Dynamics of the Equatorial Ocean
(Sprache: Englisch)
This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in...
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This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in the tropic sea, transient equatorial waves, vertically-propagating beams, equatorial Ekman layers, the Yoshida jet model, generation of coastal Kelvin waves from equatorial waves by reflection, Rossby solitary waves, and Kelvin frontogenesis. A series of appendices on midlatitude theories for waves, jets and wave reflections add further material to assist the reader in understanding the differences between the same phenomenon in the equatorial zone versus higher latitudes.Inhaltsverzeichnis zu „Dynamics of the Equatorial Ocean “
1 An Observational Overview of the Equatorial Ocean1.1 The Thermocline: the Tropical Ocean as a Two-Layer Model . . . . . .
1.2 Equatorial Currents1.3 The Somali Current and the Monsoon
1.4 Deep Internal Jets 1.5 The El Nino/Southern Oscillation (ENSO)
1.6 Upwelling in the Gulf of Guinea
1.7 Seasonal Variations of the Thermocline
1.8 Summary
2 Basic Equations and Normal Modes
2.1 Model . 2.2 Boundary conditions
2.3 Separation of Variables 2.4 Lamb's Parameter and all
2.5 Vertical Modes and Layer Models .2.6 Nondimensionalization
3 Kelvin, Yanai, Rossby and Gravity Waves
3.1 Latitudinal wave modes: an overview
3.2 Latitudinal wave modes
3.3 Dispersion relation
3.4 Analytic Approximations to Equatorial Wave Frequencies
3.4.1 Explicit formulas
3.4.2 Long wave series3.5 Separation of Time Scales
3.6 Forced Waves 3.7 How the Mixed-Rossby Gravity Wave Earned Its Name
3.8 Hough-Hermite Vector Basis 3.8.1 Introduction
3.8.2 Inner Product and Orthogonality 3.8.3 Orthonormal Basis Functions
3.9 Hough-Hermite Applications
3.10 Initialization Through Hough-Hermite Expansion
3.11 Energy Relationships
3.12 The Equatorial Beta-Plane as the Thin Limit of the Nonlinear
Shallow Water Equations on the Sphere
4 The "Long Wave" Approximation & Geostrophy
4.1 Introduction 4.2 Quasi-Geostrophy
4.3 "Meridional Geostrophy" Approximation 4.4 Boundary Conditions
4.5 Frequency Separation of Slow [Rossby/Kelvin] and Fast [Gravity]Waves
4.6 Long Wave Initial Value Problems
4.7 Reflection From an
... mehr
Eastern Boundary in the Long Wave
Approximation
4.7.1 The Method of Images
4.7.2 Dilated Images
4.7.3 Zonal Velocity
4.8 Forced Problems in the Long Wave Approximation
5 Coastally Trapped Waves and Ray-Tracing
5.1 Introduction
5.2 Coastally-Trapped Waves
5.3 Ray-Tracing for Coastal Waves
5.4 Ray-Tracing on the Equatorial Beta-plane
5.5 Coastal & Equatorial Kelvin Waves
5.6 Topographic and Rotational Rossby Waves and Potential Vorticity
6 Reflections and Boundaries
6.1 Introduction 6.2 Reflection of Midlatitude Rossby Waves from a Zonal Boundary
6.3 Reflection of Equatorial Waves from a Western Boundary 6.4 Reflection from an Eastern Boundary
6.5 The Meridional Geostrophy/Long Wave Approximation and Boundaries 6.6 Quasi-Normal Modes: Definition and Other Weakly Non-existent Phenomena
6.7 Quasi-Normal Modes in the Long Wave Approximation: Derivation
6.8 Quasi-Normal Modes in the Long Wave Approximation: Discussion
6.9 High Frequency Quasi-Free Equatorial Oscillations 6.10 Scattering & Reflection from Islands
7 Response of the Equatorial Ocean to Periodic Forcing7.1 Introduction
7.2 A Hierarchy of Models for Time-Periodic Forcing7.3 Description of the Model and the Problem
7.4 Numerical models: Reflections and "Ringing" 7.5 Atlantic versus Pacific
7.6 Summary
8 Impulsive Forcing and Spin-up
8.1 Introduction
8.2 The Reflection of the Switched-On Kelvin Wave
8.3 Spin-up of a Zonally-Bounded Ocean: Overview
8.4 The Interior (Yoshida) Solution
8.5 Inertial-Gravity Waves8.6 Western Boundary Response
