arXiv subjects

L. Biferale

Publications and source records attributed to L. Biferale.

At least 19 recordsLinked to original sources

arXiv2024

Energy Flux Decomposition in Magnetohydrodynamic Turbulence

In hydrodynamic (HD) turbulence an exact decomposition of the energy flux across scales has been derived that identifies the contributions associated with vortex stretching and strain self-amplification (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3 (2021)) to the energy flux across scales. Here we extend this methodology to general coupled advection-diffusion equations, in particular to homogeneous magnetohydrodynamic (MHD) turbulence, and we show that several subfluxes are related to each other by kinematic constraints akin to the Betchov relation in HD. Applied to data from direct numerical simulations, this decomposition allows for an identification of physical processes and for the quantification of their respective contributions to the energy cascade, as well as a quantitative assessment of their multi-scale nature through a further decomposition into single- and multi-scale terms. We find that vortex stretching is strongly depleted in MHD compared to HD, and the kinetic energy is transferred from large to small scales almost exclusively by the generation of regions of small-scale intense strain induced by the Lorentz force. In regions of large strain, current sheets are stretched by large-scale straining motion into regions of magnetic shear. This magnetic shear in turn drives extensional flows at smaller scales. Magnetic energy is transferred from large to small scales, albeit with considerable backscatter, predominantly by the aforementioned current-sheet thinning in region of high strain while the contribution from current-filament stretching - the analogue to vortex stretching - is negligible. Consequences of these results to subgrid-scale turbulence modelling are discussed.

physics.flu-dyn↗

arXiv2021

Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database

We study the applicability of tools developed by the computer vision community for features 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 3d turbulence in the presence of rotation, a case with multi-scale random features where both large-scale organised 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 penalisation. 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, http://smart-turb.roma2.infn.it, of roughly 300K 2d turbulent images is released and details on how to download it are given.

physics.flu-dyn↗

arXiv2020

TURB-Rot. A large database of 3d and 2d snapshots from turbulent rotating flows

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 http://smart-turb.roma2.infn.it

physics.flu-dyn↗

arXiv2020

On the effects of membrane viscosity on transient red blood cell dynamics

Computational Fluid Dynamics (CFD) is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of red blood cells (RBCs) at mesoscales. In many practical instances, biomedical devices work on time-scales comparable to the intrinsic relaxation time of RBCs: thus, a systematic understanding of the time-dependent response of erythrocyte membranes is crucial for the effective design of such devices. So far, this information has been deduced from experimental data, which do not necessarily adapt to the the broad variety of the fluid dynamic conditions that can be encountered in practice. This work explores the novel possibility of studying the time-dependent response of an erythrocyte membrane to external mechanical loads via ab-initio, mesoscale numerical simulations, with a primary focus on the detailed characterisation of the RBC relaxation time $t_c$ following the arrest of the external mechanical load. The adopted mesoscale model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM), coupled with the Standard Linear Solid model (SLS) to account for the RBC membrane viscosity. We underscore the key importance of the 2D membrane viscosity $\mu_{m}$ to correctly reproduce the relaxation time of the RBC membrane. A detailed assessment of the dependencies on the typology and strength of the applied mechanical loads is also provided. Overall, our findings open interesting future perspectives for the study of the non-linear response of RBCs immersed in time-dependent strain fields.

physics.flu-dyn↗

arXiv2020

Phase transitions and flux-loop metastable states in rotating turbulence

By using direct numerical simulations of up to a record resolution of 512x512x32768 grid points we discover the existence of a new metastable out-of-equilibrium state in rotating turbulence. We scan the phase space by varying both the rotation rate (proportional to the inverse of the Rossby number, $Ro$) and the dimensionless aspect ratio, $λ=H/L$, where $L$ and $H$ are the sizes of the domain perpendicular and parallel to the direction of rotation, respectively. We show the existence of three turbulent phases. For small $Ro$ but finite $λ$, we have a split cascade where the injected energy is transferred to both large and small scales. For large $λ$ and finite $Ro$ there is no inverse cascade and the energy is transferred forward in Fourier space only. Surprisingly, between these two regimes, a third phase is observed as reported here for the first time. Consequently, for certain intervals of $Ro$ and $λ$, energy is no longer accumulated at arbitrarily large scales, rather it stops at some characteristic intermediate length-scales from where it is then redistributed forward in Fourier space, leading to a flux-loop mechanism where the flow is out of equilibrium with vanishing net flux, and non-vanishing heterochiral and homochiral sub-fluxes. The system is further characterized by the presence of metastability and critical slowing down, explaining why previous experiments and numerical simulations were not able to detect this phenomenon, requiring extremely long observation time and huge computational resources.

physics.flu-dyn↗

arXiv2019

A Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields

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 insight into reweighting techniques.

physics.comp-ph↗

arXiv2019

Strong anisotropy of superfluid $^4$He counterflow turbulence

We report on a combined theoretical and numerical study of counterflow turbulence in superfluid $^{4}$He in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normal-fluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

cond-mat.other↗

arXiv2019

Synchronization to big-data: nudging the Navier-Stokes equations for data assimilation of turbulent flows

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.

physics.flu-dyn↗

arXiv2019

$^4$He Counterflow Differs Strongly from Classical Flows: Anisotropy on Small Scales

Three-dimensional anisotropic turbulence in classical fluids tends towards isotropy and homogeneity with decreasing scales, allowing --eventually-- the abstract model of "isotropic homogeneous turbulence" to be relevant. We show here that the opposite is true for superfluid $^4$He turbulence in 3-dimensional counterflow channel geometry. This flow becomes less isotropic upon decreasing scales, becoming eventually quasi 2-dimensional. The physical reason for this unusual phenomenon is elucidated and supported by theory and simulations.

