Theoretical and Mathematical Physics Achim Feldmeier Theoretical Fluid Dynamics Theoretical Fluid Dynamics Theoretical and Mathematical Physics Thisseries,foundedin1975andformerlyentitled(until2005)TextsandMonographs inPhysics(TMP),publisheshigh-levelmonographsintheoreticalandmathematical physics.ThechangeoftitletoTheoreticalandMathematicalPhysics(TMP)signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition oftheeditorialboard,comprisingbothphysicistsandmathematicians. Thebooks,writteninadidacticstyleandcontainingacertainamountofelementary background material, bridge the gap between advanced textbooks and research monographs.Theycanthus serveasabasisforadvanced studies, notonlyforlec- tures and seminars at graduate level, but also for scientists entering a field of research. Series Editors Wolf Beiglböck, Heidelberg, Germany Piotr Chrusciel, Wien, Austria Jean-Pierre Eckmann, Genève, Switzerland Harald Grosse, Wien, Austria Antti Kupiainen, Helsinki, Finland Hartmut Löwen, Düsseldorf, Germany Michael Loss, Atlanta, GA, USA Nikita A. Nekrasov, Bures-sur-Yvette, France Manfred Salmhofer, Heidelberg, Germany Stanislav Smirnov, Genève, Switzerland Leon Takhtajan, Stony Brook, NY, USA Jakob Yngvason, Wien, Austria More information about this series at http://www.springer.com/series/720 Achim Feldmeier Theoretical Fluid Dynamics 123 AchimFeldmeier Institut für PhysikundAstronomie UniversitätPotsdam Potsdam, Germany ISSN 1864-5879 ISSN 1864-5887 (electronic) Theoretical andMathematical Physics ISBN978-3-030-31021-9 ISBN978-3-030-31022-6 (eBook) https://doi.org/10.1007/978-3-030-31022-6 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland For Gudrun Preface This book deals with calculational aspects of theoretical fluid dynamics. The emphasis is on calculations and derivations, not on formal proofs. Roughly, the first half of the book is on exact solutions of stationary fluid equations in two dimensions, often including eddies, and the second half is on waves and instabilities. A more detailed description of the contents is given in the introduction. Ihavetriedtomakesomerelativelyrecentresearchliteratureavailabletoreaders who have not yet specialized in fluid dynamics. Still, the material is somewhat advanced since there are lengthy calculations and a bulk of technicalities that are usually not found in more introductory texts. There is almost nothing in this book on turbulence, boundary layers, rotating fluids, the Taylor columns, the Couette flow, solitary and cnoidal waves, the Orr– Sommerfeldequation,andwavecoupling.Eachofthesedeservesdedicatedvolumes on their own, and I felt notfamiliarenough with these topicsto write about them. Ithank all thestudents who have attendedmy courses influidmechanics atthe UniversityofPotsdamoverthelast20years,wheresomeofthematerialinthisbook was presented first. This book owes very much to the careful reading and critical comments of Prof. Kolumban Hutter from theETH Zürich, to whom I expressmy cordial thanks. I thank the library of Technical University Berlin for making available in their Freihandmagazin many scientific journals that are not yet digi- talized or to which I had no online access. Finally, I thank Springer-Verlag, espe- ciallyLisaScaloneandManopriyaSaravanan,fortheeffortsputintotheproduction ofthisbook. AndIthank mywife for herconstantinterestinthebookandfor her patienceduring theyears Iworkedonit. For confused and mislead explanations, overlooked original work, miss- ing recent references, inconsistencies, and plain errors, please contact me at [email protected]. Berlin, Germany Achim Feldmeier vii Acknowledgements The following persons, publishers, companies, institutions, and societies are