IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas

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IUTAM BOOKSERIES Volume 6

Aims and Scope of the Series The IUTAM Bookseries publishes the proceedings of IUTAM symposia under the auspices of the IUTAM Board.

Series Editors: G.M.L. Gladwell, University of Waterloo, Waterloo, Ontario, Canada R. Moreau, INPG, Grenoble, France

Editorial Board: D. van Campen, Eindhoven University of Technology, Eindhoven, The Netherlands L.B. Freund, Brown University, Providence, USA H.K. Moffatt, University of Cambridge, Cambridge, UK J. Engelbrecht, Institute of Cybernetics, Tallinn, Estonia T. Kambe, IIDS, Tokyo, Japan A. Kluwick, Technische Universit¨at, Vienna, Austria N. Olhoff, Aalborg University, Aalborg, Denmark Z. Zheng, Chinese Academy of Sciences, Beijing, China

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

IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence Proceedings of the IUTAM Symposium held in Moscow, 25_30 August, 2006

Edited by

ALEXEY V. BORISOV Institute of Computer Science, UdSU, Izhevsk, Russia

VALERY V. KOZLOV V. A. Steklov Mathematical Institute, RAS, Moscow, Russia

IVAN S. MAMAEV Institute of Computer Science, UdSU, Izhevsk, Russia and

MIKHAIL A. SOKOLOVSKIY Water Problems Institute, RAS, Moscow, Russia

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

ISBN 978-1-4020-6743-3 (HB) ISBN 978-1-4020-6744-0 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com

Printed on acid-free paper

c 2008 Springer Science + Business Media B.V. 

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Contents

IUTAM SYMPOSIUM ON HAMILTONIAN DYNAMICS, VORTEX STRUCTURES AND TURBULENCE, MOSCOW, 25–30 AUGUST 2006 Keith Moffatt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi VORTEX DYNAMICS: THE LEGACY OF HELMHOLTZ AND KELVIN Keith Moffatt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

VORTEX DYNAMICS OF WAKES Hassan Aref . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 VORTICITY EQUATION OF 2D-HYDRODYNAMICS, VLASOV STEADY-STATE KINETIC EQUATION AND DEVELOPED TURBULENCE Valery V. Kozlov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 A NEW INTEGRABLE PROBLEM OF MOTION OF POINT VORTICES ON THE SPHERE Alexey V. Borisov, Alexander A. Kilin, and Ivan S. Mamaev . . . . . . . . . . 39 NONINTEGRABILITY AND FRACTIONAL KINETICS ALONG FILAMENTED SURFACES George M. Zaslavsky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 TWO-DIMENSIONAL TURBULENCE