The role of fluctuations across a density interface

A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is related to the presence of irreversible mixing, which alters the global distribution of density levels. We propose a model in which the vertical density profile evolves through a sequence of statistical equilibrium states. The theory is then tested with laboratory experiments in a two-layer stably stratified fluid forced from below by an oscillating grid. Quantitative measurements of density fluctuations across the interface are made by planar laser induced fluorescence. These fluctuations are splitted in a "wave" part and a "turbulent" part. The wave part of the density field is well described by a previous theory due to Phillips. We argue that statistical mechanics predictions apply for the turbulent part of the density field sufficiently close to the interface. However inside the mixed layer density fluctuations are instead controlled by a balance between eddy flux downward and dissipation by cascade to small scales. We report exponential tails for the density pdf in this region

Decaying grid turbulence in a rotating stratified fluid

Rotating grid turbulence experiments have been carried out in a stably stratified fluid for relatively large Reynolds numbers (mesh Reynolds numbers up to 18000). Under the combined effects of rotation and stratification the flow degenerates into quasihorizontal motions. This regime is investigated using a scanning imaging velocimetry technique which provides time-resolved velocity fields in a volume. The most obvious effect of rotation is the inhibition of the kinetic energy decay, in agreement with the quasi-geostrophic model which predicts the absence of a direct energy cascade, as found in two-dimensional turbulence. In the regime of small Froude and Rossby numbers, the dynamics is found to be non-dissipative and associated with a symmetric and highly intermittent vertical vorticity field, that displays k(h)(-3) energy spectra. For higher Rossby numbers, fundamental differences with the quasi-geostrophic model are found. A significant decay of kinetic energy, which does not depend on the stratification, is observed. Moreover, in this regime, although both cyclones and anticyclones are initially produced, the intense vortices are only cyclones. For late times the flow consists of an assembly of coherent interacting Structures. Under the influence of both rotation and stratification, they take the form of lens-like eddies with aspect ratio proportional to f/N

Sur la turbulence bidimensionnelle : une approche par la magnétohydrodynamique

The aim of this work is to achieve and study a two-dimensional turbulence in a layer of mercury in the presence of a uniform transverse magnetic field. A theoretical analysis of the damping of three-dimensional disturbances demonstrating the stabilizing effect of the walls is first presented. A rectangular grid driving turbulence experience with transverse field allows the measurement of energy spectra in t-2k-3 (hot film) and highlight the high anisotropy of the thermal diffusion. The influence of three-dimensional disturbances is significantly less in a square box where a network of vortices 36 is generated by an electric force. The instability of the network by a matching process of the same sign vortex led to an almost homogeneous and isotropic turbulence. An inverse energy cascade with a spectrum k-5/3 is then observed and the constant corresponding Kolmogoroff 2 dimensions measured. When the friction on the bottom of the box is sufficiently low, the inverse cascade is stopped by the limits of the fluid domain. An average rotation appears spontaneously, its direction can change relatively quickly with time intervals becoming extremely long when the bottom friction decreases. An attempt to modeling by a stochastic differential equation is proposed.Le but de ce travail est de réaliser et d’étudier une turbulence bidimensionnelle dans une couche de mercure, en présence d’un champ magnétique transverse uniforme. Une analyse théorique de l’amortissement des perturbations tridimensionnelles mettant en évidence l’effet stabilisant des parois est tout d’abord présentée. Une expérience de turbulence de grille en conduite rectangulaire avec champ transverse permet de mesurer des spectres d’énergie en t-2k-3 (au film chaud) et de mettre en évidence la forte anisotropie de la diffusion thermique. L’influence des perturbations tridimensionnelle est nettement moindre dans une boîte carrée où un réseau de 36 tourbillons est engendré par une force électrique. L’instabilité de ce réseau par un processus d’appariement de tourbillons de même signe conduit à une turbulence quasi homogène et isotrope. Une cascade inverse d’énergie avec un spectre en k-5/3 est alors observée et la constante de Kolmogoroff correspondante à 2 dimensions mesurées. Lorsque le frottement sur le fond de la boîte est suffisamment faible, la cascade inverse est bloquée par les limites du domaine fluide. Une rotation moyenne apparaît alors spontanément, son sens pouvant se retourner de façon relativement rapide à des intervalles de temps devenant extrêmement longs lorsque le frottement du fond diminue. Une tentative de modélisation par une équation différentielle stochastique est proposée

Experimental study of turbulent Ekman layer

This paper reports on laboratory experiments concerning frictional rotating turbulent boundary layer in spin-up flow over flat horizontal bottom. Stereoscopic Particle Image Velocimetry technique is used to obtain two-dimensional three components fluctuating velocity fields. Velocity profiles measured in laminar regime show a remarkable agreement with the Ekman theoretical predictions. Results obtained in turbulent regime confirm the measurement method validity and allow to plan an extensive analysis of the turbulent Ekman layers

Scaling properties of dense water overflows on a continental slope

Dense overflows on a continental slope play an important role in renewing deep water as part of the global thermo-haline convective cycle of the oceans. We report here laboratory experiments reproducing this phenomenon on the large 'Coriolis' turntable in Grenoble, providing good dynamical similarity with the oceanic case. The gravity current is created by salty water injected with a constant flux, which flows down the incline slope (2m wide, 10m long, 15 degrees of inclination) with intense turbulent mixing. It is deviated by the Coriolis force to a cross-slope horizontal direction. We study both the cases of a homogeneous and density stratified ambient fluid. Velocity fields are measured by particle image velocimetry (PIV). Density profiles are also measured to determine the width, thickness and position of the gravity current, and to measure the mixing process. A self-similar behaviour is observed generalizing results for turbulent self-similar plumes and jets to this situation