Dynamical Oceanography

408 Pages·2008·22.25 MB·english

by  H. Dijkstra

Dynamical Oceanography
Henk A. Dijkstra
Dynamical Oceanography
HenkA.Dijkstra
Univ.Utrecht
Inst.MarineandAtmospheric
Research
Princetonplein5
3584CCUtrecht
Netherlands
[email protected]
ISBN:978-3-540-76375-8 e-ISBN:978-3-540-76376-5
LibraryofCongressControlNumber:2007941789
(cid:2)c 2008Springer-VerlagBerlinHeidelberg
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Preface
Thistextprovidesanintroductiontothetheoryofthelarge-scaleoceancircula-
tion. Thereareexcellenttextbooksonphysicaloceanography(PondandPickard,
1983; OU-staff, 1989; Pickard and Emery, 1990; Tomczak and Godfrey, 1994;
Pedlosky,1996;Knaus,1997),andgeophysicalfluiddynamics(Pedlosky,1987;
Cushman-Roisin,1994;Salmon,1998;Pedlosky,2003;McWilliams,2006;Val-
lis,2006). However,foratypicalcoursewhereonewantstofocusontheocean
circulation only at a challenging level for physics and mathematics students, a
combinationofmaterialfromthesebooksisneeded. Thistextisanattemptinto
thisdirectionwhichhasresultedinabookonalevelbetweenPondandPickard
(1983)andPedlosky(1996)withmuchbasicmaterialfromPedlosky(1987).
Thebookconsistsoffourparts. InpartI(chapters1-4)abriefintroduction
isgivenintotheoceancirculationandthegoverningequationsofoceanflows. In
addition, concepts are introduced that are necessary to describe and understand
thebehavioroflarge-scaleoceancurrents. InpartII(chapters5-10),thetheory
ofthemidlatitudewind-drivenoceancirculationispresented.Consideringmodel
development, there is a top-down approach and reduced equations are derived
usingasymptoticmethodsandscaling. PartIII(chapters11-12)focussesonthe
understanding of equatorial currents and El Nin˜o. In the last part IV, chapters
13 - 16, basic theory of planetary scale flows is presented, covering topics as
the thermocline problem, the Antarctic Circumpolar Current, the Arctic Ocean
circulationandthestabilityofthethermohalinecirculation.
Additionalmaterialbothinbroadening(indicatedbyaB)anddeepening(indi-
catedbyaD)ofthetopicsdiscussedisindicatedinseparatedblocks. Attheend
of each chapter several exercises are formulated and pointers to these exercises
appearintheleftmarginofthemaintext. Manyoftheseexercisesareaimedto
further develop methodological skills and to become familiar with the physical
concepts. Newmaterialisintroducedinonlyafewoftheseexercises. Solutions
totheexercisesareavailableatthewebsiteofthebookat
http://www.phys.uu.nl/∼dijkstra/DO
v
vi DYNAMICAL OCEANOGRAPHY
It should be possible to go through this text with an elementary knowledge
ofmathematicsandphysics. MathematicaltechniquessuchasGreen’sfunctions
and the method of inner and outer expansions are presented using elementary
examples. The use of proper asymptotic methods requires dimensionless equa-
tionswhileforunderstandingofphysicalconceptsdimensionalquantitiesarebest
suited. ThroughoutthetextIthereforehaveusedastrict*-subscriptnotationto
indicatedimensionaldependentquantitiesexceptinchapterswhereonlydimen-
sionalquantitiesareused.Inthiswayreducedmodelequations,suchasthequasi-
geostrophicmodelinchapter5,arederivedusingdimensionlessquantitiesandthe
dimensionalresultisstatedafterwards. Resultsandmodelswhicharefrequently
usedintheliteraturearepresentedinseparateboxesforeasyreference.Important
issuescanalsobefoundintheSummaryboxesattheendofeachchapter.
IhopethatstudentsandinterestedresearcherswilllikethewayIhavechosen
topresentthematerialandfindthisbookausefuladdition.
SEPTEMBER2007,UTRECHT
To my parents, Klaas
and Sjoukje Dijkstra
Acknowledgments
