Laurent Chevillard

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Lagrangian Dynamics and Statistical Geometric Structure of Turbulence

The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.

Modeling the pressure Hessian and viscous Laplacian in turbulence: Comparisons with direct numerical simulation and implications on velocity gradient dynamics

Modeling the velocity gradient tensor A=∇u along Lagrangian trajectories in turbulent flow requires closures for the pressure Hessian and viscous Laplacian of A. Based on an Eulerian–Lagrangian change in variables and the so-called recent fluid deformation closure, such models were proposed recently [Chevillard and Meneveau, Phys. Rev. Lett. 97, 174501 (2006)]. The resulting stochastic model was shown to reproduce many geometric and anomalous scaling properties of turbulence. In this work, direct comparisons between model predictions and direct numerical simulation (DNS) data are presented. First, statistical properties of A are described using conditional averages of strain skewness, enstrophy production, energy transfer, and vorticity alignments, conditioned upon invariants of the velocity gradient. These conditionally averaged quantities are found to be described accurately by the stochastic model. More detailed comparisons that focus directly on the terms being modeled in the closures are also present...

Lagrangian intermittencies in dynamic and static turbulent velocity fields from direct numerical simulations

Three temporal velocity signals are analyzed from direct numerical simulations of the Navier–Stokes (N–S) equations. The three signals are: (i) the velocity of fluid particles transported by the time-evolving solution (Eulerian velocity field) of the N–S equations, referred to as the dynamic case; (ii) the velocity of fluid particles transported by a solution of the N–S equations at some fixed time, referred to as the static case; and (iii) the time evolution of the solution of the N–S equations at some fixed positions, referred to as the Eulerian case. The comparison of these three signals aims at elucidating the importance of the overall spacetime evolution of the flow on Lagrangian statistics. It is observed that the static case is, to some extent, similar to the Eulerian case; a feature that can be understood as an ergodicity property of homogeneous and isotropic turbulence and can be related to the process of random sweeping. The dynamic case is clearly different. It bears the signature of the time e...

Unified multifractal description of velocity increments statistics in turbulence: Intermittency and skewness

Abstract The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we are concerned with the complete probability density function (PDF) of signed longitudinal increments at all scales. First, we focus on the symmetric part of the PDFs, taking into account the observed departure from scale invariance induced by dissipation effects. The analysis is then extended to the asymmetric part of the PDFs, with the specific goal to predict the skewness of the velocity derivatives. It opens the route to the complete description of all measurable quantities, for any Reynolds number, and various experimental conditions. This description is based on a single universal parameter function D ( h ) and a universal constant R ∗ .

On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence

Abstract. Intermittency, measured as

A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

\log \left({F(r)}/{3}\right)

Reynolds number effect on the velocity increment skewness in isotropic turbulence

, where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and eventually saturate at very small scales. This feature defines a finite intermediate range of scales between the inertial and dissipation ranges, that we shall call near-dissipation range. It is argued that intermittency is multiplied by a universal factor, independent of the Reynolds number Re, throughout the near-dissipation range. The (logarithmic) extension of the near-dissipation range varies as

A stochastic representation of the local structure of turbulence

\sqrt{\log Re}

Intermittency of Velocity Time Increments in Turbulence

. As a consequence, scaling properties of velocity increments in the near-dissipation range strongly depend on the Reynolds number.