Geophysical Waves and Flows: Theory and Applications in the Atmosphere, Hydrosphere and Geosphere

520 Pages·012.24 MB·English

by  David E. Loper

GEOPHYSICAL WAVES AND FLOWS
WavesandflowsarepervasiveonandwithinEarth.Thisbookpresentsaunifiedphysical
andmathematicalapproachtowavesandflowsintheatmosphere,oceans,rivers,volcanoes
and the mantle, emphasizing the common physical principles and mathematical methods
that apply to a variety of phenomena and disciplines. It is organized into seven parts:
introductory material; kinematics, dynamics and rheology; waves in non-rotating fluids;
wavesinrotatingfluids;non-rotatingflows;rotatingflows;andsilicateflows.Thechapters
are supplemented by 47 ‘fundaments’, containing knowledge that is fundamental to
the material presented in the main text, organized into seven appendices: mathematics;
dimensions and units; kinematics; dynamics; thermodynamics; waves; and flows. This
bookisavaluablereferenceforgraduatestudentsandresearchersseekinganintroduction
to the mathematics of waves and flows in the Earth system, and can serve as a
supplementarytextbookforanumberofcoursesingeophysicalfluiddynamics.
DAVID E. LOPER isanEmeritusProfessoratFloridaStateUniversity.Aftercompleting
his PhD in Mechanical Engineering at Case Institute of Technology, and after a brief
stint in the aerospace industry and a post-doctoral appointment at the National Center
for Atmospheric Research in Boulder CO, Professor Loper took a joint position in
Applied Mathematics and the Geophysical Fluid Dynamics Institute at Florida State
University,wherehewasnamedDistinguishedResearchProfessorandawardedaNamed
Professorship. He was a co-founder and secretary of SEDI (Study of the Earth’s Deep
Interior,aCommitteeoftheInternationalUnionofGeodesyandGeophysics)andisFellow
oftheAmericanGeophysicalUnion.
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00:54:32, subject to the Cambridge Core
GEOPHYSICAL WAVES AND FLOWS
Theory and Applications in the
Atmosphere, Hydrosphere and Geosphere
DAVID E. LOPER
FloridaStateUniversity
00:54:32, subject to the Cambridge Core
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107186194
DOI:10.1017/9781316888858
(cid:2)c CambridgeUniversityPress2017
Thispublicationisincopyright.Subjecttostatutoryexception
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noreproductionofanypartmaytakeplacewithoutthewritten
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Firstpublished2017
PrintedintheUnitedKingdombyClays,StIvesplc
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Loper,DavidE.,author.
Title:Geophysicalwavesandflows:theoryandapplicationsinthe
atmosphere,hydrosphereandgeosphere/DavidE.Loper,professor
emeritus,FloridaStateUniversity.
Othertitles:Wavesandflows
Description:Cambridge:CambridgeUniversityPress,2017.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2017032905|ISBN9781107186194(hardback:alk.paper)
Subjects:LCSH:Waves.|Geophysics.|Flows(Differentiabledynamical
systems)|Elasticwaves.|Kinematics.
Classification:LCCQC157.L672017|DDC531/.1133–dc23
LCrecordavailableathttps://lccn.loc.gov/2017032905
ISBN978-1-107-18619-4Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
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Contents
Preface pagexi
PartI IntroductoryMaterial 1
1 Introduction 3
1.1 ABroaderPerspective 4
1.2 TheConceptofaContinuousBody 5
2 GettingStarted 9
2.1 ReferenceCoordinateSystem 9
2.2 WavesandFlows 12
2.3 ScopeandOrganization 14
2.4 BitsandBobs 15
PartII Kinematics,DynamicsandRheology 21
3 KinematicsofDeformationandFlow 23
3.1 OrientationtoKinematics 23
3.2 LagrangianRepresentationofDeformationandFlow 24
3.3 RotationandStrainTensors 26
3.4 FluidDeformationandRateofStrain 28
3.5 MaterialSurface 33
3.6 Comments 33
4 DynamicsandtheStressTensor 35
4.1 Forces 35
4.2 IntroductiontotheStressTensor 36
4.3 SymmetryoftheStressTensor 38
4.4 StressandForce 40
4.5 PressureandDeviatoricStress 42
4.6 ConservationofMomentum 43
4.7 Summary 46
v
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vi Contents
5 SomeThermodynamics 48
5.1 NewAdjectives 48
5.2 DifferentialEquationofState 49
5.3 ConservationofMaterial 50
5.4 EnergyEquation 50
5.5 TheIsentropicState 51
5.6 IdealGas 52
6 ShearRheology 54
6.1 ElasticSolid 55
6.2 FluidRheology 56
6.3 CommentsontheParametersandForces 63
6.4 Mixtures 63
