Table Of Content

Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be sent to the Mathematics Editor at either Birkhauser Verlag P.O. Box 133 CH-4010 Basel Switzerland or Birkhauser Boston Inc. 675 Massachusetts Avenue Cambridge, MA 02139 USA Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhauser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the con ference. The total number of pages should not exceed 350. The first-mentioned author of each article will receive 25 free offprints. To the participants of the congress the book will be offered at a special rate. Fundamental Problematic Issues in Turbulence Albert Gyr Wolfgang Kinzelbach Arkady Tsinober Editors Springer Basel AG Editors' addresses: Albert Gyr and Wolfgang Kinzelbach Arkady Tsinober Institute of Hydromechanics Faculty of Engineering and Water Resources Management Tel Aviv University ETH Honggerberg Tel Aviv 69978 8093 ZOrich Israel Switzerland 1991 Mathematical Subject Classification 76Fxx; 76005; 35Q30 A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Fundamentel problematic issues in turbulence / Albert Gyr ... eds. -Basel ; Boston; Berlin: Birkhăuser, 1999 (Trends in mathematics) ISBN 978-3-0348-9730-3 ISBN 978-3-0348-8689-5 (eBook) DOI 10.1007/978-3-0348-8689-5 Cover iIIustration taken from the article by Metais and Urbin in this volume. This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is con cerned, specifically the rights of translation, reprinting, re-use of iIIustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 1999 Springer Basel AG Originally published by Birkhăuser Verlag in 1999 Softcover reprint of the hardcover 1s t edition 1999 Printed on acid-free paper produced from chlorine-free pulp. TCF ~ ISBN 978-3-0348-9730-3 987654321 Contents Preface.................................................................. ix 1 Mathematical issues C. R. Doering Does turbulence saturate global transport estimates? 3 A. V. Fursikov The closure problem for Friedman-Keller infinite chain of moment equations, corresponding to the Navier-Stokes system ................ 17 J. D. Gibbon Vorticity alignment results for the 3D Euler and Navier-Stokes equations ............................................. 25 R. B. Pelz, Y. Gulak, J. M. Greene, O. N. Boratav On the finite-time singularity problem in hydrodynamics 33 R. M. Kerr The outer regions in singular Euler 41 2 Control and related A. V. Fursikov On controllability of the N avier-Stokes equations 51 J. L. Lumley, P. N. Blossey, B. Podvin-Delarue Low dimensional models, the minimal flow unit and control 57 P. J. Ioannou, B. F. Farrell Active control of turbulence in boundary layer flows 67 B. F. Farrell, P. J. Ioannou Origin and growth of structures in boundary layer flows 75 O. Metais, G. Urbin Vortex control in a spatially growing round jet 83 vi Contents 3 Observational aspects J. G. Brasseur The lack of a simple paradigm in fully developed turbulence: characteristics of local concentrations of vorticity and Reynolds stress in turbulent shear flows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 J. C. Vassilicos Near-singular flow structure in small-scale turbulence 107 W. K. George Some thoughts on similarity, the POD, and finite boundaries. . . . . . . .. 117 F. Belin, F. Moisy, P. Tabeling, H. Willaime Worms in a turbulence experiment, from hot wire time series 129 J.-F. Pinton, F. Chilla, S. Fauve, R. Labbe Intermittency in the closed flow between coaxial disks. . . . . . . . . . . . . . .. 141 4 Two- and quasi-two-dimensional flows H. Arej, P. L. Boyland, M. A. Stremler, D. L. Vainchtein Turbulent statistical dynamics of a system of point vortices 151 M. Farge, N. Kevlahan, C. Bardos, K. Schneider Combining deterministic and statistical approaches to compute two-dimensional turbulent flows with walls .......................... , 163 J. R. Herring, Y. Kimura, J. Chasnov Evolution of decaying two-dimensional turbulence and self-similarity ........................................................ 175 C. Cambon Linear and nonlinear models for turbulence in the presence of waves 185 P. Caillol, V. Zeitlin On the stationary energy spectra of the stratified fluid in a weak turbulence regime.............................................. 195 F. Dupont, R. I. McLachlan, V. Zeitlin On a possible mechanism of anomalous diffusion in geophysical turbulence ............................................... 203 Contents vii 5 Basic aspects of turbulence modelling M. Germano Basic issues of turbulence modeling 213 C. Meneveau, J. O'Neil, F. Porte-Agel, S. Cerutti, M. B. Parlange Physics and modeling of small scale turbulence for large eddy simulation ................................" ... . ... . .. . ..... 221 D. Rempfer On dynamical systems obtained via Galerkin projections onto low-dimensional bases of eigenfunctions .............................. 233 M. Oberlack Symmetries of the Navier-Stokes equations and their implications for subgrid-models in large-eddy simulation of turbulence............ 247 A. Leonard Subgrid modeling for the filtered scalar transport equation.. ... . ..... 257 6 Statistical aspects G. L. Eyink Thrbulent fluctuations, predictability, and action principles 267 V. Lebedev Instantons in the theory of turbulence ............................... 277 E. A. Novikov, D. G. Dommermuth A variational approach to turbulent boundary layers ................. 