IUTAM SYMPOSIUM ON GEOMETRY AND STATISTICS OF TURBULENCE

FLUID MECHANICS AND ITS APPLICATIONS

Volume 59

Series Editor: R. MOREAU MADYIAM Ecole Nationale Superieure d'Hydraulique de Grenoble Bolte Postale 95 38402 Saint Martin d'Heres Cedex, France

Aims and Scope of the Series

The purpose of this series is to focus on subjects in which fluid mechanics plays a funda­mental role.

As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multiphase fluids, super and hy­personic flows and numerical modelling techniques.

It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particulary open to cross fertilisation with other scien­ces and disciplines of engineering. The subject of fluid mechanics will be highly relevant in domains such as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains.

The median level of presentation is the first year graduate student. Some texts are mono­graphs defining the current state of a field; others are accessible to final year undergradu­ates; but essentially the emphasis is on readability and clarity.

For a list of related mechanics titles, see final pages.

IUTAM Symposium on

Geometry and Statistics of Turbulence

Proceedings of the IUTAM Symposium held at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan, November 1-5, 1999

Edited by

T. KAMBE

University of Tokyo, Japan

T. NAKANO

Chuo University, Japan

and

T. MIYAUCHI

Tokyo Institute of Technology, Japan

.... '' SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-5614-6 ISBN 978-94-015-9638-1 (eBook) DOI 10.1007/978-94-015-9638-1

Printed on acid-free paper

All Rights Reserved © 2001 Springer Science+ Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1st edition 2001

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

lUT

AM

Sym

posi

um

Hay

ama,

Kan

agaw

a, j

apan

Nov

embe

r 1

-5,

1999

Lis

t:

1. H

. K

. M

offa

tt

2. T

. T

atsu

mi

3. I

. Im

ai

4. R

. R

ubin

stei

n 5.

J.

Jim

enez

6.

K.R

. S

reen

ivas

an

7. T

. K

amb

e 8.

C.

Doe

ring

9.

U.

Fri

sch

10.

H.

Fri

sch

11.

K.K

. N

omur

a 12

. T

. M

atsu

mot

o 13

. S.

Kat

oh

14

. Y

. O

kada

15

. B

. S

hrai

man

16

. S.

Kid

a 17

. V

. Y

akho

t 18

. P

. C

onst

anti

n

19.

R.

Pas

man

ter

20.

T.

Miy

auch

i 21

. P

.-H

.Cha

vani

s 22

. J.

-P.

Lav

al

23.

K.

Ang

ele

24.

K.

Hor

iuti

25

. T

. It

ano

26

. K

. Y

oshi

da

27.

Y.

Tsu

ji

28.

P. O

rlan

di

29.

Y.

Miy

ake

30.

J. P

eink

e 31

. R

. P

iva

32.

J.C

. W

ells

33

. A

. N

oull

ez

34.

M.

San

o 35

. T

. N

akan

o 36

. Y

. K

aned

a

37.

N.

To

ku

gaw

a 38

. G

. K

awah

ara

39.

Y.

Kit

ano

40.

S. T

suji

mu

ra

41.

R.

Ant

onia

42

. T

. G

otc

h

43.

H.

Han

azak

i 44

. T

. M

iyaz

aki

45.

0.

San

o 46

. S.

To

h

47.

K.

Yam

amot

o 48

. M

. T

akao

ka

49.

N.

Tak

ahas

hi

50.

Y.

Fuk

unis

hi

51.

K.

Suz

uki

52.

Y.

Hat

tori

53

. D

. F

ukay

ama

54.

Y.

Fuk

umot

o

55.

M.

Hin

o 56

. S.

Got

o 57

. N

. H

atak

eyam

a 58

. M

. U

mek

i 59

. A

. Is

hiza

wa

60.

T.

Ishi

hara

61

. K

. O

hk

itan

i 62

. F

. H

amba

63

. T

. H

aseg

awa

64.

Y.

