Table Of ContentDynamo 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.
