Geophysical fluid dynamics : understanding (almost) everything with rotating shallow water models

509 Pages·2018·107.3 MB·English

by  Zeitlin

GEOPHYSICAL FLUID DYNAMICS

Geophysical Fluid Dynamics
Understanding (Almost) Everything with Rotating
Shallow Water Models
Vladimir Zeitlin
LaboratoryofDynamicalMeteorology,SorbonneUniversityandÉcoleNormale
SupérieureParis,France
3
3
GreatClarendonStreet,Oxford,OX26DP,
UnitedKingdom
OxfordUniversityPressisadepartmentoftheUniversityofOxford.
ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship,
andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof
OxfordUniversityPressintheUKandincertainothercountries
©VladimirZeitlin2018
Themoralrightsoftheauthorhavebeenasserted
FirstEditionpublishedin2018
Impression:1
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin
aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe
priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted
bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics
rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe
aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe
addressabove
Youmustnotcirculatethisworkinanyotherform
andyoumustimposethissameconditiononanyacquirer
PublishedintheUnitedStatesofAmericabyOxfordUniversityPress
198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica
BritishLibraryCataloguinginPublicationData
Dataavailable
LibraryofCongressControlNumber:2017959942
ISBN978–0–19–880433–8
DOI10.1093/oso/9780198804338.001
Printedandboundby
CPIGroup(UK)Ltd,Croydon,CR04YY
LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand
forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials
containedinanythirdpartywebsitereferencedinthiswork.
TothememoryofG.Zaslavsky

Preface
The book explains the key notions and fundamental processes of the dynamics of the
fluidenvelopesoftheEarth(transposabletootherplanets)fromtheunifyingviewpoint
of rotating shallow-water model (RSW). The model, in its one- or two-layer versions,
playsadistinguishedroleingeophysicalfluiddynamics.Ithasbeenusednowforabout
a century to aid conceptual understanding of various phenomena, for elaboration of
approaches and methods to be used later in more complete models, for development
and testing of numerical codes and schemes of data assimilations, and for many other
purposes. In spite of its simplicity, the model grasps the essential features of the com-
plete‘primitiveequations’modelsoflarge-andmedium-scaleatmosphericandoceanic
motions.AlthoughRSW,mostoften,cannotgiveafullquantitativeexplanationofob-
servations,itprovidesqualitative(and,inmanycases,semi-quantitative)understanding.
It gives simple and clear representation of the principal dynamical processes and helps
to develop physical intuition. In addition, it allows for efficient high-resolution numer-
icalmethodswhichachieve,withmodestcomputationalresources,resolutionsandtime
spanshardlypossiblewiththefullprimitiveequations.Thequasi-geostrophicreduction
ofthemodelisnolesscelebrated,havingbeenused,forexample,forthefirstsuccessful
numericalweatherprediction.
After deriving one- and two-layer versions of the RSW model directly from the
primitiveequationsandexploringitsproperties,wewillexplainandillustratethefunda-
mentals of geophysical fluid dynamics with its help, and treat traditional and recently
arisen applications. We will be explaining both mathematics and physics underlying
dynamical phenomena and the methods used to analyse them, with necessary demon-
strations.However,mostoftenwewillremainonaheuristiclevelandwillbe,frequently
inthefirstplace,lookingforqualitativeinsights.Hence,wewillillustratedynamicalpro-
cessesunderconsiderationwithabundantfigures,andoftensacrificetechnicaldetailsor
relegatethemtoexercises.
The book targets fluid dynamicists, physicists, and applied mathematicians inter-
ested in the dynamics of the climate system and the modelling of atmospheric and
oceanic phenomena, mathematically minded meteorologists and oceanographers, in-
cludinggraduateandpost-graduatestudents.Itcanbeusedasacomplementtostandard
textbooks in geophysical fluid dynamics, dynamical meteorology, and physical ocean-
ography. The book is self-contained and provides, in a concise manner, all necessary
prerequisites,exceptforbasicmathematics.Itisdividedintothreeparts.PartIisageo-
physical fluid dynamics course in RSW terms and is supplied with problems/exercises
which complement demonstrations in the main text. Solutions of the problems can
be obtained from the Editorial Office on demand. Part II contains advanced top-
ics and studies of principal dynamical phenomena. Part III considers some modern
viii Preface
developments in rotating shallow-water modelling. Each chapter of the book ends by
a short résumé of the main points, and bibliographic remarks, for better orientation. A
detailedIndexservesthesamepurpose.
The first, and partially the second part are based on the course in geophysical fluid
dynamics which is being taught by the author at the Université P. and M. Curie and
ÉcoleNormaleSupérieure(Paris).Therestofthebookislargelybasedontheoriginal
worksoftheauthorwithstudentsandcollaborators.
Acknowledgements
A considerable part of material of this book is based on my work with friends and col-
laborators F. Bouchut, S. Medvedev, G. Reznik, and T. Dubos as well as with former
mastersandPhDstudents,someofthemnowcolleagues,M.BenJelloul,E.Gouzien,J.
Gula,N.Lahaye,J.Lambaerts,J.LeSommer,R.Plougonven,B.Ribstein,M.Rostami,
E.Scherer,A.Stegner,andM.Tort,allofwhichisgratefullyacknowledged.