Suz

uki

Scientific Committee

T. Kambe (Chairman) V.I. Arnold, Russia R. Benzi, Italy P. Constantin, USA U. Frisch, Prance J. Jimenez, Spain H.K. Moffatt, UK T. Tatsumi, Japan

Advisory (Local) Committee

I. Imai, Tokyo H. Ohashi, Tokyo T. Tatsumi, Kyo to

Local Organizing Committee

T. Kambe, Tokyo (Chairman) Y. Fukumoto, Fukuoka F. Hamba, Tokyo Y. Kaneda, Nagoya T. Kawamura, Tokyo T. Miyauchi, Tokyo T. Nakano, Tokyo M. Umeki, Tokyo K. Yamamoto, Tokyo

T. Gotoh, Nagoya K. Ishii, Nagoya N. Kasasgi, Tokyo S. Kida, Toki T. Miyazaki, Tokyo K. Ohkitani, Kyoto M. Yamada, Tokyo A. Yoshizawa Tokyo

Sponsors of Symposium

This Symposium was held under the sponsorship of

International Union of Theoretical and Applied Mechanics (IUTAM)

and the support of

Science Council of Japan.

The financial support has been made from the following foundations and corporations:

Inoue Foundation for Science The K ajima Foundation Hewlett-Packard Japan, Ltd. NEG Corporation

Special registration:

Zexel Corporation YKK Corporation Fuji Research Institute Corporation Sanyo Electric Co., Ltd. Daikin Industries, Ltd. Seika Corporation

Contents

Preface

A. General and Mathematical

Mathematical Physics of Thrbulence T. Tatsumi .......... .

The Topology of Scalar Fields in 2D and 3D Thrbulence H.K. Moffatt . . . . . . . . . . . . . . . . . . . . .

Bounds for Thrbulent Transport P. Constantin . . . . . . . .

Bulk Dissipation in Shear Layers with Suction C.R. Doering, R. A. Worthing and E. A. Spiegel

Trying a Metric on Atmospheric Flows R.A. Pasmanter and X.-L. Wang . . . . . . . . .

On the Analogy between 2D Vortices and Stellar Systems P. H. Chavanis . . . . . . . . . . . . . . . . . . . . .

B. Coherent Structures, Intermittency, and Cascade

Self-Similarity and Coherence in the Thrbulent Cascade J. Jimenez ..................... .

Coherent Fine Scale Structure in Thrbulence T. Miyauchi and M. Tanahashi .....

Coherent Fine Scale Eddies in Thrbulent Shear Flows and it's Relation to Anisotropy

M. Tanahashi and T. Miyauchi ........... .

Shear Stress and Dissipation Intermittency in High-Reynolds-Number Thrbulence

XV

1

3

13

23

33

39

47

55

57

67

77

Y. Tsuji. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Characteristic Time Scales and Energy Transfer in MHD Thrbulence Y. Hattori and A. Ishizawa . . . . . . . . . . . . . . . . . . . . 89

C. Probability Density Functions and Structure Functions 95

Statistics of Transverse Velocity Differences in Thrbulence V. Yakhot ...................... . 97

xii

On a Complete Statistical Characterization of Thrbulence R. Friedrich, St. Lueck, J. Peinke and Ch. Renner . . . . . . . . 107

Statistical Laws Governed by Vortex Structures in Fully Developed Thrbulence

T. Kambe .................. . . ... 117

Probability Density Function of Longitudinal Velocity Increment T. Nakano, D. Fukayama, T. Gotoh and K. Yamamoto 127

Statistics of Small-Scale Structure of Homogeneous Isotropic Thrbulence T. Ishihara, Y. Yamazaki andY. Kaneda . . . . . . . . . . . . . . 133

On Universality of Statistics of Pressure Field in Homogeneous Thrbulence

T. Gotoh and K. N agaya . . . . . . . . . . . . . . . . . . 139

A Statistical Law of Velocity Circulations in Fully Developed Thrbulence K. Yoshida and N. Hatakeyama . . . . . . . . . . . . . . . . . . . 145

