旋度与湍流
2005-1
清华大学出版社
J.Chorin Alexandre
174
无
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial.Some practical information about approximation procedures is provided in the book, as well as tools for assessing the plausibility of approximation schemes. The emphasis, however, is on the understanding of turbulence---its origin, mechanics, spectra, organized structures, energy budget, and renormalization. The physical space methodology is natural, and makes the reasoning particularly straightforward. Open questions are indicated as such throughout the book.
PrefaceIntroduction1.The Equations of Motion 1.1 The Euler and Navier-Stokes Equations 1.2 Vorticity Form of the Equations 1.3 Discrete Vortex Representations 1.4 Magnetization Variables 1.5 Fourier Representation for Periodic Flow2.Random Flow and Its Spectra 2.1 Introduction to Probability Theory 2.2 Random Fields 2.3 Random Solutions of the Navier-Stokes Equations 2.4 Random Fourier Transform of a Homogeneous Flow Field 2.5 Brownian Motion and Brownian Walks3.The Kolmogorov Theory 3.1 The Goals of Turbulence Theory:Universal Equilibrium 3.2 Kolmogorov Theory:Dimensional Considerations 3.3 The Kolmlgorov Spectrum and an Energy Cascade 3.4 Fractal Dimension 3.5 A First Discussion of Intermittency4.Equilibrium Flow in Spectral Variables and in Two Space Dimensions 4.1 Statistical Equilibrium 4.2 The“Absolute”Statistical Equilibrium in Wave Number Space 4.3 The Combinatorial Method:The Approach to Equilibrium and Negative Temperatures 4.4 The Onsager Theory and the Joyce-Montgomery Equation 4.5 The Continuum Limit and the Role of Invariants 4.6 The Approach to Equilibrium,Viscosity,and Inertial Power Laws5.Vortex Stretching6.Polymers,Percolation,Renormalization7.Vortex Equilibria a in Three-Dimensional SpaceBibliographyIndex
无
这次有点慢啊。