Homogeneous, Isotropic Turbulence
Phenomenology, Renormalization and Statistical Closures
Series: International Series of Monographs on Physics; 162;
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Product details:
- Publisher OUP Oxford
- Date of Publication 27 February 2014
- ISBN 9780199689385
- Binding Hardback
- No. of pages430 pages
- Size 247x181x28 mm
- Weight 884 g
- Language English
- Illustrations 40 b/w illustrations 0
Categories
Short description:
This book addresses the idealised problem posed by homogeneous, isotropic turbulence. It is written from the perspective of a theoretical physicist, but is designed to be accessible to all researchers in turbulence, both theoretical and experimental, and from all disciplines.
MoreLong description:
Fluid turbulence is often referred to as `the unsolved problem of classical physics'. Yet, paradoxically, its mathematical description resembles quantum field theory. The present book addresses the idealised problem posed by homogeneous, isotropic turbulence, in order to concentrate on the fundamental aspects of the general problem. It is written from the perspective of a theoretical physicist, but is designed to be accessible to all researchers in turbulence, both theoretical and experimental, and from all disciplines. The book is in three parts, and begins with a very simple overview of the basic statistical closure problem, along with a summary of current theoretical approaches. This is followed by a precise formulation of the statistical problem, along with a complete set of mathematical tools (as needed in the rest of the book), and a summary of the generally accepted phenomenology of the subject. Part 2 deals with current issues in phenomenology, including the role of Galilean invariance, the physics of energy transfer, and the fundamental problems inherent in numerical simulation. Part 3 deals with renormalization methods, with an emphasis on the taxonomy of the subject, rather than on lengthy mathematical derivations. The book concludes with some discussion of current lines of research and is supplemented by three appendices containing detailed mathematical treatments of the effect of isotropy on correlations, the properties of Gaussian distributions, and the evaluation of coefficients in statistical theories.
At the end of reading this book I felt exuberant in several distinct ways: progress has been made, but there are still vast areas of turbulence that are hardly understood; there is beautiful mathematics underpinning the analyses in HIT in particular and turbulence in general; and one has a sense of optimism that theoretical progress is gaining momentum.
Table of Contents:
Part I: The fundamental problem, the basic statistical formulation, and the phenomenology of energy transfer
Overview of the statistical problem
Basic equations and definitions in x-space and k-space
Formulation of the statistical problem
Turbulence energy: its inertial transfer and dissipation
Part II: Phenomenology: some current research and unresolved issues
Galilean invariance (GI)
Kolmogorov's (1941) theory revisited
Turbulence dissipation and decay
Theoretical constraints on mode reduction and the turbulence response
Part III: Statistical theory and future directions
The Kraichnan-Wyld-Edwards (KWE) covariance equations
Two-point closures: some basic issues
Renormalization group (RG) applied to turbulence
Work in progress and future directions
Part IV: Appendices
Implications of isotropy and continuity for correlation tensors
Properties of Gaussian distributions
Evaluation of the L(k; j) coefficient
