Emin Özsoy Geophysical Fluid Dynamics I An Introduction to Atmosphere—Ocean Dynamics: Homogeneous Fluids Springer Textbooks in Earth Sciences, Geography and Environment The Springer Textbooks series publishes a broad portfolio of textbooks on Earth Sciences, Geography and Environmental Science. Springer textbooks provide comprehensive introductions as well as in-depth knowledge for advanced studies. Aclear,reader-friendlylayoutandfeaturessuchasend-of-chaptersummaries,work examples, exercises, and glossaries help the reader to access the subject. Springer textbooks are essential for students, researchers and applied scientists. More information about this series at http://www.springer.com/series/15201 Emin Özsoy Geophysical Fluid Dynamics I An Introduction — to Atmosphere Ocean Dynamics: Homogeneous Fluids 123 Emin Özsoy Eurasia Institute of EarthSciences Istanbul TechnicalUniversity Istanbul,Turkey ISSN 2510-1307 ISSN 2510-1315 (electronic) SpringerTextbooks inEarth Sciences, GeographyandEnvironment ISBN978-3-030-16972-5 ISBN978-3-030-16973-2 (eBook) https://doi.org/10.1007/978-3-030-16973-2 ©SpringerNatureSwitzerlandAG2020 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. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland BernouilliequationdisplayedattheexteriorwallofİstanbulMuseumofModernArt,overlookingthe Bosphorus.“Hydrodynamica(Applied)”,size4.2mx62m,presentedbyLiamGillickandEsther ShipperGallery,duringthe14thİstanbulBiennial“TUZLUSU/SALTWATER”,catalogue,pages 408–409,5.9.2015–1.11.2015.PhotobyEminÖzsoy,takenduringasailboattriptothesiteorga- nizedbyTülayÇokacar AMiniatureOcean:spiraleddies,fronts,segmentsoftheBosphorusJet,hydrauliccontrolsatstraits, inter-basintransports,complexhydrodynamicandturbulentstructurescoincidingwithadinoflag- ellate bloom (red tide) in the Marmara Sea, presented by Emin Özsoy during the 14th Istanbul Biennial, “TU- ZLU SU / SALTWATER”, catalogue, pages 308–309, 5.9.2015–1.11.2015, by courtesyofNASAEarthObservatory.ThisisacolorenhancedversionoftheimageonMay17,2015 (https://earthobservatory.nasa.gov/images/85947/blooms-in-the-sea-of-marmara). Credits: NASA EarthObservatory … to first captains, seafarers, geographers, and oceanographers of the Seas of the Old World, where all has begun … Preface The present book is the first of two volumes aiming basic review of Geophysical FluidDynamics(GFD)forthestudentandresearcherinterestedinbasic,step-wise development from first principles and simple models that mimic the complex behavior of our ocean and atmosphere. GFDaimsatheoreticaldescription offluiddynamicsatearthlyscales.Newage of super-computing, modeling, satellite and communication technologies present a “bigscience”complementtoGFD,originallybuiltuponempiricalobservationsby travelers, navigators, and geographers across the globe, interpreted in recent times through mathematical analyses. An articulate review of the history, rationale for study and status of GFD by Vallis1 contends that some of the main goals and past triumphsofGFDlieinexplaining“fluid-dynamicalemergentphenomena”(system behavior very different from that of individual components, for instance, in the outstandingcasesoftheGulfStream,hurricanes,etc.).Theneededexplanationhas oftencalledfortheoryleadingtoadvancesinGFD.Perhapsitispartofourfortune thatchancesandmeanstoobserveemergentphenomenaatgeophysicalscaleshave only become available in recent history, with increased human activity, technical capacity, and skill. Historically, any significant advance in GFD had to wait for advances in fluid mechanics in the later part of eighteenth century. Its major development was accomplished in the second half of twentieth century. While soundly moving into the twenty-first century, GFD has yet to tackle humanity’s greatest problems involving climate dynamics. The recognition of earth’s rotation as the essential element seems to be due to Hadley in1735,andLaplacein1776.Thescientificrootsofoceanography,onthe other hand, go back to 1679 when Marsili2 used the “scientific method” of the Galilean revolution, to perform actual measurements at sea to explain “emergent 1VallisG.K.,2016.Geophysicalfluiddynamics:whence,whitherandwhy?,Proc.R.Soc.A472: 20160140. 