Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures

Hardcover | March 27, 2014

byW. David McComb

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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 thefundamental 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 therest 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 withrenormalization 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 statisticaltheories.

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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 thefundamental aspects of the general problem. It ...

W. David McComb has had wide experience in both engineering and physics departments. After early career experience in research and development in the nuclear power industry, he returned to university to study theoretical physics. Following the completion of a PhD in turbulence theory, he took up the post of Senior Scientific Officer in...

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Format:HardcoverDimensions:480 pages, 9.69 × 6.73 × 0.01 inPublished:March 27, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199689385

ISBN - 13:9780199689385

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Table of Contents

Part I: The fundamental problem, the basic statistical formulation, and the phenomenology of energy transfer1. Overview of the statistical problem2. Basic equations and definitions in x-space and k-space3. Formulation of the statistical problem4. Turbulence energy: its inertial transfer and dissipationPart II: Phenomenology: some current research and unresolved issues5. Galilean invariance (GI)6. Kolmogorov's (1941) theory revisited7. Turbulence dissipation and decay8. Theoretical constraints on mode reduction and the turbulence responsePart III: Statistical theory and future directions9. The Kraichnan-Wyld-Edwards (KWE) covariance equations10. Two-point closures: some basic issues11. Renormalization group (RG) applied to turbulence12. Work in progress and future directionsPart IV: AppendicesA. Implications of isotropy and continuity for correlation tensorsB. Properties of Gaussian distributionsC. Evaluation of the L(k; j) coefficient

Editorial Reviews

"This book is a unique contribution to the field, providing the reader with a unified presentation of actual theories and recent results. It displays a smart and lucid presentation of controversies, shortcomings, and misleading conceptions. This book is a hugely important contribution to theliterature on turbulence, which will be highly valuable to all students, researchers, and engineers interested in turbulence." --Pierre Sagaut, Universite Pierre et Marie Curie-Paris 6