Role of initial separation for Richardson scaling of turbulent two-particle dispersion

The role of initial separation for inertial range scaling of turbulent two-particle dispersion is reassessed in light of recent results. (slightly expanded version of Comment published in Physical Review Letters).Comment: comment published in Physical review letters (doi below

Saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D turbulence

Inertial range scaling exponents for both Lagrangian and Eulerian structure functions are obtained from direct numerical simulations of isotropic turbulence in triply periodic domains at Taylor-scale Reynolds number up to 1300. We reaffirm that transverse Eulerian scaling exponents saturate at $\approx 2.1$ for moment orders $p \ge 10$, significantly differing from the longitudinal exponents (which are predicted to saturate at $\approx 7.3$ for $p \ge 30$ from a recent theory). The Lagrangian scaling exponents likewise saturate at $\approx 2$ for $p \ge 8$. The saturation of Lagrangian exponents and Eulerian transverse exponents is related by the same multifractal spectrum, which is different from the known spectra for Eulerian longitudinal exponents, suggesting that that Lagrangian intermittency is characterized solely by transverse Eulerian intermittency. We discuss possible implication of this outlook when extending multifractal predictions to the dissipation range, especially for Lagrangian acceleration.Comment: 6 pages, 6 figure

Role of pressure in generation of intense velocity gradients in turbulent flows

We investigate the role of pressure, via its Hessian tensor $\mathbf{H}$, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range $140-1300$. Decomposing $\mathbf{H}$ into local isotropic ($\mathbf{H}^{\rm I}$) and nonlocal deviatoric ($\mathbf{H}^{\rm D}$) components reveals that $\mathbf{H}^{\rm I}$ depletes vortex stretching (VS), whereas $\mathbf{H}^{\rm D}$ enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables VS. However, in regions of intense vorticity, identified using conditional statistics, contribution from $\mathbf{H}$ dominates over nonlinearity, leading to overall depletion of VS. We also observe near-perfect alignment between vorticity and the eigenvector of $\mathbf{H}$ corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) $\mathbf{H}^{\rm I}$, and recently identified self-attenuation mechanism [Buaria et al. {\em Nat. Commun.} 11:5852 (2020)], whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of $\mathbf{H}$ on strain-amplification is weak. It opposes strain self-amplification, together with VS, but its effect is much weaker than VS. Correspondingly, the eigenvectors of strain and $\mathbf{H}$ do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modeling endeavors, for instance in Lagrangian modeling of velocity gradient dynamics, where conditional $\mathbf{H}$ is explicitly modeled.Comment: 14 pages, 10 figure

Forecasting small scale dynamics of fluid turbulence using deep neural networks

Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and incorporate Reynolds number dependence explicitly to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers, and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small scale features of turbulence.Comment: 12 pages, 5 figure

Intermittency of turbulent velocity and scalar fields using 3D local averaging

An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $\theta$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_\lambda$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_\lambda$). The intermittency exponent of the energy dissipation rate is $\mu \approx 0.23$, whereas that of enstrophy is slightly larger; trends with $R_\lambda$ suggest that this will be the case even at extremely large $R_\lambda$. The intermittency exponent of the scalar dissipation rate is $\mu_\theta \approx 0.35$ for $Sc=1$. These findings are in essential agreement with previously reported results in the literature. We further show that $\mu_\theta$ decreases monotonically with increasing $Sc$, either as $1/\log Sc$ or a weak power law, suggesting that $\mu_\theta \to 0$ as $Sc \to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.Comment: 7 pages, 5 figure

Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers

Recently, Shete et al. [Phys. Rev. Fluids 7, 024601 (2022)] explored the characteristics of passive scalars in the presence of a uniform mean gradient, mixed by stationary isotropic turbulence. They concluded that at high Reynolds and Schmidt numbers, the presence of both inertial-convective and viscous-convective ranges, renders the statistics of the scalar and velocity fluctuations to behave similarly. However, their data included Schmidt numbers of 0.1, 0.7, 1.0 and 7.0, only the last of which can (at best) be regarded as moderately high. Additionally, they do not consider already available data in the literature at substantially higher Schmidt number of up to 512. By including these data, we demonstrate here that the differences between velocity and scalar statistics show no vanishing trends with increasing Reynolds and Schmidt numbers, and essential differences remain in tact at all Reynolds and Schmidt numbers.Comment: accepted and to be published in Physical Review Fluids as a Commen

Lagrangian investigations of turbulent dispersion and mixing using petascale computing

In many fields of science and engineering important to society, such as study of air/water quality, pollutant dispersion, cloud physics, design of improved combustion devices, etc., the ability of turbulent flow to provide efficient transport of entities such as pollutants, vapor droplets, fuel/oxidizer, etc. is of critical importance. To understand and hence develop proper predictive tools for such transported entities, it is necessary to understand turbulence from a Lagrangian perspective (of an observer moving with the flow), including the interaction between turbulent transport and molecular diffusion. Usually, in both direct numerical simulations (DNS) and experiments, a population of fluid particles is tracked forward in time (forward tracking) from specified initial conditions to understand how a cloud of material spreads in a turbulent flow. However the process of turbulent mixing occurs when material located at different regions at previous times is brought together at a later time. In such a scenario, it is more important to track the particles backward in time (backward tracking). Backward tracking is also important from a modeling perspective, which would help address questions about the dynamical origins of a patch of contaminant material, or a highly convoluted multi-particle cluster. Furthermore, it can also be shown that the n-th moment of a passive scalar field can be directly related to the backward in time statistics of an n-particle cluster. Although conceptually simple, backward tracking is very difficult to accomplish due to time irreversibility of Navier-Stokes equations, and thus not very well understood in literature. In this work, we use DNS of stationary isotropic turbulence to investigate the process of backward and forward dispersion using state of the art computing facilities. A new massively parallel computational framework has been developed to enable particle tracking in DNS at Petascale problem sizes, performing up to 40X faster than the previous implementation. We have also implemented an efficient and statistically robust approach to extract backward and forward statistics via the post-processing of trajectory data stored in DNS of fluid particles and diffusing molecules (that undergo Brownian motion relative to the fluid). Detailed results are first obtained for pairs of fluid particles. An important consequence of applying Kolmogorov’s similarity hypotheses to Lagrangian statistics of particle pairs is the universal t3 scaling (Richardson’s scaling) at intermediate times. Backward dispersion is found to be faster at intermediate times resulting in a higher Richardson constant, though the scaling is not as robust as in forward dispersion. Extensions to higher-order moments of the separation are also addressed. Statistics of the trajectories of molecules taken singly and in pairs are investigated. The separation statistics of molecular pairs exhibit more robust Richardson scaling compared to fluid particles. An important innovation in this work is to demonstrate explicitly the practical utility of a Lagrangian description of turbulent mixing, where molecular displacements and separations in the limit of small backward initial separations can be used to calculate the evolution of scalar fluctuations resulting from a known source function in space. Lagrangian calculations of production and dissipation rates of the scalar fluctuations are shown to agree very well with Eulerian results for the case of passive scalars driven by a uniform mean-gradient. The well-known scalar dissipation anomaly is accordingly addressed in a Lagrangian context. Extensions to three- and four-particle clusters of fluid particles and molecules are also addressed.Ph.D

Non-local amplification of intense vorticity in turbulent flows

International audienc

Vorticity-strain rate dynamics and the smallest scales of turbulence

International audienceBuilding upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events and the smallest scales of turbulence. We demonstrate that our approach is in excellent agreement with the best available data from direct numerical simulations of isotropic turbulence, with Taylor-scale Reynolds number up to 1300. We additionally highlight a shortcoming of prevailing intermittency models due to their disconnection from observed correlation between vorticity and strain. Our work accentuates the importance of this correlation as a crucial step in developing an accurate understanding of intermittency in turbulence