cond-mat.other↗

arXiv2018

On the inverse energy transfer in rotating turbulence

Rotating turbulence is an example of a three-dimensional system in which an inverse cascade of energy, from the small to the large scales, can be formed. While usually understood as a byproduct of the typical bidimensionalization of rotating flows, the role of the three-dimensional modes is not completely comprehended yet. In order to shed light on this issue, we performed direct numerical simulations of rotating turbulence where the 2D modes falling in the plane perpendicular to rotation are removed from the dynamical evolution. Our results show that while the two-dimensional modes are key to the formation of a stationary inverse cascade, the three-dimensional degrees of freedom play a non-trivial role in bringing energy to the larger scales also. Furthermore, we show that this backwards transfer of energy is carried out by the homochiral channels of the three-dimensional modes.

physics.flu-dyn↗

arXiv2018

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

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, i.e. 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.

physics.flu-dyn↗

arXiv2018

Cascades and transitions in turbulent flows

Turbulence is 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 3D/2D isotropic cases characterized by the presence of a strictly direct/inverse energy cascade, respectively. We review 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 cascades, the different scenarios include: split cascades 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 condensate is formed. We classify all transitions 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, MHD 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 the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We discuss the presence of anomalous scaling laws in connection with the intermittent nature of the energy dissipation in configuration space. An overview is also provided concerning cascades in other applications such as bounded flows, quantum, relativistic and compressible turbulence, and active matter, together with implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.

physics.flu-dyn↗

arXiv2018

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

The effects of different filtering strategies on the statistical properties of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations (DNS) with up to $2048^3$ 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.

physics.flu-dyn↗

arXiv2018

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess ab-initio the robustness and limitations of such theoretical models, our simulations are also key to discuss - in controlled situations - some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the transparency transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

physics.flu-dyn↗

arXiv2017

Finding Efficient Swimming Strategies in a Three Dimensional Chaotic Flow by Reinforcement Learning

We apply a reinforcement learning algorithm to show how smart particles can learn approximately optimal strategies to navigate in complex flows. In this paper we consider microswimmers in a paradigmatic three-dimensional case given by a stationary superposition of two Arnold-Beltrami-Childress flows with chaotic advection along streamlines. In such a flow, we study the evolution of point-like particles which can decide in which direction to swim, while keeping the velocity amplitude constant. We show that it is sufficient to endow the swimmers with a very restricted set of actions (six fixed swimming directions in our case) to have enough freedom to find efficient strategies to move upward and escape local fluid traps. The key ingredient is the learning-from-experience structure of the algorithm, which assigns positive or negative rewards depending on whether the taken action is, or is not, profitable for the predetermined goal in the long term horizon. This is another example supporting the efficiency of the reinforcement learning approach to learn how to accomplish difficult tasks in complex fluid environments.

physics.flu-dyn↗

arXiv2017

Turbulent statistics and intermittency enhancement in coflowing superfluid $^4$He

The large scale turbulent statistics of mechanically driven superfluid $^4$He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures $T \in[1.3,2.1]$K. The numerics employ self-consistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particularly efficient in the temperature range between 1.8K and 2K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low $T$ and close to $T_λ$ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

cond-mat.other↗

arXiv2017

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

The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure two-dimenional (2D) or three-dimensional (3D) flows and vice versa. The purpose of the present paper is to make a step in this direction through a combination of numerical and analytical work. The analytical part is mainly concerned with the behavior of 2D3C flows in isolation and the connection between the geometry of the nonlinear interactions and the resulting energy transfer directions. Special emphasis is given to the role of helicity. We show that a generic 2D3C flow can be described by two stream functions corresponding to the two helical sectors of the velocity field. The projection onto one helical sector (homochiral flow) leads to a full 3D constraint and to the inviscid conservation of the total (three dimensional) enstrophy and hence to an inverse cascade of the kinetic energy of the third component also. The coupling between several 2D3C flows is studied through a set of suitably designed direct numerical simulations (DNS), where we also explore the transition between 2D and fully 3D turbulence. In particular, we find that the coupling of three 2D3C flows on mutually orthogonal planes subject to small-scale forcing leads to stationary 3D out-of-equilibrium dynamics at the energy containing scales. The transition between 2D and 3D turbulence is then explored through adding a percentage of fully 3D Fourier modes in the volume.

physics.flu-dyn↗

arXiv2017

Local and non-local energy spectra of superfluid $^3$He turbulence

Below the phase transition temperature $Tc \simeq 10^{-3}$K He-3B has a mixture of normal and superfluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the time-honored Hall-Vinen-Bekarevich-Khalatnikov coarse-grained equations of superfluid turbulence. We combine pseudo-spectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid He-3B turbulence. For T<0.37 Tc, with relatively weak mutual friction, we confirm the previously found "subcritical" energy spectrum E(k), given by a superposition of two power laws that can be approximated as $E(k)~ k^{-x}$ with an apparent scaling exponent 5/3 0.37 Tc and with strong mutual friction, we observed numerically and confirmed analytically the scale-invariant spectrum $E(k)~ k^{-x}$ with a (k-independent) exponent x > 3 that gradually increases with the temperature and reaches a value $x\simeq 9$ for $T\approx 0.72 Tc$. In the near-critical regimes we discover a strong enhancement of intermittency which exceeds by an order of magnitude the corresponding level in classical hydrodynamic turbulence.

cond-mat.other↗