Renormalization Methods Applied to Turbulence Theory
In these notes the turbulence problem is interpreted as one in many-body physics. We consider the many-body problem, along with the concept of renormalization, and show how the methods of renormalized perturbation theory have been applied to turbulence. T
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Series Editors: The Rectors Manuel Garcia Velarde - Madrid Mahir Sayir - Zurich Wilhelm Schneider - Wien
The Secretary General Bernhard Schrefler - Padua
Former Secretary General Giovanni Bianchi - Milan
Executive Editor Carlo Tasso- Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 442
THEORIES OF TURBULENCE
EDITED BY MARTIN OBERLACK DARMSTAT UNIVERSITY OF TECHOLOGY FRIEDRICH H. BUSSE UNIVERSITY OF BAYREUTH
Springer-Verlag Wien GmbH
This volume contains 147 illustrations
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2002 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 2002
SPIN 10890855
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographicallimitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-83694-1 DOI 10.1007/978-3-7091-2564-9
ISBN 978-3-7091-2564-9 (eBook)
Preface The present book evolved from the summer course on Theories of Turbulence held at the International Centre For Mechanical Sciences (CISM) in Udine/Italy from 17.-21. September 2001. The original idea for the course was born in 1997 during a discussion with Prof. Dr. P. D. Panagiotopolous, a former member of the scientific council of CISM. Sadly, Prof. Panagiotopolous passed away in 1998 at the early age of 48. In recognition of his deep contributions to the mechanical sciences and as a mark of our gratitude to him for the inspiration of this course we dedicate the present book to him. It addresses a variety of analytical and numerical approaches to problems of turbulent fluid flow with the main goal of providing insights into the nature of turbulence. The topics of the six chapters range from higher bifurcations and coherent structures through symmetry principles and renormalization theories to one- and two-point models and sub-grid scale modelling for large eddy simulations. Mathematical tools such as group theory and statistics are presented as needed for the theoretical developments. Applications to examples of turbulent flows range from isotropic turbulence and homogeneous turbulence with a constant mean velocity gradient to "semi-complex" flows with one or two homogeneous directions such as turbulent pipe, channel and alike flows. The six chapters in this book are organized as follows: In the first chapt
