Turbulence in Fluids: Stochastic and Numerical ModellingTurbulence 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 have been advocated during these last ten years: the first one is "statistical", and tries to model the evolution of averaged quantities of the flow. This com has followed the glorious trail of Taylor and Kolmogorov, munity, which believes in the phenomenology of cascades, and strongly disputes the possibility of any coherence or order associated to turbulence. On the other bank of the river stands the "coherence among chaos" community, which considers turbulence from a purely deterministic po int of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community are also associated the experimentalists who seek to identify coherent structures in shear flows. |
Contents
Introduction to turbulence in fluid mechanics | 1 |
Onepoint closure modelling | 7 |
206 | 8 |
Copyright | |
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assume baroclinic instability barotropic boundary layer Boussinesq approximation calculation Chapter closure coherent structures conservation consider constant correlation corresponding decay defined density diffusion dimensional direct-numerical simulations dissipation dynamics eddies eddy-viscosity Ekman layer energy spectrum enstrophy enstrophy cascade equal Euler equations evolution experimental Figure finite flux Fourier space function gaussian geostrophic helicity homogeneous horizontal incompressibility inertial range initial instability integral scale inviscid isotropic turbulence Kelvin-Helmholtz kinetic energy kinetic energy spectrum Kolmogorov Kraichnan Lesieur longitudinal Mach number Métais mixing layer molecular motion Navier-Stokes equations numerical simulation obtained parameter passive scalar perturbation potential vorticity predictability result Reynolds number Rossby number Rossby waves rotation scalar shown shows skewness factor spanwise spatial spectral tensor stressed temperature term theory three-dimensional turbulence turbulent flow two-dimensional turbulence U₁ vector velocity field velocity profile VIII viscosity vortex filaments wave number wave vector yields zero მყ