New Perspectives in Thrbulence

Lawrence Sirovich Editor

New Perspectives in Turbulence

With 131 illustrations

Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona

Lawrence Sirovich Center for Fluid Mechanics, Division of Applied Mathematics, Brown University, Providence, RI 02912

Mathematics Subject Classification Codes: 76Fxx, 76D05, 76E25, 60Gxx, 82A50

Library of Congress Cataloging-in-Publication Data

New perspectives in turbulence / Lawrence Sirovich, editor. p. cm.

Based on papers from a meeting held at Salve Regina College, Newport, R.I., June 12-15, 1989.

Includes bibliographical references.

1. Thrbulence-Congresses. I. Sirovich. L. 1933-QA913.N49 1991 532'.0527-dc20 91-2648

©1991 Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1991 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is for­bidden. The use of general descriptive names, trade names, trademarks, etc., in this pub­lication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Permission to photocopy for internal or personal use, or the internal or personal use of specific clients, is granted by Springer-Verlag New York, Inc. for libraries registered with the Copyright Clearence Center (CCC), provided that the base fee of $0.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress St., Salem, MA 01970, USA. Special requests should be addressed directly to Springer-Verlag New York, 175 Fifth Avenue, New York, NY 10010, USA.

Photocomposed copy prepared from author files using 'lEX, U-TEX, and Aw'lEX·

98765432 1 Printed on acid-free paper.

ISBN-13: 978-1-4612-7817-7 e-ISBN-13: 978-1-4612-3156-1

DOl: 10.1007/978-1-4612-3156-1

Preface

This collection of articles has its origin in a meeting which took place June 12-15, 1989, on the grounds of Salve Regina College in Newport, Rhode Island. The meeting was blessed by beautiful, balmy weather and an idyllic setting. The sessions themselves took place in Ochre Court, one of the elegant and stately old summer cottages for which Newport is acclaimed. Lectures were presented in the grand ballroom overlooking the famous Cliff Walk and Block Island Sound.

Counter to general belief, the pleasant surroundings did not appear to encourage truancy or in any other way diminish the quality of the meeting. On the contrary, for the four days of the meeting there was a high level of excitement and optimism about the new perspectives in turbulence, a tone that carried over to lively dinner and evening discussions. The participants represented a broad range of backgrounds, extending from pure mathemat­ics to experimental engineering. A dialogue began with the first speakers which cut across the boundaries and gave to the meeting a mood of unity which persisted.

Alas, the written word cannot bring to life the real time quality of the meeting. Nevertheless, the reader of this book will learn that the arti­cles that follow are all of a high caliber. (It should be mentioned that George Zaslovsky, who was unable to attend the meeting, also contributed a manuscript.) Articles were interchanged among the authors and an effort made to have the articles reflect some of the interaction that took place.

A strenuous attempt was made to get manuscripts from all the speakers. However, as comparison with the speaker list shows some contributions are missing. Rather than delay the appearance of this volume any longer, it was decided to bring closure to the project at this point.

Thanks are due to D.Y. Hsieh, for not only serving as Organizing Chair­man, but also for his splendid and insightful report on the tragic events which had taken place in China only days before the meeting, and from which he had just returned. Very special thanks are also due to Julia Nes­bitt, who was greatly responsible for having made this a very special meet­ing, and to Madeline Brewster, who made the preparation of this book possible.

L.S., Saltaire, May 1990

Contents

Preface v Contributors ix Presentations Xl

Participants xv

Chapter 1 Stochastic Modeling of Isotropic Thrbulence 1 Robert H. K raichnan

Chapter 2 Rapid Distortion Theory as a Means of Exploring the Structure of Thrbulence 55 Julian C.R. Hunt, D.J. Carruthers and J.C.H. Fung

Chapter 3 Order and Disorder in Thrbulent Flows 105 John L. Lumley

Chapter 4 The Thrbulent Fluid as a Dynamical System 123 David Ruelle

Chapter 5 Empirical Eigenfunctions and Low Dimensional Systems 139 Lawrence Sirovich

