IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence: Proceedings of the IUTAM Symposium held in Moscow, 25–30 August, 2006 PDF
Preview IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence: Proceedings of the IUTAM Symposium held in Moscow, 25–30 August, 2006
IUTAMSYMPOSIUMONHAMILTONIAN DYNAMICS, VORTEX STRUCTURES, TURBULENCE IUTAM BOOKSERIES Volume 6 AimsandScopeoftheSeries The IUTAM Bookseries publishes the proceedings of IUTAM symposia undertheauspices oftheIUTAMBoard. Series Editors: G.M.L. Gladwell,Universityof Waterloo, Waterloo, Ontario, Canada R. Moreau, INPG, Grenoble, France Editorial Board: D.vanCampen, EindhovenUniversityofTechnology,Eindhoven,TheNetherlands L.B.Freund,BrownUniversity,Providence,USA H.K.Moffatt,UniversityofCambridge,Cambridge,UK J.Engelbrecht,InstituteofCybernetics,Tallinn,Estonia T.Kambe,IIDS,Tokyo,Japan A.Kluwick, TechnischeUniversita¨t,Vienna,Austria N.Olhoff,AalborgUniversity,Aalborg,Denmark Z.Zheng,ChineseAcademyofSciences,Beijing,China Foralistofrelatedmechanicstitles,seefinalpages. IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence Proceedings of the IUTAM Symposium held in Moscow, 25_30 August, 2006 Editedby 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 AC.I.P.CataloguerecordforthisbookisavailablefromtheLibraryofCongress. ISBN978-1-4020-6743-3(HB) ISBN978-1-4020-6744-0(e-book) PublishedbySpringer, P.O.Box17,3300AADordrecht,TheNetherlands. www.springer.com Printedonacid-freepaper (cid:1)c 2008SpringerScience+BusinessMediaB.V. No part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recordingor otherwise, without writte n permission from the Publisher, with the exception of any material supplied specifically for the purpose of being enteredand 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 ON A BOUNDED DOMAIN GertJan van Heijst and Herman Clercx ............................. 65 ANALOGY OF A VORTEX-JET FILAMENT WITH THE KIRCHHOFF ELASTIC ROD AND ITS DYNAMICAL EXTENSION Yasuhide Fukumoto .............................................. 77 vi Contents ADIABATIC INVARIANCE IN VOLUME-PRESERVING SYSTEMS Anatoly Neishtadt, Dmitri Vainchtein, and Alexei Vasiliev............. 89 UNSTABLE-PERIODIC-FLOW ANALYSIS OF COUETTE TURBULENCE Shigeo Kida, Takeshi Watanabe, and Takao Taya ....................109 MOTION OF AN ELLIPTIC VORTEX RING AND PARTICLE TRANSPORT Yoshi Kimura ...................................................119 HETONIC QUARTET: EXPLORING THE TRANSITIONS IN BAROCLINIC MODONS Ziv Kizner ......................................................125 DYNAMICS OF A SOLID AFFECTED BY A PULSATING POINT SOURCE OF FLUID Andrey Morgulis and Vladimir Vladimirov ..........................135 PHASE TRANSITIONS TO SUPERROTATION IN A COUPLED FLUID — ROTATING SPHERE SYSTEM Chjan C. Lim ...................................................151 VORTEX KELVIN MODES WITH NONLINEAR CRITICAL LAYERS Sherwin A. Maslowe and Nilima Nigam.............................163 NON-DIVERGENT 2D VORTICITY DYNAMICS AND THE SHALLOW WATER EQUATIONS ON THE ROTATING EARTH Nathan Paldor...................................................177 HIGH-DIMENSIONAL HAMILTONIAN DYNAMICAL SYSTEMS: THEORY AND COMPUTATIONAL REALIZATION FOR THEORETICAL CHEMISTRY Stephen Wiggins .................................................189 ON STATISTICAL MECHANICS OF VORTEX LINES Victor Berdichevsky ..............................................205 NUMERICAL VERIFICATION OF WEAKLY TURBULENT LAW OF WIND WAVE GROWTH Sergei I. Badulin, Alexander V. Babanin, Vladimir E. Zakharov, and Donald T. Resio .............................................211 Contents vii THE SIZE DISTRIBUTION FUNCTION FOR MIXED-LAYER THERMALS IN THE CONVECTIVE ATMOSPHERE Alexander N. Vul’fson ............................................227 FAMILIES OF TRANSLATING NEUTRAL VORTEX STREET CONFIGURATIONS Kevin A. O’Neil .................................................237 LAGRANGIAN FLOW GEOMETRY OF TRIPOLAR VORTEX Lorena A. Barba and Oscar U. Velasco Fuentes ......................247 CLUSTERING AND MIXING OF FLOATING PARTICLES BY SURFACE WAVES Sergei Lukaschuk, Petr Denissenko, and Gregory Falkovich ............257 RESOLUTION OF NEAR–WALL PRESSURE IN TURBULENCE ON THE BASIS OF FUNCTIONAL APPROACH Efim Kudashev ..................................................269 TRIPLET OF HELICAL VORTICES Valery L. Okulov, Igor V. Naumov, Wen Z. Shen, and Jens N. Sørensen ............................................281 LONG-WAVE TRANSITION TO INSTABILITY OF FLOWS IN HORIZONTALLY EXTENDED DOMAINS OF POROUS MEDIA Andrej Il’ichev and George Tsypkin ................................291 NON-DISSIPATIVE AND LOW-DISSIPATIVE SHOCKS WITH REGULAR AND STOCHASTIC