Extreme statistics and extreme events in dynamical models of turbulence.

We present a study of the intermittent properties of a shell model of turbulence with statistics of ∼10^{7} eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows us to quantify the inertial range anomalous scaling properties of the velocity fluctuations up to the 24th-order moment. Through a careful assessment of the statistical and systematic uncertainties, we show that none of the phenomenological and theoretical models previously proposed in the literature to predict the anomalous power-law exponents in the inertial range are in agreement with our high-precision numerical measurements.

Instanton-based importance sampling for extreme fluctuations in a shell model for turbulent energy cascade.

Many out-of-equilibrium flows present non-Gaussian fluctuations in physically relevant observables, such as energy dissipation rate. This implies extreme fluctuations that, although rarely observed, have a significant phenomenology. Recently, path integral methods for importance sampling have emerged from formalism initially devised for quantum field theory and are being successfully applied to the Burgers equation and other fluid models.

Generative adversarial networks to infer velocity components in rotating turbulent flows.

Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of the linear Extended Proper Orthogonal Decomposition (EPOD) method, a nonlinear Convolutional Neural Network (CNN) and a Generative Adversarial Network (GAN). We attack the important task of inferring one velocity component out of the measurement of a second one, and two cases are studied: (I) both components lay in the plane orthogonal to the rotation axis and (II) one of the two is parallel to the rotation axis.

Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks.

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.

Erratum: Flow Navigation by Smart Microswimmers via Reinforcement Learning [Phys. Rev. Lett. 118, 158004 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.

Mesoscale perspective on the Tolman length.

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 R_{s} and determine the Tolman length from the coefficient of the first order correction.

A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement.

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.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity.

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC.

Structure and isotropy of lattice pressure tensors for multirange potentials.

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.

Oscillations Modulating Power Law Exponents in Isotropic Turbulence: Comparison of Experiments with Simulations.

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 R_{λ}∼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.

Base flow decomposition for complex moving objects in linear hydrodynamics: Application to helix-shaped flagellated microswimmers.

The motion of microswimmers in complex flows is ruled by the interplay between swimmer propulsion and the dynamics induced by the fluid velocity field. Here we study the motion of a chiral microswimmer whose propulsion is provided by the spinning of a helical tail with respect to its body in a simple shear flow. Thanks to an efficient computational strategy that allowed us to simulate thousands of different trajectories, we show that the tail shape dramatically affects the swimmer's motion.

Collective olfactory search in a turbulent environment.

Finding the source of an odor dispersed by a turbulent flow is a vital task for many organisms. When many individuals concurrently perform the same olfactory search task, sharing information about other members' decisions can potentially boost the performance. But how much of this information is actually exploitable for the collective task? Here we show, in a model of a swarm of agents inspired by moth behavior, that there is an optimal way to blend the private information about odor and wind detections with the public information about other agents' heading direction.

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 the mesoscale. 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 broad variety of fluid dynamic conditions that can be encountered in practice.

Statistical Properties of Turbulence in the Presence of a Smart Small-Scale Control.

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 nonlinear 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.

Self-Similar Subgrid-Scale Models for Inertial Range Turbulence and Accurate Measurements of Intermittency.

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.

Instanton based importance sampling for rare events in stochastic PDEs.

We present a new method for sampling rare and large fluctuations in a nonequilibrium system governed by a stochastic partial differential equation (SPDE) with additive forcing. To this end, we deploy the so-called instanton formalism that corresponds to a saddle-point approximation of the action in the path integral formulation of the underlying SPDE. The crucial step in our approach is the formulation of an alternative SPDE that incorporates knowledge of the instanton solution such that we are able to constrain the dynamical evolutions around extreme flow configurations only.

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.

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

We compare different approaches towards an effective description of multiscale velocity field correlations in turbulence. Predictions made by the operator-product expansion, the so-called fusion rules, are placed in juxtaposition to an approach that interprets the turbulent energy cascade in terms of a Markov process of velocity increments in scale. We explicitly show that the fusion rules are a direct consequence of the Markov property provided that the structure functions exhibit scaling in the inertial range.

Equivalence of nonequilibrium ensembles in turbulence models.

Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of nonequilibrium statistical mechanics. In the case of fluid dynamical systems, one issue is to test whether different models for viscosity lead to the same macroscopic properties of the fluid systems in different regimes. Such models include, besides the standard choice of constant viscosity, cases where the time symmetry of the evolution equations is exactly preserved, as it must be in the corresponding microscopic systems, when available.

Time irreversibility in reversible shell models of turbulence.

Turbulent flows governed by the Navier-Stokes equations (NSE) generate an out-of-equilibrium time irreversible energy cascade from large to small scales. In the NSE, the energy transfer is due to the nonlinear terms that are formally symmetric under time reversal. As for the dissipative term: first, it explicitly breaks time reversibility; second, it produces a small-scale sink for the energy transfer that remains effective even in the limit of vanishing viscosity.

Nonuniversal behaviour of helical two-dimensional three-component turbulence.

The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong helical forcing, the out-of-plane component ceases to behave as a passive advected quantity and develops a nontrivial dynamics which deeply changes its large-scale properties. We show that a small-scale helicity injection correlates the input on the 2D component with the one on the out-of-plane component.

Optimal subgrid scheme for shell models of turbulence.

We discuss a theoretical framework to define an optimal subgrid closure for shell models of turbulence. The closure is based on the ansatz that consecutive shell multipliers are short-range correlated, following the third hypothesis of Kolmogorov formulated for similar quantities for the original three-dimensional Navier-Stokes turbulence. We also propose a series of systematic approximations to the optimal model by assuming different degrees of correlations across scales among amplitudes and phases of consecutive multipliers.