Dynamo and Dynamics, a Mathematical Challenge PDF
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Dynamo and Dynamics, a Mathematical Challenge NATO Science Series ASeriespresentingtheresultsofscientificmeetingssupportedundertheNATOScience Programme. TheSeriesispublishedbylOSPress,Amsterdam,andKluwerAcademicPublishersinconjunction withtheNATOScientificAffairsDivision Sub-Series I. LifeandBehaviouralSciences lOSPress II. Mathematics,PhysicsandChemistry KluwerAcademicPublishers III.ComputerandSystemsScience lOSPress IV.EarthandEnvironmentalSciences KluwerAcademicPublishers TheNATOScienceSeriescontinuestheseriesofbookspublishedformerlyastheNATOASISeries. The NATO Science Programme offerssupportforcollaboration incivil sciencebetween scientistsof countriesoftheEuro-AtlanticPartnershipCouncil.Thetypesofscientificmeetinggenerallysupported are"AdvancedStudyInstitutes"and"AdvancedResearchWorkshops",andtheNATOScienceSeries collects together the results of these meetings.The meetings are co-organized bij scientists from NATOcountriesandscientistsfrom NATO'sPartnercountries- countriesoftheCISandCentraland EasternEurope. Advanced StudyInstitutesarehigh-leveltutorialcoursesofferingin-depthstudyoflatestadvances inafield. Advanced ResearchWorkshops are expert meetingsaimed atcritical assessment ofa field, and identificationofdirectionsforfutureaction. Asaconsequenceoftherestructuring oftheNATOScienceProgrammein 1999,theNATOScience Serieswasre-organizedtothefoursub-seriesnotedabove.Pleaseconsultthefollowingwebsitesfor informationonpreviousvolumespublishedintheSeries. hltp:l/www.nato.int/science http://www.wkap.nl hltp://www.iospress.nl http://www.wtv-books.de/nato-pco.htm SeriesII:Mathematics,PhysicsandChemistry- Vol.26 Dynamo and Dynamics, a Mathematical Challenge edited by P. Chossat I.N.L.N. (CNRS, UMR 6618), Valbonne, France D. Ambruster Department of Mathematics, Arizona State University, Tempe, Arizona, U.S.A. and 1. Oprea Faculty of Mathematics, University of Bucarest, Romania ~. " Springer Science+Business Media, B.V. Proceedings of the NATO Advanced Research Workshop on Oynamo and Oynamics, a Mathematical Challenge Cargese, France 21-26 August, 2000 A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-0-7923-7070-3 ISBN 978-94-010-0788-7 (eBook) DOI 10.1007/978-94-010-0788-7 Printad on acid-traa papar AII Rights Reserved © 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 1 st 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. TABLEOFCONTENTS Preface ix Participants X111 Part 1:Laboratorydynamos,theoryandexperiments Anonstationarydynamoexperimentinabrakedtorus P.Frick, SDenisov, S. Khripchenko, V.Noskov, D. SokoloffandR. Stepanov Riga DynamoExperiment A. Gailitis, 0. Lielausis, E. Platads, G. Gerbeth andF.Stefani 9 Generationofmagnetic field intheCouette-Taylorsystem P.Laure, P.ChossatandF.Daviaud 17 Dynamoaction, betweennumercial experimentsandliquidsodiumdevices J. Leorat, P.Lal/emand, J.L. GuermondandF.Plunian 25 MHDinvon KarmanSwirlingflows L. Marie, J. Burguete,A. ChifJaudel, F.Daviaud, D. Ericher, C Gasquet, F.Petrelis, S. Fauve, M. Bourgoin, M. Moulin, P.Odier,J.