Introduction to Theoretical and Mathematical Fluid Dynamics

577 Pages·2023·14.148 MB·English

by  Bhimsen K. Shivamoggi

IntroductiontoTheoreticalandMathematicalFluidDynamics

Introduction to Theoretical and
Mathematical Fluid Dynamics
Bhimsen K. Shivamoggi
UniversityofCentralFlorida
Orlando,Florida,UnitedStates
ThirdEdition
Thiseditionfirstpublished2023
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LibraryofCongressCataloging-in-PublicationData
Names:Shivamoggi,BhimsenK.,author.
Title:Introductiontotheoreticalandmathematicalfluiddynamics/
BhimsenKrishnaraoShivamoggi,UniversityofCentralFlorida,Orlando,
UnitedStates.
Description:Hoboken,NJ:JohnWiley&Sons,2023|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2021041747(print)|LCCN2021041748(ebook)|ISBN
9781119101505(hardback)|ISBN9781119101512(pdf)|ISBN9781119101529
(epub)|ISBN9781119765158(obook)
Subjects:LCSH:Fluiddynamics.|Fluiddynamics–Mathematicalmodels.
Classification:LCCQA911.S4622021(print)|LCCQA911(ebook)|DDC
532/.05–dc23
LCrecordavailableathttps://lccn.loc.gov/2021041747
LCebookrecordavailableathttps://lccn.loc.gov/2021041748
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Inmemoryofmybelovedmother,Pramila.

vii
Contents
PrefacetotheThirdEdition xv
Acknowledgments xvii
PartI BasicConceptsandEquationsof
FluidDynamics 1
1 IntroductiontotheFluidModel 3
1.1 TheFluidState 4
1.2 DescriptionoftheFlow-Field 5
1.3 VolumeForcesandSurfaceForces 7
1.4 RelativeMotionNearaPoint 10
1.5 Stress–StrainRelations 13
2 EquationsofFluidFlows 15
2.1 TheTransportTheorem 16
2.2 TheMaterialDerivative 18
2.3 TheLawofConservationofMass 18
2.4 EquationofMotion 19
2.5 TheEnergyEquation 19
2.6 TheEquationofVorticity 22
2.7 TheIncompressibleFluid 23
2.8 BoundaryConditions 24
2.9 A Program for Analysis of the Governing
Equations 25
3 HamiltonianFormulationofFluid-FlowProblems 27
3.1 HamiltonianDynamicsofContinuousSystems 28
3.2 Three-DimensionalIncompressibleFlows 32
3.3 Two-DimensionalIncompressibleFlows 35
viii Contents
4 SurfaceTensionEffects 39
4.1 ShapeoftheInterfacebetweenTwoFluids 39
4.2 CapillaryRisesinLiquids 41
PartII DynamicsofIncompressibleFluidFlows 45
5 FluidKinematicsandDynamics 47
5.1 StreamFunction 47
5.2 EquationsofMotion 50
5.3 IntegralsofMotion 50
5.4 CapillaryWavesonaSphericalDrop 51
5.5 Cavitation 54
5.6 RatesofChangeofMaterialIntegrals 55
5.7 TheKelvinCirculationTheorem 57
5.8 TheIrrotationalFlow 58
5.9 Simple-FlowPatterns 62
(i) TheSourceFlow 62
(ii) TheDoubletFlow 63
(iii) TheVortexFlow 66
(iv) DoubletinaUniformStream 66
(v) UniformFlowPastaCircularCylinderwithCirculation 67
6 TheComplex-VariableMethod 71
6.1 TheComplexPotential 71
6.2 ConformalMappingofFlows 74
6.3 HydrodynamicImages 82
6.4 PrinciplesofFree-StreamlineFlow 84
(i) Schwarz-ChristoffelTransformation 84
(ii) HodographMethod 93
7 Three-DimensionalIrrotationalFlows 99
7.1 SpecialSingularSolutions 99
(i) TheSourceFlow 99
(ii) TheDoubletFlow 101
7.2 d’Alembert’sParadox 104
7.3 ImageofaSourceinaSphere 105
7.4 FlowPastanArbitraryBody 107
7.5 UnsteadyFlows 109
7.6 Renormalized(orAdded)MassofBodiesMoving
throughaFluid 111
Contents ix
8 VortexFlows 115
8.1 VortexTubes 115
8.2 InducedVelocityField 117
8.3 Biot-Savart’sLaw 117
8.4 vonKármánVortexStreet 121
8.5 VortexRing 124
8.6 Hill’sSphericalVortex 129
8.7 VortexSheet 131
8.8 VortexBreakdown:BrookeBenjamin’sTheory 135
9 RotatingFlows 143
9.1 GoverningEquationsandElementaryResults 143
9.2 Taylor-ProudmanTheorem 144
9.3 PropagationofInertialWavesinaRotatingFluid 146
9.4 PlaneInertialWaves 147
9.5 ForcedWavemotioninaRotatingFluid 150
(i) TheEllipticCase 153
(ii) TheHyperbolicCase 154
9.6 SlowMotionalongtheAxisofRotation 155
9.7 RossbyWaves 160
10 WaterWaves 167
10.1 GoverningEquations 168
10.2 AVariationalPrincipleforSurfaceWaves 169
10.3 WaterWavesinaSemi-InfiniteFluid 171
10.4 WaterWavesinaFluidLayerofFiniteDepth 172
10.5 Shallow-WaterWaves 174
(i) AnalogywithGasDynamics 175
(ii) BreakingofWaves 176
10.6 WaterWavesGeneratedbyanInitialDisplacement
overaLocalizedRegion 176
10.7 WavesonaSteadyStream 182
(i) One-DimensionalGravityWaves 183
(ii) One-DimensionalCapillary-GravityWaves 184
(iii) ShipWaves 185
10.8 GravityWavesinaRotatingFluid 188
10.9 TheoryofTides 193
10.10 HydraulicJump 195
(i) TidalBores 195
(ii) TheDam-BreakProblem 199
10.11 NonlinearShallow-WaterWaves 202