7 StaticStateandPerturbations 67
7.1 StaticState 67
7.2 StaticStructure 68
7.3 PerturbationEquations 79
7.4 BoundaryLayers 80
7.5 DynamicStability 81
8 IntroductiontoRotatingFluids 83
8.1 RotationalConcepts 84
8.2 EquationsGoverningRotatingFlows 87
8.3 VorticityandPressureEquations 91
8.4 VerticallyAveragedContinuityEquation 93
8.5 GeostrophicBalance 95
8.6 Quasi-GeostrophicEquations 97
PartIII WavesinNon-RotatingFluids 101
9 IntroductiontoWaves 103
9.1 GeneralWaveBehavior 105
9.2 OrientationtoWaveAnalysis 106
9.3 SoundWaves 108
10 ElasticWaves 112
10.1 LongitudinalBodyWaves 112
10.2 TransverseBodyWaves 113
10.3 LongitudinalEdgeWaves 114
10.4 TransverseEdgeWaves 115
10.5 SeismicBodyWaves 115
11 Deep-WaterWaves 119
11.1 WaterWaveEquation 119
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Contents vii
11.2 SurfaceBoundaryConditions 121
11.3 SurfaceWaves 122
11.4 DiscussionofWaves 124
11.5 OceanWaves 125
11.6 WaterofFiniteDepth 132
12 LinearShallow-WaterWaves 134
12.1 Tsunamis 135
12.2 Luni-SolarTides 136
12.3 Seiches 141
12.4 CoastalWaves 141
13 NonlinearShallow-WaterWaves 146
13.1 Re-Formulation 146
13.2 ScalingandNon-Dimensionalization 147
13.3 Linear,Non-Dispersive 149
13.4 NonlinearandNon-Dispersive 149
13.5 LinearandDispersive 150
13.6 NonlinearandDispersive 150
14 OtherNon-RotatingWaves 155
14.1 CapillaryWaves 155
14.2 InterfacialWaves 157
14.3 InternalGravityWaves 163
PartIV WavesinRotatingFluids 167
15 Geostrophic,InertialandRossbyWaves 169
15.1 GeostrophicWaves 169
15.2 InertialWaves 170
15.3 RossbyWaves 171
16 RotationallyModifiedWaves 174
16.1 PoincaréWaves 174
16.2 RotatingInterfacialWaves 175
16.3 RotatingInternalGravityWaves 179
17 EquatorialWaves 182
17.1 DevelopmentofEquatorial-WaveEquations 182
17.2 EquatorialKelvinWaves 184
17.3 EquatorialRossbyWaves 185
18 CoastalandTopographicWaves 188
18.1 CoastalKelvinWaves 188
18.2 TopographicRossbyWaves 189
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viii Contents
PartV Non-RotatingFlows 193
19 OrientationtoOne-DimensionalFlow 195
19.1 One-DimensionalFlowEquations 197
20 SteadyChannelFlow 203
20.1 SteadyFlowinaUniformChannel 203
20.2 SteadyFlowinaChannelHavingVariableElevation 206
21 UnsteadyChannelFlow:HydraulicShockWaves 209
21.1 JumpConditions 210
21.2 KinematicsofHydraulicShocks 211
21.3 DynamicsofHydraulicShocks 213
21.4 FlashFloods 214
22 GravitationallyForcedFlows 218
22.1 Formulation 218
22.2 SomeLaminarFlows 220
23 ASimpleModelofTurbulentFlow 227
23.1 TransitiontoTurbulence 228
23.2 EngineeringApproachtoTurbulentChannelFlow 230
23.3 Mean-FlowEquations 232
23.4 BoundaryRoughness 235
23.5 Mixing-LengthTheory 236
23.6 TurbulentVelocityProfileNeartheBottom 239
23.7 DragCoefficient 240
23.8 TurbulentDiffusionofHeat 241
24 SomeNon-RotatingTurbulentFlows 242
24.1 TurbulentKatabaticWinds 242
24.2 Avalanches 245
24.3 CumulonimbusClouds 247
PartVI FlowsinRotatingFluids 251
25 EkmanLayers 253
25.1 FormulationandSolution 254
25.2 EkmanTransport 260
25.3 RelationsBetweenTransportandStress 262
25.4 EkmanPumping 264
25.5 EkmanLayersonSpecificBoundaries 266
25.6 CommentsonEkmanLayers 271
26 AtmosphericFlows 273
26.1 GeneralCirculation 273
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Contents ix
26.2 ThermalWinds 275
26.3 JetStreams 276
27 OceanicCurrents 277
27.1 Formulation 278
27.2 SverdrupBalanceandTransport 283
27.3 BoundaryCurrents 284
27.4 ThermohalineCirculation 288
28 Vortices 292
28.1 SurveyofVortices 292
28.2 VortexEquations 296
28.3 SimpleVortices 298
28.4 ApproachtoRealisticVortices 300
28.5 Hurricanes 310
PartVII SilicateFlows 315
29 EquationsGoverningSilicateFlows 317
29.1 MantleParameters 319
29.2 ParameterizedLower-MantleStructure 320
30 CoolingtheEarth 323
30.1 PlateTectonics 323
30.2 SlabsandMantlePlumes 324
30.3 Volcanism 325
30.4 GlobalHeatFlow 326
30.5 RadioactiveHeating 327
30.6 ConditionsattheCore–MantleBoundary 328
30.7 MantleMassandHeatBalances 330
31 CoolingtheMantle 334
31.1 ModesofMantleConvection 334
(cid:3)(cid:3)
31.2 FormationoftheD Layer 335
31.3 ParameterizationofMantleConvection 336
31.4 MantleThermalStructure 336
32 CoolingtheCore 339
(cid:3)(cid:3)
32.1 D Layer 339
32.2 MantlePlumes 345
33 OverviewofVolcanicFlows 354
33.1 TypesofMagmas 355
33.2 CategorizingVolcanicEruptions 356
33.3 TriggeringVolcanicEruptions 357
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