmonotonic stress response in the form of a stress maximum referred to as “stress overshoot.” This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress σM and strain γM that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon startup of shear from the local flow behavior to the global rheological observables.
Minimal phase-coupling model for intermittency in turbulent systems
J.A. Arguedas-Leiva, E. Carroll, L. Biferale, M. Wilczek, and M. D. Bustamante
Phys. Rev. Research 4, L032035 - Published 29 August 2022
Abstract: Turbulent systems exhibit a remarkable multiscale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A quantitative relation between real-space structure, statistics, and phase synchronization is currently missing. Here, we address this problem in the framework of a minimal deterministic phase-coupling model, which enables a detailed investigation by means of dynamical systems theory and multiscale high-resolution simulations. We identify the spectral power law steepness, which controls the phase coupling, as the control parameter for tuning the non-Gaussian properties of the system. Whereas both very steep and very shallow spectra exhibit close-to-Gaussian statistics, the strongest departures are observed for intermediate slopes comparable with the ones in hydrodynamic and Burgers turbulence. We show that the non-Gaussian regime of the model coincides with a collapse of the dynamical system to a lower-dimensional attractor and the emergence of phase synchronization, thereby establishing a dynamical-systems perspective on turbulent intermittency.
Continuum modeling of shear startup in soft glassy materials
R. Benzi, T. Divoux, C. Barentin, S. Manneville, M. Sbragaglia, and F. Toschi
Phys. Rev. E 104, 034612 - Published 27 September 2021
Abstract: Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σγ such that YSFs are solid for stresses σ imposed below σγ, whereas they flow like liquids for σ>σγ. Under an applied shear rate γ, the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress &sigmaM and strain &gammaM as a function of γ, which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σM(&gamma) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling &sigmaM(γ). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.
Global energy spectrum of the general oceanic circulation
B. A. Storer, M. Buzzicotti, H. Khatri, S. M. Griffies and H. Aluie
Nature Communications volume 13, Article number: 5314 (2022)
Abstract: Advent of satellite altimetry brought into focus the pervasiveness of mesoscale eddies (100) km in size, which are the ocean's analogue of weather systems and are often regarded as the spectral peak of kinetic energy (KE). Yet, understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small "representative" regions that cannot capture the vast dynamic range at planetary scales. Here, we use a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three decades of length-scales reveal the Antarctic Circumpolar Current as the spectral peak of the global extra-tropical circulation, at ≈ 104 km, and a previously unobserved power-law scaling over scales larger than 103 km. A smaller spectral peak exists at ≈ 300 km associated with mesoscales, which, due to their wider spread in wavenumber space, account for more than 50% of resolved surface KE globally. Seasonal cycles of length-scales exhibit a characteristic lag-time of ≈ 40 days per octave of length-scales such that in both hemispheres, KE at 102 km peaks in spring while KE at 103 km peaks in late summer. These results provide a new window for understanding the multiscale oceanic circulation within Earth’s climate system, including the largest planetary scales.
A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement
X. Xue, L. Biferale, M. Sbragaglia and F. Toschi
The European Physical Journal E volume 44, Article number: 142 (2021)
Abstract: We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in the absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean settling velocity is quantitatively assessed, especially in comparison with unconfined situations. Results show that the expected effects of confinement are very well captured by the numerical simulations, wherein the confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the proposed methodology in highlighting the effects of confinement on the motion of particles in the presence of thermal fluctuations.
Taming Lagrangian Chaos with Multi-Objective Reinforcement Learning
C. Calascibetta, L. Biferale, F. Borra, A. Celani and M. Cencini
We consider the problem of two active particles in 2D complex flows with the multi-objective goals of minimizing both the dispersion rate and the energy consumption of the pair. We approach the problem by means of Multi Objective Reinforcement Learning (MORL), combining scalarization techniques together with a Q-learning algorithm, for Lagrangian drifters that have variable swimming velocity. We show that MORL is able to find a set of trade-off solutions forming an optimal Pareto frontier. As a benchmark, we show that a set of heuristic strategies are dominated by the MORL solutions. We consider the situation in which the agents cannot update their control variables continuously, but only after a discrete (decision) time, τ. We show that there is a range of decision times, in between the Lyapunov time and the continuous updating limit, where Reinforcement Learning finds strategies that significantly improve over heuristics. In particular, we discuss how large decision times require enhanced knowledge of the flow, whereas for smaller τ all a priori heuristic strategies become Pareto optimal.