D. Passive Scalar Advections 151

Lagrangian Method for Multiple Correlations in Passive Scalar Advection U. Frisch, A. Mazzino, A Noullez and M. Vergassola . . . . . . . . 153

Anomalous Scaling in Passive Scalar Advection and Lagrangian Shape Dynamics

I. Arad and I. Procaccia . . . . . . . . . . . . .

Correlation between Energy and Temperature Dissipation Rates in Thrbulent Flows

. ... 175

R.A. Antonia, T. Zhou and G. Xu . . . . . . . . . . . . . . . . 185

Simulation of Scalar Fluctuation Field by a Non-Buoyant Plume in Grid-Generated Thrbulence by Random Fourier Modes Method

Y. Sakai, T. Suzuki and I. Nakamura . . . . . . . . . . . . . . . . 191

E. Vortices, Vorticity, and Strain Dynamics 197

Spatiotemporal Structure of Thbular Vortices in Thrbulence S. Kida, H. Miura and T. Adachi . . . . . . . . . . . . . . . . . . 199

Geometric Aspects of the Interaction of Vorticity and Strain in Homogeneous Sheared Thrbulence

K. K. Nomura . . . . . . . . . . . . . . . . . . . . . . . . ... 205

Motion of a Curved Vortex Filament: Higher-Order Asymptotics Y. Fukumoto .............................. 211

Statistics of Thrbulence around a Columnar Vortex T. Miyazaki, H. Ishii and J.C.R. Hunt . . . . . . . . . . . 217

xiii

Study of the Geometry fo Flow Patterns in a Compressible Wake H. Maekawa. . . . . . . . . . . . . . . . . . . . . . . . . ... 223

Interaction of a Vortex Ring Linked with a Vortex Filament K. Suzuki, M. Abe, M. Hirano and 0. Sana . . . . . . . . . . . 229

Mechanism of Flame Propagation along a Vortex Tube T. Hasegawa, S. Nishiki and S. Michikami . . . . . . . . . 235

F. Large Scale Motions, LES, and Closure 241

Mapping Closure for Non-Gaussian Velocity Fields M. Takaoka .................. . . 243

Coherent Structure and Subgrid-Scale Energy Transfer in Turbulence K. Horiuti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

A Dynamical Model for Turbulence J-P. Laval, B. Dubrulle and S. Nazarenko . . ..... 255

Two- and Three-dimensional Behavior of the Large Scales in Rotating Turbulence

R. Rubinstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

G. Thermal Turbulence, Stratified and Rotating Turbulence 267

Comments on High Rayleigh Number Convection J.J. Niemela, L. Skrbek, K.R. Sreenivasan and R.J. Donnelly . . . 269

The Dynamics of Structures ofT-Vorticity in 2d Free Convection Turbulence

S. Toh and T. Matsumoto ................... .

Structure of Homogeneous Rotating Turbulence under Stable Density Stratification

S. Tsujimura, 0. !ida andY. Nagano

Linear Processes in Unsteady Stratified Sheared Turbulence

. 279

. 285

H. Hanazaki and J.C.R. Hunt . . . . . . . . . . . . . . . . . . . . . 291

H. Transition Mechanisms 297

Direct Numerical Simulation of Transition in Plane Poiseuille Flow K. Yamamoto, N. Takahashi and T. Kambe . . . . . . . . . . . 299

On the Regeneration Mechanism of Turbulence in the Channel Flow S. Toh and T. Itano .......................... 305

xiv

I. Modulation of Turbulence 311

Turbulence in Polymer Solutions M. Chertkov . . . . . . . . . . ......... 313

Turbulence Modulation due to Solid Particles Moving with Vortex Shedding

T. Kajishima, S. Takiguchi andY. Miyake 319

Spectral Features of Axial Velocity and Concentration in a High Schmidt Number Turbulent Jet

Y. Sakai, Y. Okada, I. Nakamura and N. Kobayashi . . . . . . . . 325

J. Pipe-Flow and Channel-Flow Turbulence

Structures and Intermittency in Rotating Pipes P. Orlandi, R.A. Antonia and Q. Zhao . . .