2Marsili, L. F., 1681: Osservazioni intorno al Bosforo Tracio overo Canale di Costantinopoli, Rappresentate in Lettera alla Sacra Real Maesta Cristina Regina di Svezia da Luigi Ferdinando Marsili.NicoloAngeloTinassi,108pp. ix x Preface phenomena” of the Bosphorus exchange currents,3 to answer scientific questions that were left uncertain at Gibraltar Strait and elsewhere till few centuries later. Thepuzzleonthetheoryofoceancurrentshassurvivedinthe“SeasoftheOld World”sincetheGalileanageandperhapsnotfullysolveduntilthelastcentury.The book cover and the dedicated images in the first pages contrast the simplicity of Bernouilli principle with the defying complexity of “a miniature ocean”, spanning multipletimescales. Suchisthebasicnatureoffluiddynamics,fullofsurprisesandalwayscapableof creating and resolving new problems at all scales, despite the simple physics involved in the Navier–Stokes equations. Yet, the expansive nature of fluid dynamics is perhaps best illustrated by the standing challenge by the Clay Math- ematics Institute to prove uniqueness of solutions to Navier–Stokes equations. Now we appreciate that instability is an essential property of fluid motions, leadingtoincreasingawarenessoftheneedtocombineobservationsandmodelsvia data assimilation, for increased predictability offorecast states. Surprisesareevenmoreabundantinlivingearthcomparedtofluidearth,aswell for thesolid earth that lies beneath. Complexity of these systems often defies deep understanding because surprise is a rule rather than exception in nature, with imminent new findings often overruling what is learned by incomplete observa- tions. Human activity since the beginning of anthropocene has altered global ecosystems,makingthoseinterpretationsevenharder.Understandingearthsystems has often been influenced by social history,4 leaving future generations the task to respond to environmental burdens of all past human activities. The book provides essential mathematical development that walks through elementary description offluid dynamics toward a review of complex geophysical flows, but restricting attention to homogeneous fluids in this volume. While doing so, care is taken to provide essential steps in derivations often briefly stated else- where in expert literature. Yet, the area of interest is quite wide and perhaps our analysescanonlyprovideanelementaryviewforfurtherinquiry.Inthisregard,the readerisdirectedtoexpertliteratureofgreatercoverageonGFD,partiallylistedin the bibliography section. This volume is devoted to homogeneous fluids, both at laboratory and geo- physical scales, providing essentials for a reader who may either wish to settle for fundamentals or access a road map to safely proceed into the labyrinth of more advanced topics. The following volume will then build on this basis to add ther- modynamics and stratification effects. The presented material has been selectively developed from past lectures on dynamical oceanography and meteorology, offered as part of graduate programs at the Institute of Marine Sciences and Eurasia Institute of Earth Sciences 3Pinardi, N., Özsoy, E., Latif, M. A., Moroni, F., Grandi, A., Manzella, G., De Strobel, F. and V.Lyubartsev(2018).Measuringthesea:thefirstoceanographiccruise(1679–1680)andtheroots ofoceanography,Phys.Oceanogr.,48(4),845-860. 4Attali,J.,2017.Histoiresdelamer,LibrairieArthemeFayard,327p. Preface xi (respectively of the Middle East Technical University, Mersin and I_stanbul Tech- nical University, I_stanbul), and also as part of a school at the International Center for Theoretical Physics, Trieste. Many thanks are due to various individuals who either generously provided motivation, encouragement, or positively contributed tothe knowledge baseof the book.ÜmitÜnlüata,formeradvisorandmentoroftheauthor,wasforemostamong those gifted people whose leadership, scientific collaboration, and sharing GFD knowledge around the “Seas of the Old World” have had fundamental impact. Participationofformergraduatestudentsandresearchersinthevariouscoursesthat helped development of the material is gratefully acknowledged. Erdemli, Mersin, İstanbul, Ankara, Didyma, Turkey Emin Özsoy February 2019