Optimal policies for Bayesian olfactory search in turbulent flows
R. A. Heinonen, L. Biferale, A. Celani, and M. Vergassola
In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will only detect the cue intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work, we cast this search problem in the language of a partially observable Markov decision process (POMDP) and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We discuss additionally the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits — and pitfalls — of employing a reward shaping function.
Large-scale convective flow sustained by thermally active Lagrangian tracers
L. Agasthya, A. Bartel, L. Biferale, M. Ehrhardt, F. Toschi
Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical study based on tracer particles that are thermally coupled to the fluid. We imagine that particles can adjust their internal temperature reacting to some local fluid properties and follow simple, hard-wired active control protocols. We study the case where instabilities are induced by switching the particle temperature from hot to cold depending on whether it is ascending or descending in the flow. A macroscopic transition from a stable to unstable convective flow is achieved, depending on the number of active particles and their excess negative/positive temperature. The stable state is characterized by a flow with low turbulent kinetic energy, strongly stable temperature gradient, and no large-scale features. The convective state is characterized by higher turbulent kinetic energy, self-sustaining large-scale convection, and weakly stable temperature gradients. The particles individually promote the formation of stable temperature gradients, while their aggregated effect induces large-scale convection. When the Lagrangian temperature scale is small, a weakly convective laminar system forms. The Lagrangian approach is also compared to a uniform Eulerian bulk heating with the same mean injection profile and no such transition is observed. Our empirical approach shows that thermal convection can be controlled by pure Lagrangian forcing and opens the way for other data-driven particle-based protocols to enhance or deplete large-scale motion in thermal flows.
Multi-scale data reconstruction of turbulent rotating flows with Gappy POD, Extended POD and Generative Adversarial Networks
T. Li, M. Buzzicotti, L. Biferale, F. Bonaccorso, S. Chen, M. Wan
Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades, which lead to non-Gaussian statistics at both large and small scales. Data assimilation also serves as a tool to rank physical features within turbulence, by evaluating the performance of reconstruction in terms of the quality and quantity of the information used. Additionally, benchmarking various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity, and explicability. In this study, we use linear and non-linear tools based on the Proper Orthogonal Decomposition (POD) and Generative Adversarial Network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the non-linear GAN does not outperform one of the linear POD techniques. On the other hand, supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training. Robustness against the measurement noise is also discussed.
Evolution of a Stratified Turbulent Cloud under Rotation
T. Li, Minping Wan, S. Chen
Localized turbulence is common in geophysical flows, where the roles of rotation and stratification are paramount. In this study, we investigate the evolution of a stratified turbulent cloud under rotation. Recognizing that a turbulent cloud is composed of vortices of varying scales and shapes, we start our investigation with a single eddy using analytical solutions derived from a linearized system. Compared to an eddy under pure rotation, the stratified eddy shows the physical manifestation of a known potential vorticity mode, appearing as a static stable vortex. In addition, the expected shift from inertial waves to inertial-gravity waves is observed. In our numerical simulations of the turbulent cloud, carried out at a constant Rossby number over a range of Froude numbers, stratification causes columnar structures to deviate from vertical alignment. This deviation increases with increasing stratification, slowing the expansion rate of the cloud. The observed characteristics of these columnar structures are consistent with the predictions of linear theory, particularly in their tilt angles and vertical growth rates, suggesting a significant influence of inertial-gravity waves. Using Lagrangian particle tracking, we have identified regions where wave activity dominates over turbulence. In scenarios of milder stratification, these inertial-gravity waves are responsible for a significant energy transfer away from the turbulent cloud, a phenomenon that attenuates with increasing stratification.
Thread-safe lattice Boltzmann for high-performance computing on GPUs
A. Montessori, M. Lauricella, A. Tiribocchi, M. Durve, M. La Rocca, G. Amati, F. Bonaccorso, S. Succi
We present thread-safe, highly-optimized lattice Boltzmann implementations, specifically aimed at exploiting the high memory bandwidth of GPU-based architectures. At variance with standard approaches to LB coding, the proposed strategy, based on the reconstruction of the post-collision distribution via Hermite projection, enforces data locality and avoids the onset of memory dependencies, which may arise during the propagation step, with no need to resort to more complex streaming strategies. The thread-safe lattice Boltzmann achieves peak performances, both in two and three dimensions and it allows to sensibly reduce the allocated memory ( tens of GigaBytes for order billions lattice nodes simulations) by retaining the algorithmic simplicity of standard LB computing. Our findings open attractive prospects for high-performance simulations of complex flows on GPU-based architectures.
