Turbulence in Fluids Fourth Revised and Enlarged Edition By MARCEL LESIEUR

Turbulence in Fluids Fourth Revised and Enlarged Edition

By MARCEL LESIEUR

Contents

1 Introduction to Turbulence in Fluid Mechanics

2 Basic Fluid Dynamics

3 Transition to Turbulence

4 Shear Flow Turbulence

5 Fourier Analysis of Homogeneous Turbulence

6 Isotropic Turbulence: Phenomenology and Simulations

7 Analytical Theories and Stochastic Models

8 Two-Dimensional Turbulence

9 Beyond Two-Dimensional Turbulence in GFD

10 Statistical Thermodynamics of Turbulence

11 Statistical Predictability Theory

12 Large-Eddy Simulations

13 Towards “Real World Turbulence

Preface

Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is

the problem to be solved. Extremely schematically, two opposing points of view had been advoc ated during these last thirty years: the first one was “statistical”, and tried to model the evolution of averaged quantities of the flow. This community, which had followed the glorious trail of Taylor and Kolmogorov, believed in the phenomenology of cascades, and strongly disputed the possibility of any coherence or order associated to turbulence. On the other bank of the river standed the “coherence among chaos” community, which considered turbulence from a purely deterministic point of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community were also associated the experimentalists and computer simulators who sought to identify coherent vortices in flows. Situation is more complex now, and the existence of these two camps is less clear. In fact a third point of view pushed by people from the physics community has emerged, with the concepts of renormalization group theory, multifractality, mixing, and Lagrangian approaches. My personal experience in turbulence was acquired in the first group since I spent several years studying the stochastic models (or two-point closures) applied to various situations such as helical turbulence, turbulent diffusion, or two-dimensional turbulence. These techniques were certainly not the ultimate solution to the problem, but they allowed me to get acquainted with various disciplines such as aeronautics, astrophysics, hydraulics, meteorology, ocean ography, which were all, for different reasons, interested in turbulence. It is certainly true that I discovered the fascination of fluid dynamics through the somewhat abstract studies of turbulence. This monograph is in fact an attempt to reconcile the statistical point of view and the basic concepts of fluid mechanics which determine the evolution of flows arising in the various fields envisaged above. These basic principles, accompanied by the instability-theory predictions and the results of numer ical simulations, give valuable information on the behaviour of turbulence and of the structures which compose it. But a statistical analysis of these struc tures can, at the same time, supply information about strong nonlinear energy transfers within the flow. I have tried to present here a synthesis between two graduate courses given in Grenoble during these last years, namely a “Turbulence” course and a “Geophysical Fluid Dynamics” course. I would like to thank my colleagues of the Ecole Nationale d’Hydraulique et M´ ecanique and Universit´ e Joseph Fourier, who offered me the opportunity of giving these two courses. The stu dents who attended these classes were, through their questions and remarks, of great help. I took advantage of a sabbatical year spent at the Aerospace Engineering Department of University of Southern California to write the first draft of this monograph: this was rendered possible by the generous hospitality of John Laufer and his collaborators. The second edition benefitted also from a graduate course taught at Stanford University during a visit to the Center for Turbulence Research. The support and extra time offered through my ap pointment to the “Institut Universitaire de France” made the third edition possible. The fourth edition was written thanks to a CNRS delegation and a sabbatical semester offered by Grenoble Institute of Technology (INPG)

Download The Book For Free In PDF Format

Download