Dept. of Physics, University of Rome, Tor Vergata (on leave)
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
Large-scale convective flow sustained by thermally active Lagrangian tracers
Journal of Fluid Mechanics, 953, art. no. A5, 2022 LinkAgasthya, L., Bartel, A., Biferale, L., Ehrhardt, M., Toschi, F.
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 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. Individually, the particles 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.
Minimal phase-coupling model for intermittency in turbulent systems
Physical Review Research, 4 (3), art. no. L032035, 2022 LinkL Biferale, F Bonaccorso, M Buzzicotti, PC Di Leoni, K Gustavsson
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
Nonequilibrium ensembles for the three-dimensional Navier-Stokes equations
Physical Review E, 105 (6), art. no. 065110 LinkMargazoglou, G., Biferale, L., Cencini, M., Gallavotti, G., Lucarini, V.
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.
Acceleration statistics of tracer and light particles in compressible homogeneous isotropic turbulence
Journal of Fluid Mechanics, 935, art. no. 35, 2022 LinkWang, X., Wan, M., Biferale, L.
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=1 . For tracer particles, the flatness factor of acceleration components, , increases gradually for [0.3,1] . On the contrary, for bubbles develops a maximum around 0.6 . The probability density function of longitudinal acceleration of tracers is increasingly skewed towards the negative value as increases. By contrast, for light particles, the skewness factor of longitudinal acceleration, , first becomes more negative with the increase of , and then goes back to 0 when 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
Physical Review Fluids, 7 (2), art. no. 023103, 2022 LinkBorra, F., Biferale, L., Cencini, M., Celani, A.
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.
λ-NavierStokes turbulence
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380 (2219), art. no. 20210243, 2022 LinkAlexakis, A., Biferale, L.
We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the NavierStokes 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 in the forward energy cascade range and at changing the Reynolds number . We show that for a fixed injection rate, as λ→λc , the kinetic energy diverges with a scaling law ε∝(λλc)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 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 NavierStokes turbulence as an expansion around this newly found critical point is discussed.
Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks
Physics of Fluids, 34 (1), art. no. 015128, 2022 LinkAgasthya, L., Clark Di Leoni, P., Biferale, L.
We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Bénard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging and are able to achieve satisfactory reconstruction of the velocity fields only when data for temperature is provided with high spatial and temporal density. When data becomes sparse, the PINNs performance worsens, not only in a point-to-point error sense but also, and contrary to nudging, in a statistical sense, as can be seen in the probability density functions and energy spectra.
Mesoscale perspective on the Tolman length
Physical Review E, 105 (1), art. no. 015301, 2022 LinkLulli, M., Biferale, L., Falcucci, G., Sbragaglia, M., Shan, X.
We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension 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 . LBM allows one to precisely compute at the surface of tension Rs and determine the Tolman length from the coefficient of the first order correction. The corresponding values of display universality for different equations of state, following a power-law scaling near the critical temperature. 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.
A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement
European Physical Journal E, 44 (11), art. no. 142, 2021 LinkXue, X., Biferale, L., Sbragaglia, M., Toschi, F.
We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method (FLBM) 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 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 to 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 presence of thermal fluctuations.
TURB-Rot. A large database of 3d and 2d snapshots from turbulent rotating flows
PreprintL. Biferale, F. Bonaccorso, M. Buzzicotti, P. Clark di Leoni
We present TURB-Rot, a new open database of 3d and 2d snapshots of turbulent velocity fields, obtained by Direct Numerical Simulations (DNS) of the original Navier-Stokes equations in the presence of rotation. The aim is to provide the community interested in data-assimilation and/or computer vision with a new testing-ground made of roughly 300K complex images and fields. TURB-Rot data are characterized by multi-scales strongly non-Gaussian features and rough, non-differentiable, fields over almost two decades of scales. In addition, coming from fully resolved numerical simulations of the original partial differential equations, they offer the possibility to apply a wide range of approaches, from equation-free to physics-based models. TURB-Rot data are reachable at smart-turb.roma2.infn.it
Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning
Chaos 29, 103138, 2019 PreprintL Biferale, F Bonaccorso, M Buzzicotti, PC Di Leoni, K Gustavsson
To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip velocity with fixed intensity, Vs , but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasi-optimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process, and are therefore not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when V s is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small
Self-similar Subgrid-scale Models for Inertial Range Turbulence and Accurate Measurements of Intermittency
Physical Review Letters 123 (1), 014503, 2019 PreprintL Biferale, F Bonaccorso, M Buzzicotti, KP Iyer