-F.Pinton,A. Guigon, J.B. Luciani, F.NamerandJ. Leorat 35 DynamoactioninaforcedTaylor-Greenvortex C Nore, ME Brachet, H. PolitanoandA. Pouquet 51 Onthe possibilityofanhomogeneous MHDdynamo inthe laboratory R. 0 'Connell, R. Kendrick, M. Nornberg, E. Spence,A. BaylissandCB. Forest 59 SaturationofaPonomarenkotypefluid dynamo A. Nunez, F.PetrelisandS. Fauve 67 DynamoActiondueto EkmanlayerInstability Y. Ponty,A. GilbertandA. Soward 75 Huntingfordynamos: eightdifferentliquidsodiumflows W.L. Shew, D.R. Sisan andD.P.Lathrop 83 Thermal flow inarotatingsphericalgapwithadielectrophoreticcentral force field B. Sitte, W.Brasch, M. Junk, V.TravnikovandC Egbers 93 VI PreliminaryMeasurementoftheTurbulentMagneticDitfusivityinthreedimensions Jc. Thelen andR Cattaneo 101 SaturationmechanisminamodeloftheKarlsruhedynamo A. 1ilgnerandRH. Busse 109 Part2:Planetaryandstellardynamos,hydrodynamicalmodelsandsimulations Shearedhelical turbulenceandthehelicityconstraintinlarge-scaledynamos A. Bigazzi,A. BrandenburgandK. Subramanian 117 Theinversecascadeinturbulentdynamos A. Brandenburg 125 Rotatingmagnetoconvectionindependenceon stratification,diffusiveprocesses, andboundaryconditions J Brestenskj!, S. SevcikandJ Simkanin 133 Small-andlarge-scaledynamoactioninsimpleforced flows N.H. Brummell, R Cattaneoands.M. Tobias 145 Convectiondrivendynamosinrotatingspherical fluid shells RH. BusseandE. Grote 153 Dynamosinrotatingandnonrotatingconvectionintheform ofasymmetricsquares A. DemircanandN. Seehafer 163 Magnetoconvection T. Emonet, R CattaneoandN.O. Weiss 173 Ontheapplicationofgrid-spectralmethodtothesolutionofgeodynamoequations p.Hejda, I.CupalandM.Reshetnyak 181 Super- andcounter-rotatingjetsandvorticesinstronglymagneticspherical Couetteflow R. Hollerbach 189 Large-andsmall-scaledynamoaction D.WHughes, R Cattaneo andJ-c. Thelen 199 Dynamoproblemsinspherical andnearlyspherical geometries D.J Ivers andC.G. Phillips 207 vii Anelasticplanetarymagnetohydrodynamics S.V.Starchenko 217 Part3:Astrophysicaldynamos,observationsandtheory TheGalacticDynamo K.M. Ferriere 225 TurbulentDiamagnetismandGalacticDynamo A.S. Gaboy, D.D. SokoloffandA. Shukurov 233 ParkerinstabilitywithCoriolisforce andmagneticreconnectionas apartofthe galacticfast dynamoaction M.Hanasz, K. Otmianowska-MazurandH.Lesch 239 Magnetic helicityflux andthenonlineargalacticdynamo N. Kleeorin, D. Moss, I. RogachevskiiandD. Sokoloff 247 Helioseismictestsofdynamomodels A.G. Kosovichev 253 AsymptoticWKBJ-studiesofsolardynamowaves: IDand2Dcases K.M. Kuzanyan 261 Dynamoeffectwith inertialmodes ina spherical shell? M. RieutordandL. Valdettaro 271 Twotypes ofnonlinearitiesinmagneticdynamo I. RogachevskiiandN Kleeorin 279 Thesolardynamo:axial symmetryand homogeneitybroken A.Ruzmaikin 289 Alpha-quenched<x2!}dynamowavesinstellarshells A. Soward, A. BassomandY. Pony 297 Two-dimensional diskdynamos with vertical outflowsintoahalo B. vonRekowski, W.Dobler,A. ShukurovandA. Brandenburg 305 Part4: Dynamosasdynamicalsystems,low-ordermodelsandphenomenology Structurallystableheterocliniccycles andthedynamodynamics D.Armbruster, P ChossatandI. Oprea 313 viii Two-componentdynamical modelofthesolarcycle E.E. Benevolenskaya 323 Symmetriesofthesolardynamo: comparingtheorywithobservation 1.M. Brooke,1. Pelt, R Pulkkinen andI. Tuominen 331 Suicidalandparthenogeneticdynamos H. Fuchs, K.H. RadlerandM Rheinhardt 339 Heterocliniccyclesand fluidmotionsinrotatingspheres R. Lauterbach 347 Convection-drivendynamos, amplitudeequationsandlarge-scalefields Re. Matthews 355 Aheteroclinicmodelofgeodynamoreversals andexcursions l. Melbourne, MR.E. ProctorandA.M Rucklidge 363 Aspectsofthedynamicsunderlyingsolarandstellardynamomodels R. Tavakol, E. CovasandD. Moss 371 Modulationandsymmetry-breakinginlow-ordermodelsofthesolardynamo NO. Weiss, EKnoblochandS.M Tobias 381 PREFACE Thisbookcontainsthe lecturesgivenatthe workshop"Dynamoand dynamics,a mathematicalchallenge" heldinCargesefromAugust21 to26,2000.The workshop differedfrom mostpreviousconferencesonthedynamoeffectintwoimportantrespects. First,itwasatthis