STRUCTURES IN NON-LINEAR MEDIA WITH DISPERSION Igor B. Bakholdin................................................303 HYPERCHAOS IN PIEZOCERAMIC SYSTEMS WITH LIMITED POWER SUPPLY Alexandr Yu. Shvets and Tatyana S. Krasnopolskaya .................313 ABOUTANALYTICSOLVABILITYOFNONSTATIONARY FLOW OF IDEAL FLUID WITH A FREE SURFACE Roman V. Shamin ...............................................323 NONINTEGRABLE PERTURBATIONSOF TWOVORTEX DYNAMICS Denis Blackmore.................................................331 viii Contents ROSSBY SOLITARY WAVES IN THE PRESENCE OF A CRITICAL LAYER Philippe Caillol and Roger H. Grimshaw ............................341 ADJUSTMENT OF LENS-LIKE STRATIFIED AXISYMMETRIC VORTICES TO PULSONS Georgi G. Sutyrin................................................353 EVOLUTION OF AN INTENSE VORTEX IN A PERIODIC SHEARED FLOW Georgi Sutyrin and Xavier Carton .................................363 VORTEX INTERACTION IN AN UNSTEADY LARGE-SCALE SHEAR/STRAIN FLOW Xavier Perrot and Xavier Carton ..................................373 MODIFIED SHALLOW WATER EQUATIONS. SIMPLE WAVES AND RIEMANN PROBLEM Kirill V. Karelsky and Aralel S. Petrosyan ..........................383 ESTIMATION OF OPTIMAL FOR CHAOTIC TRANSPORT FREQUENCY OF NON-STATIONARY FLOW OSCILLATION Yury Izrailsky, Konstantin Koshel, and Dmitry Stepanov ..............393 A UNIFIED LINEAR WAVE THEORY OF THE SHALLOW WATER EQUATIONS ON A ROTATING PLANE Nathan Paldor and Andrey Sigalov .................................403 CHAOTIC ADVECTION AND NONLINEAR RESONANCES IN A PERIODIC FLOW ABOVE SUBMERGED OBSTACLE Peter A. Davies, Konstantin V. Koshel, and Mikhail A. Sokolovskiy ....415 TRAPPED VORTEX CORES IN INTERNAL SOLITARY WAVES PROPAGATING IN A THIN STRATIFIED LAYER EMBEDDED IN A DEEP HOMOGENEOUS FLUID Oleg G. Derzho ..................................................425 ON THE STABILITY OF STRATIFIED QUASI-GEOSTROPHIC CURRENTS WITH VERTICAL SHEAR ABOVE ISOLATED TOPOGRAPHIC FEATURES Valery N. Zyryanov ..............................................435 DYNAMICS OF TWO RINGS OF VORTICES ON A SPHERE Alexey V. Borisov and Ivan S. Mamaev.............................445 Contents ix ON THE MOTION OF TWO MASS VORTICES IN PERFECT FLUID Sergey M. Ramodanov ............................................459 RUBBER ROLLING: GEOMETRY AND DYNAMICS OF 2-3-5 DISTRIBUTIONS Kurt Ehlers and Jair Koiller ......................................469 ON THE MOTION OF A+1 VORTICES IN A TWO-LAYER ROTATING FLUID Mikhail A. Sokolovskiy and Jacques Verron..........................481 CASCADES OF PERIOD MULTIPLYING IN THE PLANAR HILL’S PROBLEM Alexandr B. Batkhin and Natalia V. Batkhina .......................491 IUTAM SYMPOSIUM ON HAMILTONIAN DYNAMICS, VORTEX STRUCTURES AND TURBULENCE, MOSCOW, 25–30 AUGUST 2006 Professor Keith Moffatt, Vice-President, IUTAM WELCOME REMARKS It is my great honour to welcome you on behalf of the Bureau of IUTAM to this Symposium on Hamiltonian dynamics, vortex structures and turbulence. The Symposium has been in preparation for two years, and I congratulate our hosts here at the Steklov Institute of the Russian Academy of Sciences forhavingpreparedanexcellentandwide-rangingprogramme,andforhaving succeeded in attracting such a distinguished gathering to debate problems in fluiddynamicsmanyofwhichhavealonghistory,yetstilltodaypresentmany challenges of a fundamental nature. The letters IUTAM, as you all know, stand for the International Union of Theoretical and Applied Mechanics. This Union is one of the International Scientific Union members of ICSU, the International Council for Science, which this year celebrates its 75th anniversary. The roots of IUTAM itself go back to the early Congresses in Mechanics, the first of which was held in Delft in the Netherlands, in 1924. IUTAM was formally established as an International Union at the 7th Congress, which was held in London in 1948. The 13th Congress of Theoretical and Applied Mechanics was held here in Moscow in 1972, under the Presidency of the great Mushkhelishvili. The most recent 21st Congress was held in Warsaw in 2004, and the next will be held in Adelaide, South Australia, in 2008. In addition to the Congresses, IUTAM also sponsors its Symposia, about 8 per year on average, covering all branches of fluid and solid mechanics, andrigidbodydynamics.ThepresentSymposiumfollowsinastrongtradition of Symposia dealing with aspects of vortex dynamics and turbulence. I note just a few of the most relevant that have been held in the last few years, for all of which published Proceedings are now available: 1999, Sedona, Arizona, USA: Laminar-Turbulent Transition
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