Chapter 6 Spatiotemporal Chaos in Interfacial Waves 165 Jerry P. Gollub and R. Ramshankar

Chapter 7 The Complementary Roles of Experiments and Simulation in Coherent Structure Studies 195 Mogens V. Melander, Hyder S. Husain and Fazle Hussain

viii Contents

Chapter 8 Remarks on the Navier-Stokes Equations 229 Peter Constantin

Chapter 9 Scaling and Structures in the Hard Thrbulence Region of Rayleigh-Benard Convection 263 Leo P. Kadanoff

Chapter 10 Probabilistic Multifractals and Negative Dimensions 271 Ashvin B. Chhabm and K.R. Sreenivasan

Chapter 11 On Thrbulence in Compressible Fluids 289 M. Y. Hussaini, G. Erlebacher, and S. Sarkar

Chapter 12 Statistical Aspects of Vortex Dynamics in Thrbulence 315 Zhen-Su She, Eric Jackson and Steven A. Orszag

Chapter 13 The Lagrangian Picture of Fluid Motion and its Implication for Flow Structures 329 J.T. Stuart

Chapter 14 Dynamical Chaos: Problems in Thrbulence 349 R.Z. Sagdeev and G.M. Zaslavsky

Contributors

D.J. Carruthers Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom

Ashvin B. Chabra Mason Laboratory, Box 2159, Yale University, New Haven, Connecticut 06520·

Peter Constantin Department of Mathematics, University of Chicago, Chicago, Illinois 60637

G. Erlebacher Institute for Computer Applications in Science and Engi­neering, NASA Langley Research Center, Hampton, Virginia 23665

J .C.H. Fung Department of Applied Mathematics and Theoretical Phys­ics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom

J.P. Gollub Physics Department, Haverford College, Haverford, Pennsyl­vania 19041 and Physics Department, The University of Pennsylva­nia, Philadelphia, Pennsylvania 19104

Hyder S. Husain Department of Mechanical Engineering, University of Houston, Houston, Texas 77204-4792

Fazle Hussain Department of Mechanical Engineering, University of Hous­ton, Houston, Texas 77204-4792

M.Y. Hussaini Institute for Computer Applications in Science and En­gineering, NASA Langley Research Center, Hampton, Virginia 23665

J.C.R. Hunt Department of Applied Mathematics and Theoretical Phys­ics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom

Eric Jackson Applied & Computational Mathematics, Princeton Univer­sity, Princeton, New Jersey 08554

Leo P. Kadanoff The Research Institutes, University of Chicago, Chicago, Illinois 60637

x Contributors

Robert H. Kraichnan 303 Portillo Drive, Los Alamos, New Mexico 87544

John L. Lumley Sibley School of Mechanical and Aerospace Engineer­ing, Cornell University, Ithaca, New York 14853

Mogens V. Melander Department of Mathematics, Southern Methodist University, Dallas, Texas

Steven A. Orszag Applied & Computational Mathematics, Princeton Uni­versity, Princeton, New Jersey 08554

R. Ramshankar Carrier Corporation

R.Z. Sagdeev Space Research Institute, Profsoyuznaya 84/32, Moscow 117810, USSR

S. Sarkar Institute for Computer Applications in Science and Engineer­ing, NASA Langley Research Center, Hampton, Virginia 23665

Zhen-Su She Applied & Computational Mathematics, Princeton Univer­sity, Princeton, New Jersey 08554

Lawrence Sirovich Center for Fluid Mechanics, Division of Applied Math­ematics, Brown University, Providence, Rhode Island 02912

J.T. Stuart Division of Applied Mathematics, Brown University, Provi­dence, Rhode Island 02912 and Mathematics Department, Imperial College, London SW7 2BZ, United Kingdom

G.M. Zaslavsky Space Research Institute, Profsoyuznaya 84/32, Moscow 117810, USSR

Presentations

Stochastic Modeling of Isotropic Turbulence Robert H. Kraichnan Kraichnan Associates

Rapid Distortion Theory as a Means of Exploring the Structure of Turbulence Julian C.R. Hunt, D.J. Carruthers and J.C.H. Fung University of Cambridge