A class of spectral subgrid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of subgrid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale extension where anomalous exponents are measured by roughly 1 order of magnitude when compared to direct numerical simulations or to other popular subgrid closures at the same resolution. We find a first indication that intermittency for high-order moments is not captured by many of the popular phenomenological models developed so far
Statistical properties of turbulence in the presence of a smart small-scale control
Physical Review Letters 124 (8), 084504, 2020PreprintM Buzzicotti, L Biferale, F Toschi
By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a non-linear extra viscosity acting preferentially on high vorticity regions. We show that the presence of such smart small-scale drag can strongly reduce intermittency and non-Gaussian fluctuations. Our results pave the way towards a deeper understanding on the fundamental role of degrees of freedom in turbulence as well as on the impact of (pseudo)coherent structures on the statistical small-scale properties. Our work can be seen as a first attempt to develop smart-Lagrangian forcing/drag mechanisms to control turbulence
Synchronization to big-data: nudging the Navier-Stokes equations for data assimilation of turbulent flows
Physical Review X 10 (1), 011023, 2020PreprintP. Clark Di Leoni, A. Mazzino, L. Biferale
Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it to the toughest problem in fluid dynamics: three dimensional homogeneous and isotropic turbulence. By doing numerical experiments we perform a systematic assessment of how well the technique reconstructs large- and small-scales features of the flow with respect to the quantity and the quality/type of data supplied to it. The types of data used are: (i) field values on a fixed number of spatial locations (Eulerian nudging), (ii) Fourier coefficients of the fields on a fixed range of wavenumbers (Fourier nudging), or (iii) field values along a set of moving probes inside the flow (Lagrangian nudging). We present state-of-the-art quantitative measurements of the scale-by-scale {\it transition to synchronization} and a detailed discussion of the probability distribution function of the reconstruction error, by comparing the nudged field and the {\it truth} point-by-point. Furthermore, we show that for more complex flow configurations, like the case of anisotropic rotating turbulence, the presence of cyclonic and anticyclonic structures leads to unexpectedly better performances of the algorithm. We discuss potential further applications of nudging to a series of applied flow configurations, including the problem of field-reconstruction in thermal Rayleigh-Bénard convection and in magnetohydrodynamics (MHD), and to the determination of optimal parametrisation for small-scale turbulent modeling. Our study fixes the standard requirements for future applications of nudging to complex turbulent flows
Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields
Physical Review E 99 (5), 053303, 2019 PreprintG. Margazoglou, L. Biferale, R. Grauer, K. Jansen, D. Mesterházy, T. Rosenow, and R. Tripiccione
We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm samples space-time histories of the dynamical degrees of freedom under the influence of random noise. First, we validate and benchmark the HMC algorithm by reproducing multiscale properties of the one-dimensional Burgers equation driven by Gaussian and white-in-time noise. Second, we show how to implement an importance sampling protocol to significantly enhance, by orders of magnitudes, the probability to sample extreme and rare events, making it possible to estimate moments of field variables of extremely high order (up to 30 and more). By employing reweighting techniques, we map the biased configurations back to the original probability measure in order to probe their statistical importance. Finally, we show that by biasing the system towards very intense negative gradients, the HMC algorithm is able to explore the statistical fluctuations around instanton configurations. Our results will also be interesting and relevant in lattice gauge theory since they provide unique insights into reweighting techniques
Superfluid Helium in Three-Dimensional Counterflow Differs Strongly from Classical Flows: Anisotropy on Small Scales
Physical Review Letters 122 (14), 144501, 2019 PreprintL Biferale, D Khomenko, V L'vov, A Pomyalov, I Procaccia, G Sahoo
Three-dimensional anisotropic turbulence in classical fluids tends towards isotropy and homogeneity with decreasing scales, allowing—eventually—the abstract model of homogeneous and isotropic turbulence to be relevant. We show here that the opposite is true for superfluid 4He turbulence in three-dimensional counterflow channel geometry. This flow becomes less isotropic upon decreasing scales, becoming eventually quasi-two-dimensional. The physical reason for this unusual phenomenon is elucidated and supported by theory and simulations
Helicoidal particles in turbulent flows with multi-scale helical injection
Journal of Fluid Mechanics 869, 646-673, 2019 PreprintL Biferale, K Gustavsson, R Scatamacchia
We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier–Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii)–(iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence
Cascades and transitions in turbulent flows
Physics Reports, Volumes 767-769, 1-101, 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
Inferring flow parameters and turbulent configuration with physics-informed data-assimilation and spectral nudging
Physical Review Fluids 3, 104604, 2018 PreprintP 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
OPENINGS
ELLIS-ESA Workshop, 2021
International Centre for Theoretical Sciences, Bangalore, India, 2020
Institut Henri Poincare, Paris, 2019
Colloquium, Scuola Normale Superiore, Pisa, 2017
Workshop on Instantons and Extreme Events in Turbulence and Dynamical Systems, Rio de Janeiro, 2015
Geometrical and statistical fluid dynamics, Simons Center, Stony Brook 2017
ISI researcher ID
Personal VQR Evaluation results (Valutazione Qualita' Ricerca)
Scientific Activity (key words): Complex fluids. Turbulence. Intermittency and Anomalous Scaling laws. Anisotropic Flows. Turbulent Transport. Machine-Learning. Reinforcement Learning. 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.
