Emmanuel Lévêque

Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows

A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as v T =(C s δ) 2 (| S |—|〈 S 〉|): the magnitude of the mean shear |〈 S 〉|is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor | S |; C S is the standard Smagorinsky constant and Δ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Re τ = 395 and Re τ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.

Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence

We introduce an original acoustic method to track the motion of tracer particles in high Reynolds number turbulent flows. We present in detail the experimental technique and show that it yields a measurement of the Lagrangian velocity variations of single particles, resolved across the inertial range turbulence. Second-order quantities such as the velocity autocorrelation function and time spectrum are in agreement with Kolmogorov 1941 phenomenology. Higher-order quantities reveal a very strong intermittency in the Lagrangian dynamics. Using both the results of the measurements and of direct numerical simulations, we show that the origin of intermittency can be traced back to the existence of long-time correlations in the dynamics of the Lagrangian acceleration. Finally, we discuss the role played by vortices in the Lagrangian dynamics.

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 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 ∗ .

Dynamics of inertial particles in a turbulent von Kármán flow

We study the dynamics of neutrally buoyant particles with diameters varying in the range [1, 45] in Kolmogorov scale units (η) and Reynolds numbers based on Taylor scale ( Re λ ) between 590 and 1050. One component of the particle velocity is measured using an extended laser Doppler velocimetry at the centre of a von Karman flow, and acceleration is derived by differentiation. We find that the particle acceleration variance decreases with increasing diameter with scaling close to ( D /η) −2/3 , in agreement with previous observations, and with a hint for an intermittent correction as suggested by arguments based on scaling of pressure spatial increments. The characteristic time of acceleration autocorrelation increases more strongly than previously reported in other experiments, and possibly varying linearly with D /η. Further analysis shows that the probability density functions of the acceleration have smaller wings for larger particles; their flatness decreases as well, as expected from the behaviour of pressure increments in turbulence when intermittency corrections are taken into account. We contrast our measurements with previous observations in wind-tunnel turbulent flows and numerical simulations.

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

Abstract. Intermittency, measured as

Quantum turbulence at finite temperature: The two-fluids cascade

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

Lagrangian Velocity Fluctuations in Fully Developed Turbulence: Scaling, Intermittency, and Dynamics

, 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

Energy cascade and the four-fifths law in superfluid turbulence

\sqrt{\log Re}