gratefullyacknowledgedforgrantingthepermissiontousecopyrightedfiguresand photographs: Prof. Douglass Auld Figure 11.1 Figure 11.3 Prof. Christopher E. Brennen Figure 4.4—Reproduced from Brennen (1970) Caltech thesis library Figure 5.19—Reproduced from Konrad (1976) Cambridge University Press: Journal of Fluid Mechanics Figure 5.12—Reproduced from Abernathy and Kronauer (1962) Figure 5.18—Reproduced from Baker and Shelley (1990) Figure 5.23—Reproduced from Walker et al. (1987) Figure 5.26—Reproduced from Moffatt (1969) Figure 8.15—Reproduced from Longuet-Higgins and Fox (1978) Centre d’études acadiennes Figure 7.18 Elsevier: Physics Letters Figure 5.21—Reproduced from Joyce and Montgomery (1972) Encyclopaedia Britannica Figure 7.5—Reproduced from Darwin (1902) Google Earth Figure 8.4 ix x Acknowledgements Prof. Jon Ove Hagen, Prof. Bjørn Gjevik Figure 7.4 Achim Hering Figure 11.4 Hydrotechnik Lübeck GmbH (Werner Evers) Figure 8.9 International Journal of Fluid Dynamics Figure 5.9—Reproduced from Lo et al. (2000) London Mathematical Society: Proceedings of the London Mathematical Society Figure 7.10—Reproduced from Taylor (1922) Prof. Marc McCaughrean Figure 3.16 Sandra Mihm Figure 5.2 NASA Figure 3.2 Figure 3.11 Figure 3.12 Figure 4.2 Figure 5.3 Figure 7.7 Figure 7.11 Figure 10.1 Arnold Price Figure 7.17 Royal Society of London: Proceedings of the Royal Society and Philosophical Transactions of the Royal Society Figure 5.11—Reproduced from Rosenhead (1931) Figure 7.6—Reproduced from Proudman and Doodson (1924) Figure 8.19—Reproduced from Akers et al. (2014) Figure 11.2—Reproduced from Kolsky et al. (1949) Prof. Satoshi Sakai Figure 10.2 Meinhard Spitzer Figure 8.16 Springer Nature: Nature Figure 5.10—Reproduced from Zhang et al. (2000) Acknowledgements xi U. S. Army Corps of Engineers, Tulsa District Figure 3.1 Wikipedia (see https://creativecommons.org/licenses/by-sa/2.0/) Figure 3.10 Figure 4.3 Figure 5.4 Figure 8.11 Figure 11.9 Prof. Richard Wolfson Figure 11.11—Reproduced from Wolfson and Holzer (1982) YouTube Figure 5.1 Berlin, Germany Achim Feldmeier Useful Readings Abernathy, F.H., and R.E. Kronauer. 1962. The formation of vortex streets. Journal of Fluid Mechanics13:1. Akers, B.F., D.M. Ambrose, and J.D. Wright. 2014. Gravity perturbed Crapper waves. ProceedingsoftheRoyalSocietyA470:20130526. Baker, G.R., and M.J. Shelley. 1990. On the connection between thin vortex layers and vortex sheets.JournalofFluidMechanics215:161. Brennen, C.E. 1970. Cavity surface wave patterns and general appearance. Journal of Fluid Mechanics44:33. Darwin, G.H. 1902. Tides. Encyclopaedia Britannica, 9th ed. https://www.1902encyclopedia. com/T/TID/tides.html. Joyce,G.,andD.Montgomery.1972.Simulationofthe‘negativetemperature’instabilityforline vortices.PhysicsLetters39A:371. Kolsky, H., J.P. Lewis, M.T. Sampson, A.C. Shearman, and C.I. Snow. 1949. Splashes from underwaterexplosions.ProceedingsoftheRoyalSocietyofLondonA196:379. Konrad, J.H. 1976. An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Internal Report CIT-8-PU. Pasadena:CaliforniaInstituteofTechnology. Lo,S.H.,P.R.Voke,andN.J.Rockliff.2000.Three-dimensionalvorticesofaspatiallydeveloping planejet.InternationalJournalofFluidDynamics4,Article1. Longuet-Higgins, M.S., and M.J.H. Fox. 1978. Theory of the almost-highest wave. Part 2. Matchingandanalyticextension.JournalofFluidMechanics85:769. Moffatt,H.K.1969.Thedegreeofknottednessoftangledvortexlines.JournalofFluidMechanics 35:117. Proudman, J.,and A.T.Doodson. 1924.Theprincipal constituentofthetidesof theNorthSea. PhilosophicalTransactionsoftheRoyalSocietyofLondonA224:185. Rosenhead,L.1931.Theformationofvorticesfromasurfaceofdiscontinuity.Proceedingsofthe RoyalSocietyofLondonA134:170.