303 S. Ciliberto, E. Leveque, C. Baudet, G. Ruiz-Chavarria Scaling laws of a passive scalar energy flux in fully developed turbulence ........................................................... 307 F. Toschi, G. Amati, R. Piva, S. Succi, R. Benzi Intermittency in channel-flow turbulence.. . . . .. . . .. ... . . .. . ... . .. . ... 313 P. Orlandi, R. A. Antonia, P. G. Esposito Structure functions in homogeneous and non-homogeneous turbulent flows ...................................................... 319 O. Metais, E. Lamballais, M. Lesieur Pressure fluctuations in a turbulent channel .......................... 329 W. van de Water Statistics of longitudinal and transverse velocity increments .......... 337 A. Pumir, L. Blumenfeld Thrbulent transport in a liquid layer ,heated on its free surface ....... 347 viii Contents Ch. Renner, B. Reisner, St. Luck, J. Peinke, R. Friedrich On the statistics of small-scale turbulence and its universality 353 B. Reisner, Ch. Renner, St. Luck, J. Peinke, F. Chilla, R. Friedrich A new method to characterize inhomogeneous turbulence............ 361 M. J. Huang Multiscale similarity of isotropic homogeneous turbulence 365 7 Passive objects E. Ott The role of Lagrangian chaos in the creation of multifractal measures ................................................ 381 P. E. Dimotakis, H. J. Catrakis, A. W. Cook, J. M. Patton On the geometry of two-dimensional slices of irregular level sets in turbulent flows .................................................... 405 G. Falkovich Universal and nonuniversal properties of the passive scalar statistics ...................................................... 419 P. K. Yeung Multi-scalar mixing and Lagrangian approaches...................... 427 N. Kleeorin, I. Rogachevskii Turbulent transport of vector (magnetic) field: intermittency and anomalous scalings .................................................. 435 T. Elperin, N. Kleeorin, I. Rogachevskii Intermittency and anomalous scalings of inertial particles distribution in turbulent flow ........................................ 445 E. Villermaux, C. Innocenti, J. Duplat Scalar fluctuation PDF's and kinetics of turbulent mixing. . . . . . . . . . .. 457 J.-F. Pinton, P. Odier, S. Fauve Magnetohydrodynamics in turbulent swirling flow.................... 467 List of participants and authors ...................................... 471 Preface The Second Monte Verita Colloquium Fundamental Problematic Issues in Turbu lence was held in Monte Verita, Switzerland, on March 23-27, 1998. The main goal of the Colloquium was to bring together in the relaxed atmo sphere of Monte Verita a group of leading scientists (consisting of representatives of different generations) and to discuss informally and free of the influence of funding agencies and/or other "politics" of nonscientific nature the basic issues of turbulence. The intention was to put major emphasis on the exposition of the problematic aspects and discussion(s) - not mere reporting of results, i.e. not hav ing just one more meeting. For this purpose it was originally thought to leave all the afternoons free of formal presentations at all. However, this intention became unrealistic due to a number of reasons, and, in the first place, due to strong pres sure from various parts of the scientific community and non-scientific constraints to broaden the scope and to increase the number of participants as compared to the First Colloquium held in 1991. This resulted in a considerable reduction of time for discussions. Nevertheless, the remaining time for discussions was much larger than usually allocated at scientific conferences. On the scientific side the main idea was to bring together scientists work ing in turbulence from different fields, such as mathematics, physics, engineering and others. In this respect the Colloquium was definitely very successful and re sulted in a number of interesting interactions and contacts. Clearly everybody was interested in all aspects of the problem which consisted of mathematical is sues (morning session, March 23, 1998), control and related (afternoon session, March 23, 1998), observational aspects (morning session, March 24, 1998), two and quas{-two-dimensional flows (afternoon session, March 24, 1998), basic as pects of turbulence modelling (morning session, March 25, 1998), statistical issues (morning and afternoon sessions, March 26, 1998) and passive scalars (morning session, March 27, 1998). A special and the last session of the Colloquium was devoted to the final discussion with the emphasis on the physics of scaling in turbulence and related issues. Among the main questions addressed in the discussions were those related to the controllability of turbulent flows, possible qualitative difference between pure two-dimensional and real quasi-two-dimensional turbulent flows, common features of two-dimensional and three-dimensional turbulence, universality (or not ) of small scale turbulence and their relation with the large scales, on how realistic are the prospects of reduced description of turbulent flows, necessity of dealing more with the physics of turbulence, in general, and in turbulence modelling and (beyond) scaling properties, in particular. It seems that the last issue, i.e the physics of turbulence, is the key one for the progress in any aspect of the problem. This issue deserves a special topical meeting in the nearest future. Zurich, October 1998 A. Cyr, W. Kinzelbach, A. Tsinober 1 Mathematical issues