Lightweight Lattice Boltzmann
A. Tiribocchi, A. Montessori, G. Amati, M. Bernaschi, F. Bonaccorso, S. Orlandini, S. Succi, M. Lauricella
A GPU-accelerated version of the lattice Boltzmann method for efficient simulation of soft materials is introduced. Unlike standard approaches, this method reconstructs the distribution functions from available hydrodynamic variables (density, momentum, and pressure tensor) without storing the full set of discrete populations. This scheme shows satisfactory numerical stability, significantly lower memory requirements, and data access cost. A series of benchmark tests of relevance to soft matter, such as collisions of fluid droplets, is discussed to validate the method. The results can be of particular interest for high-performance simulations of soft matter systems on future exascale computers.
Classifying Turbulent Environments via Machine Learning
M. Buzzicotti, F. Bonaccorso
The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in different turbulent backgrounds, to predict the probability of rare events and/or to infer physical parameters labelling different turbulent set-ups. To achieve such goal one can use different tools depending on the system's knowledge and on the quality and quantity of the accessible data. In this context, we assume to work in a model-free setup completely blind to all dynamical laws, but with a large quantity of (good quality) data for training. As a prototype of complex flows with different attractors, and different multi-scale statistical properties we selected 10 turbulent 'ensembles' by changing the rotation frequency of the frame of reference of the 3d domain and we suppose to have access to a set of partial observations limited to the instantaneous kinetic energy distribution in a 2d plane, as it is often the case in geophysics and astrophysics. We compare results obtained by a Machine Learning (ML) approach consisting of a state-of-the-art Deep Convolutional Neural Network (DCNN) against Bayesian inference which exploits the information on velocity and enstrophy moments. First, we discuss the supremacy of the ML approach, presenting also results at changing the number of training data and of the hyper-parameters. Second, we present an ablation study on the input data aimed to perform a ranking on the importance of the flow features used by the DCNN, helping to identify the main physical contents used by the classifier. Finally, we discuss the main limitations of such data-driven methods and potential interesting applications.
Spatio-temporal coarse-graining decomposition of the global ocean geostrophic kinetic energy
M. Buzzicotti, B. A. Storer, H. Khatri, S. M. Griffies, H. Aluie
We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022) using a coarse-graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain-averaged results, spherical harmonics spectra are too noisy at gyre-scales (>1000 km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra-tropics mesoscales (100-500~km) have a root-mean-square (rms) velocity of ~15 cm/s, which increases to ~30-40~cm/s locally in the Gulf Stream and Kuroshio and to ~16-28~cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy-per-area, which is higher in the north due to continental boundaries. We estimate that =25-50\% of total geostrophic energy is at scales smaller than 100~km, and is un(der)-resolved by pre-SWOT satellite products. Spectra of the time-mean component show that most of its energy (up to 70%) resides in stationary mesoscales (<500km), highlighting the preponderance of standing small-scale structures in the global ocean. By coarse-graining in space and time, we compute the first spatio-temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length-scale evolves over a wide range of time-scales with a consistent peak at =200 km and =2-3~weeks.
Analysis of the heat transfer fluctuations in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets
F. Pelusi, S. Ascione, M. Sbragaglia, M. Bernaschi
Employing numerical simulations, we provide an accurate insight into the of heat transfer mechanisms in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets. We focus on the unsteady dynamics characterizing the thermal convection of these complex fluids close to the transition from conductive to convective states, where the heat transfer phenomenon, expressed in terms of the Nusselt number Nu, is characterized by pronounced fluctuations triggered by collective droplets motion [Pelusi et al., Soft Matter 17(13), 3709 - 3721 (2021)]. By systematically increasing the droplet concentration, we show how these fluctuations emerge along with the segregation of "extreme events" in the boundary layers, causing intermittent bursts in the heat flux fluctuations. Furthermore, we quantify the extension S and the duration of the coherent droplet motion accompanying these extreme events via a suitable statistical analysis involving the droplets displacements. We show how the increase in droplet concentration results in a power-law behaviour of the probability distribution function of S and and how this outcome is robust at changing the analysis protocol. Our work offers a comprehensive picture, linking macroscopic heat transfer fluctuations with the statistics of droplets at the mesoscale.