Vorticity and TurbulenceThis book provides an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The book is organized as follows: the first three chapters constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible. This book will be appropriate for professionals in the fields of applied mathematics, mechanical engineering, or physics, as well as graduate students in these noted areas. |
Other editions - View all
Common terms and phrases
analysis approximate assume axis boundary Brownian motion Brownian walk Buttke calculation cascade Chapter Chorin configurations Consider constant constraints correlation cross-section decrease defined density dimensional dissipation distribution E₁ energy ensemble enstrophy entropy Euler equations exponent Figure fluid mechanics folding Fourier transform fractal dimension function Gaussian Hamiltonian Hausdorff homogeneous incompressible increases independent inertial range infinite integral interaction invariant inviscid Kolmogorov Kolmogorov spectrum Kolmogorov theory lattice length macroscopic Navier-Stokes equations particles percolation threshold phase space Phys plane plaquette polymer probability problem radius random field random variables renormalization result Section self-avoiding shell small scales smooth spectral statistical equilibrium statistical mechanics structure superfluid supp Suppose temperature three space dimensions three-dimensional turbulent flow two-dimensional vector velocity field viscosity vortex filaments vortex lines vortex loops vortex methods vortex system vortex tubes vorticity vorticity field wave number zero