Order and Disorder in Turbulent Flows John L. Lumley Cornell University

The Turbulent Fluid as a Dynamical System David Ruelle Institut des Hautes Etudes Scientifiques

Empirical Eigenfunctions and Low Dimensional Systems Lawrence Sirovich Brown University

Stochastic Structures in Turbulence Ronald J. Adrian University of Illinois

Spatiotemporal Chaos in Interfacial Waves Jerry P. Gollub and R. Ramshankar Haverford College

The Complementary Roles of Experiments and Simulation in Coherent Structure Studies Mogens V. Melander, Hyder S. Husain and Fazle Hussain University of Houston

xii Presentations

Renormalization Group and Probability Distributions in Turbulence Victor Yakhot Princeton University

Remarks on the Navier-Stokes Equations Peter Constantin University of Chicago

Novel Experiments Aimed at Controlling Turbulent Shear Flow 1. Wygnanski University of Arizona

Scaling and Structures in the Hard Turbulence Region of Rayleigh­Benard Convection Leo P. Kadanoff University of Chicago

Probabilistic Multifractals and Negative Dimensions Ashvin B. Chhabra and K.R. Sreenivasan Yale University

Simulation of 'Iransition to Turbulence Leonhard Kleiser Institute for Theoretical Fluid Mechanics

Simulation of 'Iransition to Turbulence M. Yousuff Hussaini NASA Langley Research Center

Statistical Aspects of Vortex Dynamics in Turbulence Zhen-Su She, Eric Jackson and Steven A. Orszag Princeton University

The Lagrangian Picture of Fluid Motion and its Implication for Flow Structures J.T. Stuart Imperial College

Appearance of 'Iransition ,in Boundary Layers Thorwald Herbert Ohio State University

Presentations xiii

Broadband Instabilities in Bounded Elliptical Vortex Flow: Early Theories and Experiments Willem V.R. Malkus Massachusetts Institute of Technology

Participants

Abernathy, Frederich Adams, Eric Adrian, Ronald Alving, Amy Aubry, Nadine Balachandar, S. Ball, Kenneth Bisshopp, Fred Brasseur, James Castaing, Bernard Chasnov, Jeffrey Chauve, M.P. Chen, Haibo Chen, Hudong Chen, Shiyi Childress, Stephen Cimbala, John Cole, Julian Constantin, Peter Cross, Michael Deane, Anil Everson, Richard Fernholz, H.H. Fineberg, Jay Fong, Jefferson Gollub, Jerry Handler, Robert Hartke, Greg Herbert, Thorwald Hermanson, James Hohenberg, Pierre Holt, Steve

Hsieh, Din-Yu Hsu, Guan-Shong Hunt, Julian Hussain, Fazle Hussaini, Yousuff Jackson, Eric Kadanoff, Leo Karlsson, Sture Kiad, Shigeo Kirby, Michael Kleiser, Leonhard Knight, Bruce Kollmann, Wolfgang Korman, Murray Kraichnan, Robert Kumar, Ajay Lasheras, Juan Lin, C.C. Liu, Joseph Lumley, John Malkus, Willem Maxey, Martin Mayer-Kress, G. McMichael, James Meiburg, Eckart Meng, James Mohring, Willi Morkovin, Mark Nachman, Arje N adolink, Richard Nelkin, Mark Newton, Paul

Ng, Bart Nikjooy, Mohammad Orszag, Steve Panchapakesan, N.R. Park, Hung Mok Platt, Nathan Polifke, Wolfgang Raghn, Surya Reisenthel, Patrick Ruelle, David Sanghi, Sanjeev She, Zheu-Su Shi, Xungang Sirovich, Lawrence Sreenivasan, Katepalli Stuart, J. Trevor Su, Chau-Hsing Tangborn, Andrew Tarman, Hakan Titi, Edriss Veerman, Peter Voth, Eric Waleffe, Fabian Warhaft, Zellman Wark, Candace Woodruff, Steve Wygnanski, I. Wyngaard, John Yakhot, Victor Yang, Zhongmin Yoon, Kyung Hwan Zhou, Heng