This page intentionally left blank AVoyageThroughTurbulence Turbulenceiswidelyrecognizedasoneoftheoutstandingproblemsofthephysical sciences,butitstillremainsonlypartiallyunderstooddespitehavingattractedthe sustainedeffortsofmanyleadingscientistsforwelloveracentury. InAVoyageThroughTurbulence,wearetransportedthroughacrucialperiodofthe historyofthesubjectviabiographiesoftwelveofitsgreatpersonalities,startingwith OsborneReynoldsandhispioneeringworkofthe1880s.Thisbookwillprovide absorbingreadingforeveryscientist,mathematicianandengineerinterestedinthe historyandcultureofturbulence,asbackgroundtotheintensechallengesthatthis universalphenomenonstillpresents. A Voyage Through Turbulence Editedby PETER A. DAVIDSON UniversityofCambridge YUKIO KANEDA NagoyaUniversity KEITH MOFFATT UniversityofCambridge KATEPALLI R. SREENIVASAN NewYorkUniversity cambridge university press Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521198684 (cid:2)C CambridgeUniversityPress2011 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2011 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Avoyagethroughturbulence/[editedby]P.A.Davidson...[etal.]. p. cm. Includesbibliographicalreferences. ISBN978-0-521-19868-4(hardback) 1.Turbulence. I.Davidson,P.A.(PeterAlan),1957– II.Title. QA913.V69 2011 532(cid:3).0527–dc23 2011022992 ISBN978-0-521-19868-4Hardback ISBN978-0-521-14931-0Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. Contents Listofcontributors pageix Preface xi 1 OsborneReynolds:aturbulentlife 1 BrianLaunderandDerekJackson 1.1 Introduction 1 1.2 Professorialcareer 11 1.3 Endpiece 31 References 37 2 PrandtlandtheGo¨ttingenschool 40 EberhardBodenschatzandMichaelEckert 2.1 Introduction 40 2.2 Theboundarylayerconcept,1904–1914 42 2.3 Aworkingprogramforatheoryofturbulence 47 2.4 SkinfrictionandturbulenceI:the1/7thlaw 52 2.5 Themixinglengthapproach 54 2.6 SkinfrictionandturbulenceII:thelogarithmic lawandbeyond 56 2.7 FullydevelopedturbulenceI:1932to1937 62 2.8 FullydevelopedturbulenceII:1938 67 2.9 FullydevelopedturbulenceIII:1939to1945 74 2.10 Prandtl’stwomanuscriptsonturbulence, 1944–1945 78 2.11 Conclusion 87 References 92 3 TheodorevonKa´rma´n 101 A.LeonardandN.Peters 3.1 Introduction 101 v vi Contents 3.2 Thelogarithmiclawofthewall 104 3.3 Isotropicturbulence 109 3.4 Epilogue 123 References 124 4 G.I.Taylor:theinspirationbehindtheCambridgeschool 127 K.R.Sreenivasan 4.1 Openingremarks 127 4.2 Briefchronologicalaccount,focusingmostlyon scientificcareer 131 4.3 Ideasoriginatedintheperiod1915–1921 133 4.4 Theinterveningperiod 141 4.5 Ideasexploredintheperiod1935–1940 143 4.6 AwindowintoTaylor’spersonalitythrough hiscorrespondence 153 4.7 Somereflections 169 References 179 5 LewisFryRichardson 187 RobertoBenzi 5.1 Introduction 187 5.2 The4/3law 190 5.3 Richardsoncascadeandnumericalweatherprediction 199 5.4 Fractaldimension 204 5.5 Conclusions 206 References 207 6 TheRussianschool 209 GregoryFalkovich 6.1 Physicistandpilot 209 6.2 Mathematician 212 6.3 Appliedmathematicians 221 6.4 Theoreticalphysicist 229 6.5 Epilogue 233 References 234 7 StanleyCorrsin 238 CharlesMeneveauandJamesJ.Riley 7.1 Earlyyears 238 7.2 FirstcontributionsatCaltech 239 7.3 ArrivalinBaltimore 243 7.4 Structureofscalarfieldsinisotropicturbulence 245 7.5 Scalartransportanddiffusion 248 Contents vii 7.6 Homogeneousturbulence:decayandshear 255 7.7 Thegeometryandintermittencyofturbulence 259 7.8 Turbulenceandchemicalreactions 263 7.9 TheJohnsHopkinsenvironment 266 7.10 Finalyears 269 References 271 8 GeorgeBatchelor:thepost-warrenaissanceofresearch inturbulence 276 H.K.Moffatt 8.1 Introduction 276 8.2 Marseille(1961):awatershedforturbulence 278 8.3 Personalbackground 280 8.4 BatchelorandtheKolmogorovtheoryofturbulence 281 8.5 Batchelorandtheturbulentdynamo 285 8.6 Thedecayofhomogeneousturbulence 287 8.7 Batchelor’s1953monograph,TheTheoryof HomogeneousTurbulence 289 8.8 Rapiddistortiontheory 292 8.9 Turbulentdiffusion 293 8.10 Two-dimensionalturbulence 294 8.11 Laterpapers 296 8.12 GeorgeBatchelorasEditorandasHeadofDepartment 297 8.13 Internationalactivity 299 8.14 Conclusion 301 References 301 9 A.A.Townsend 305 IvanMarusicandTimothyB.Nickels 9.1 Earlyyears 305 9.2 MovetoCambridge 306 9.3 Waryears 307 9.4 ReturntoCambridge 308 9.5 PuttingK41tothetest 309 9.6 Shearflows 313 9.7 TheTownsendhypotheses 314 9.8 Turbulentshearflowsandeddies 321 9.9 Meteorologicalandotherflows 323 9.10 Concludingremarks 325 References 325 viii Contents 10 RobertH.Kraichnan 329 GregoryEyinkandUrielFrisch 10.1 Introduction 329 10.2 Closures: realizability, Galilean invariance and the randomcouplingmodels;MHDturbulence 332 10.3 Statisticalmechanicsandtwo-dimensionalturbulence 342 10.4 Intermittency 352 10.5 Miscellanyandconclusions 359 References 364 11 SatishDhawan 373 RoddamNarasimha 11.1 Introduction 373 11.2 TheCaltechyears 375 11.3 AtBangalore 380 11.4 Dhawan’sapproachtobuildingengineeringscience 387 References 390 12 PhilipG.Saffman 393 D.I.PullinandDanielI.Meiron 12.1 Introduction 393 12.2 Theproblemofturbulentdiffusion 397 12.3 Contributionstothetheoryofhomogeneousturbulence 402 12.4 Saffmanascritic 419 References 421 13 Epilogue:aturbulencetimeline 426 TheEditors Bibliographyandcomments 429