internationalconferencethattheexperimentalobservationof homogeneousfluiddynamoswasfirstreported. Second,theconferencegathered scientistsfromverydifferentfields, thusshowingthatthepynamoproblemhasbecome an interdisciplinarysubjectinvolving notonlyastrophysicistsandgeophysicists,butalso scientistsworking indynamicalsystemstheory,hydrodynamics,and numerical simulation,aswellasseveral groupsinexperimentalphysics. Thisbookthusreports importantresultsonvariousdynamostudiesinthesedifferent contexts: -Decadesafterthediscoveryofthefirst analyticexamplesoflaminarfluid dynamos,the self-generationofamagneticfield byaflow ofliquidsodiumhasbeenreported bythe Karlsruhe and Rigagroups. Althoughtherewerenodoubtsconcerningtheself generation bythe laminarRoberts-type orPonomarenko-typeflowsthatwereused, these experimentshaveraised interestingquestionsabouttheinfluenceoftheturbulent fluctuations onthedynamothreshold andonthesaturationlevelofthemagneticfield. -Theincreaseincomputingpowernowallowsthesimulationofplanetarydynamos in almostrealistic geometriesandprovidessomeresults inagreementwith the observations.Moreover,directnumericalsimulationsoftheMHDequationsyield insightsinto thedifferentpossibleequilibriabetweenmagneticandkineticdegreesof freedom, leadingtodifferentsaturationlevelsofthe magneticfield generated. -Recentobservationsofstellarandgalacticmagneticfields arediscussedmostlyinthe contextofmeanfield magnetohydrodynamics.Thesestudiesare likely to improveour understandingofthe internalstructureandthedynamicsofthesun,and toclarifythe originandtheroleofgalacticmagneticfields andtheirconnectionwithvarious dynamicalprocessesoccuringintheinterstellarmedium. ix x -Thetoolsofdynamicalsystemstheory areusedtofurtheraqualitativeunderstanding ofdynamodynamics. Usingsymmetryarguments, thefull MHDequationscanbe reduced inthevicinityofbifurcationpoints,leadingto low-dimensionaldynamical systemsprovidingpossiblemodelsforthesolarcycleorforthereversalsoftheEarth's magneticfield. However, therearestilllargegapstobefilledbetweenthesedifferentlevelsof description inorderto obtainafull understandingofdynamoprocesses: -Itisstilldifficulttoconnectlow-dimensionalmodels with numericalsimulationsofthe full problemandtodetermine howrobustaretheobservedphenomenainthepresenceof many turbulentmodes. -Directnumericalsimulationsarestillrestrictedtovaluesofthefluidparameterswhich are very unrealistic whencomparedtolaboratoryexperiments.Turbulencemay insome caseshavelittleinfluenceonthedynamothresholdbutislikelytostronglymodifythe saturationlevelofthemagneticfield. -Anexperimentaldemonstrationofanunconstrainedturbulentdynamoisstill lacking andaturbulentdynamowitha negligiblemeanflow appearsevenmoredifficultto achieve, although phenomenologicalmodels withthesepropertieshavebeenknownfor alongtime. -Alargegapalsoexists betweenlaboratoryexperimentsand"natural"dynamos. AlthoughtheeffectoftheCoriolisforcecanbeeasilystudied,manyastrophysical plasmas stronglydifferfrom liquidmetalsandmayinvolve.effectsthatarenotdescribed bythe simpleMHDequationsvalidfor liquidmetals.Therearestillmanyunknowns, bothforstellarand planetarydynamos, thatcomplicatethesimulationoftherelevant mechanismsinlaboratoryexperiments.Itisalso unlikelythat laboratoryexperiments willsucceedinattainingmagneticReynoldsnumbersthatsignificantlyexceedthe dynamo threshold. -Finally,atamoremathematicallevel,theproblemofdescribingabifurcationtowards adynamofrom astronglyturbulentvelocityfield involvesbothtechnicaldifficultiesand probablenewqualitativeeffects.
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