Homogeneous, Isotropic Turbulence

Phenomenology, Renormalization and Statistical Closures

W. David McComb

International Series of Monographs on Physics

Presents statistical theory (i.e. renormalization methods) in the language of fluid dynamics, rather than the arcane jargon of quantum field theory
Gives equal weight to phenomenology and renormalization theories, and discusses the relationships between the two approaches
Formulates the problem clearly and precisely, and provides a critical assessment of the ways in which theories can be tested
Gives a concise, clear, and comprehensive statement of the mathematical equations and formulae which make up the essential tools for fundamental research in turbulence
Treats both the real-space and wavenumber-space formulations, and encourages the reader to move fluently between them

Homogeneous, Isotropic Turbulence

Phenomenology, Renormalization and Statistical Closures

W. David McComb

International Series of Monographs on Physics

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.

Homogeneous, Isotropic Turbulence

Phenomenology, Renormalization and Statistical Closures

W. David McComb

International Series of Monographs on Physics

Part I: The fundamental problem, the basic statistical formulation, and the phenomenology of energy transfer
1. Overview of the statistical problem
2. Basic equations and definitions in x-space and k-space
3. Formulation of the statistical problem
4. Turbulence energy: its inertial transfer and dissipation
Part II: Phenomenology: some current research and unresolved issues
5. Galilean invariance (GI)
6. Kolmogorov's (1941) theory revisited
7. Turbulence dissipation and decay
8. Theoretical constraints on mode reduction and the turbulence response
Part III: Statistical theory and future directions
9. The Kraichnan-Wyld-Edwards (KWE) covariance equations
10. Two-point closures: some basic issues
11. Renormalization group (RG) applied to turbulence
12. Work in progress and future directions
Part IV: Appendices
A. Implications of isotropy and continuity for correlation tensors
B. Properties of Gaussian distributions
C. Evaluation of the L(k; j) coefficient

Homogeneous, Isotropic Turbulence

Phenomenology, Renormalization and Statistical Closures

W. David McComb

International Series of Monographs on Physics

Author Information

W. David McComb, Emeritus Professor of Physics, Edinburgh University

The author 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 the Theoretical Physics Division at AERE, Harwell. Thereafter he held successively lectureships in engineering science and physics, a readership in physics, and a personal chair in statistical physics at Edinburgh University. On his retirement in 2006, he was appointed Professor Emeritus, and now also holds a Senior Professorial Fellowship. He has been guest professor at the University of Delft, and visiting fellow at Wolfson College and the Isaac Newton Institute, Cambridge. During the period 2007-09 he held a Leverhulme Emeritus Fellowship.

Homogeneous, Isotropic Turbulence

Phenomenology, Renormalization and Statistical Closures

W. David McComb

International Series of Monographs on Physics

Reviews and Awards

"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." -- Thomas J. Bridges, Contemporary Physics

"Homogeneous, Isotropic Turbulence is the most comprehensive and authoritative book on the core fundamental problem of fluid turbulence - it is long overdue. It provides clear and detailed expositions of all the important aspects of this field including phenomenology, statistical closure theory, the renormalization group and subgrid modelling. It assesses and resolves longstanding misunderstandings and major controversies with rigor and flair. The notation is elegant and modern and it is set to become a classic reference and text for engineers, physicists, mathematicians and geophysical fluid dynamicists with interests in turbulence, as well as for advanced undergraduate and graduate students." --Jorgen Frederiksen, CSIRO Marine and Atmospheric Research

"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 the literature on turbulence, which will be highly valuable to all students, researchers, and engineers interested in turbulence." --Pierre Sagaut, Université Pierre et Marie Curie-Paris 6