Table Of ContentTheoretical and Mathematical Physics
Achim Feldmeier
Theoretical
Fluid
Dynamics
Theoretical Fluid Dynamics
Theoretical and Mathematical Physics
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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
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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.