Statistics of Open-Channel Turbulence by Using Simultaneous Measurements of All Three Components of Turbulent Fluctuations with Two-Sets LDAs

I. Nezu and K. Onitsuka

Generation Mechanism of Turbulence-Driven Secondary Currents in Open-Channel Flows

K. Onitsuka and I. Nezu ................... .

Turbulence Measurements and Conditional Sampling Analysis on Coherent Vortices in Unsteady Open-Channel Flows over Dune Bed

331

. 333

. 339

. 345

A. Kadota, I. Nezu and K. Suzuki . . . . . . . . . . . . . . . . . . . 351

Dye Visualization and P.I.V. in the Cross-Stream Plane of a Turbulent Channel Flow

J.C. Wells, Y. Yamamoto, Y. Yamane, S. Egashira and H. Nakagawa 357

K. Boundary Layers and Near-Wall Turbulence 365

Vorticity Structures and Intermittency in Near Wall Turbulence R. Piva, C.M. Casciola, G. Amati and P. Gualtieri . . . . . 367

The Use of PIV in Turbulent Boundary Layer Flows K. Angele and B. Muhammad-Klingmann

Boundary Layer Intermittency Model P. Gualtieri and G. Pulci Doria

Universal Property of Autonomous Layer in Near-Wall Turbulence

373

379

K. Tsujimoto and Y. Miyake . . . . . . . . . . . . . . . . . . 385

List of Participants 391

PREFACE

This volume contains the papers presented at the IUTAM Symposium on Geometry and Statistics of Turbulence, held in November 1999, at the Shonan International Village Center, Hayama (Kanagawa-ken), Japan.

The Symposium was proposed in 1996, aiming at organizing concen­trated discussions on current understanding of fluid turbulence with empha­sis on the statistics and the underlying geometric structures. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUTAM) to accept the proposal was greeted with enthusiasm. Turbulence is often characterized as having the properties of mixing, inter­mittency, non-Gaussian statistics, and so on. Interest is growing recently in how these properties are related to formation and evolution of struc­tures. Note that the intermittency is meant for passive scalars as well as for turbulence velocity or rate of dissipation.

There were eighty-eight participants in the Symposium. They came from thirteen countries, and fifty-seven papers were presented. The presenta­tions comprised a wide variety of fundamental subjects of mathematics, statistical analyses, physical models as well as engineering applications. Among the subjects discussed are (a) Degree of self-similarity in cascade, (b) Fine-scale structures and degree of Markovian property in turbulence, (c) Dynamics of vorticity and rates of strain, (d) Statistics associated with vortex structures, (e) Topology, structures and statistics of passive scalar advection, (f) Partial differential equations governing PDFs of velocity in­crements, (g) Thermal turbulences, (h) Channel and pipe flow turbulences, and others.

We would like to thank all the contributors for making this Proceedings a landmark of turbulence research open to the coming next century. The papers collected in this volume were reviewed by all members of the Local Organizing Committee.

The assistance by the members of the Scientific committee is gratefully acknowledged. Sincere thanks are also extended to the Advisory committee and also to all the members of Local organizing committee for their efforts making the Symposium very successful. We are particularly grateful to Prof. F. Hamba as a Treasurer for this Symposium.

XV

xvi

Financial support to the Symposium was provided by the IUTAM. In addition, generous supports are gratefully acknowledged for the two founda­tions: Inoue Foundation for Science and The Kajima Foundation and for the eight corporations: Hewlett-Packard Japan, NEG Corporation, Zexel Corporation, YKK Corporation, Fuji Research Institute Corporation, Sanyo Electric Corporation, Daikin Industries, and Seika Corporation.

Finally the cooperation of the Kluwer academic publishers for publi­cation of the present Proceedings is very much appreciated as well as the financial assistance.

July 2000 Editors Tsutomu Kambe

Tohru Nakano Toshio Miyauchi