The book is based on the (mandatory) course on Dynamical Oceanography
whichIgaveforseveralyearsattheInstituteforMarineandAtmosphericresearch
Utrecht (IMAU) which is within the Department of Physics and Astronomy of
UtrechtUniversity,theNetherlands.IwanttothankWilldeRuijterforhissupport
of all my activities at the IMAU and for his efforts to make the IMAU such a
pleasantandinterestingplacetowork. Hiscommentsonthechapters1to6have
been very valuable and for the material in the chapters 1 to 3, I have benefitted
fromnotesofhiscourse‘IntroductiontoPhysicalOceanography’.
MyformerPh.D.studentLianketeRaaisthankedfortheefficientcollabora-
tionduringthecoursesonDynamicalOceanographyatIMAU.Hercommentson
the chapters 13 and 14 are gratefully acknowledged as well as her input on the
exercises. Leela Frankcombe read the entire manuscript and corrected much of
the text and many equations. Ole Anders Nøst (Norsk Polar Institute, Norway)
kindlyprovidedfilesoffiguresforchapter15.
MypublishersatSpringer(firstGeertJanGeraedsandlaterChrisBendall)are
thankedfortheirstimulustocompletethisbook. LaurenceMysakisthankedfor
hisusefulcommentsonpartsofanearlyversionofthetextandforsuggestingto
includeachapterontheArcticOceancirculation.
ThemanystudentswhohavebeenactivelyinvolvedintheIMAUcourseson
DynamicalOceanographyovertheyearsarethankedfortheirpatience, enthusi-
asm and input. Finally, my wife Julia contributed to the writing of this book in
herownspecialway.Ithankherforherpatienceandunderstanding.
ix
Contents
Preface v
Acknowledgments ix
Part I Introduction
1. A FIRST IMPRESSION 3
1.1 The ocean basins 4
1.2 Exploration of the oceans 7
1.2.1 A tiny bit of history 7
1.2.2 The modern era 9
1.3 Characteristics of seawater 10
1.3.1 Salinity 10
1.3.2 The surface distribution of temperature and salinity 11
1.3.3 T - S diagrams and water masses 13
1.3.4 Static stability 16
1.4 Exercises on chapter 1 23
2. PRESENT OCEAN CIRCULATION 27
2.1 Forcing fields 28
2.1.1 Wind stress 28
2.1.2 Heat flux 28
2.1.3 Freshwater flux 30
2.2 Ocean circulation 33
2.2.1 Surface circulation 33
2.2.2 Thermohaline circulation 35
2.2.3 Heat and freshwater transport 36
2.3 Oceans and climate 39
2.4 Motivating problems and approach 42
2.4.1 Western boundary currents 42
2.4.2 Internal variability of ocean flows 42
xi
xii DYNAMICAL OCEANOGRAPHY
2.4.3 Special equatorial phenomena 44
2.4.4 Phenomena on the planetary scale 44
2.5 Exercises on chapter 2 47
3. MATHEMATICAL DESCRIPTION 51
3.1 A priori scales 52
3.1.1 Geometry 52
3.1.2 Coriolis acceleration 53
3.1.3 Stratification 56
3.1.4 Mixing of momentum, heat and salt 57
3.1.5 Ratio of scales 59
3.2 Large-scale balances 60
3.2.1 Equations of motion 61
3.2.2 Spherical coordinates 62
3.2.3 Boundary conditions 63
3.3 Dominant balances 65
3.4 Exercises on chapter 3 68
4. VORTICITY 71
4.1 The vorticity equation 72
4.2 Vorticity transport 73
4.2.1 Vortex stretching and tilting 73
4.2.2 Baroclinic vorticity production 74
4.2.3 Diffusion of vorticity 76
4.3 Potential vorticity 77
4.4 Shallow-water equations 79
4.4.1 Hydrostatic equilibrium 79
4.4.2 Inertial flows 81
4.5 Exercises on chapter 4 86
Part II Midlatitude circulation
5. WIND-DRIVEN CIRCULATION 91
5.1 The North Atlantic surface circulation 92
5.2 The barotropic circulation on the β-plane 94
5.2.1 The β-plane approximation 94
5.2.2 Boundary conditions 97
5.2.3 Model equations 98
5.3 Stationary solutions 99
5.3.1 The geostrophic flow 103
5.3.2 The bottom Ekman layer 105
5.3.3 The free surface Ekman layer 110
5.3.4 Continuity of the vertical velocity 113