8.7 Sverdrup Flow on the Equatorial Beta-Plane8.8 Spin-Up: General Considerations
8.9 Equatorial Spin-up: Details8.10 Equatorial Spin-up: Summary
9 Yoshida Jet and Theories of the Undercurrent
9.1 Introduction 9.2 Wind-Driven Circulation in an Unbounded Ocean: f-plane
9.3 The Yoshida Jet 9.4 An Interlude: Solving Inhomogeneous Differential Equations at Low Latitudes
9.4.1 Forced eigenoperators: Hermite series 9.4.2 Hutton-Euler Acceleration of Slowly Converging Hermite Series
9.4.3 Regularized Forcing
9.4.4 Bessel Function Explicit Solution for the Yoshida Jet
9.4.5 Rational Approximations: Two-Point Pade Approximantsand Rational Chebyshev Galerkin Methods
9.5 Unstratified Models of the Undercurrent 9.5.1 Theory of Fofonoff and Montgomery (1955)
9.5.2 Model of Stommel (1960) 9.5.3 Gill(1971) and Hidaka (1961)
10 Stratified Models of Mean Currents
10.1 Introduction
10.2 Modal Decompositions for Linear, Stratified Flow 10.3 Different Balances of Forces
10.3.1 Bjerknes Balance 10.4 Forced Baroclinic Flow
10.4.1 Other Balances10.5 The Sensitivity of the Undercurrent to Parameters
10.6 Observations of the Tsuchiya Jets
10.7 Alternate Methods for Vertical Structure with Viscosity
10.8 McPhaden's Model of the EUC and SSCC's: Results
10.9 A Critique of Linear Models of the Continuously-Stratified Ocean
11 Waves and Beams in the Continuously Stratified Ocean
11.1 Introduction 11.1.1 Equatorial beams: A Theoretical Inevitability
11.1.2 Slinky Physics and Impedance Mismatch, or How WaterCn Be As Reflective As Silvered Glass
11.1.3 Shallow Barriers to Downward Beams 11.1.4 Equatorial methodology
11.2 Alternate Form of the Vertical Structure Equation
11.3 The Thermocline as a Mirror
11.4 The Mirror-Thermocline Concept: A Critique
11.5 The Zonal Wavenumber Condition for Strong Excitation of a Mode
11.6 Kelvin Beams: Background
11.7 Equatorial Kelvin Beams: Results
12 Stable Waves in Shear12.1 Introduction
12.2 U (y): Pure Latitudinal Shear12.3 Waves in Two-Dimensional Shear
12.4 Vertical Shear and the Method of Multiple Scales
13 Inertial Instability and Deep Equatorial Jets13.1 Introduction: Stratospheric Pancakes & Equatorial Deep Jets
13.2.1 Linear Inertial Instability
13.3 Centrifugal Instability: Rayleigh's Parcel Argument
13.4 Equatorial Gamma-Plane Approximation
13.5 Dynamical Equator
13.6 Gamma-plane Instability
13.7 Mixed Kelvin-Inertial Instability 13.8 Summary
14 Kelvin Wave Instability
14.1 Proxies and the Optical Theorem
14.2 Six Ways to Calculate Kelvin Instability
14.2.1 Power Series for the Eigenvalue
14.2.2 Hermite-Padé Approximants
14.2.3 Numerical
14.3 Instability for the Equatorial Kelvin Wave In the Small Wavenumber Limit
14.3.1 Beyond-All-Orders Rossby Wave Instability
14.3.2 Beyond-All-Orders Kelvin Wave Instability in Weak Shear in the Long Wave Approximation
14.4 Kelvin Instability in Shear: the General Case
15 Nonmodal Instability
15.1 Introduction15.2 Couette and Poiseuille Flow & Subcritical Bifurcation
15.3 The Fundamental Orr
15.4 Interpretation: the "Venetian Blind Effect"
15.5 Refinements to the Orr Solution
15.6 The "Checkerboard" and Bessel Solution
15.6.1 The "Checkerboard" Solution
15.7 The Dandelion Strategy
15.8 Three-Dimensional Transients
15.9 ODE Models & Nonnormal Matrices 15.10Nonmodal Instability in the Tropics
15.11Summary
16 Nonlinear Equatorial Waves
16.1 Introduction
16.2 Weakly Nonlinear Multiple Scale Perturbation Theory
16.2.1 Reduction From Three Space Dimensions to One
16.2.2 Three Dimensions & Baroclinic Modes
16.3 Solitary and Cnoidal Waves
16.4 Dispersion and Waves
16.4.1 Derivation of the Group Velocity Through the Method of Multiple Scales 16.5 Integrability, Chaos and the Inverse Scattering method
16.6 Low Order Spectral Truncation (LOST) 16.7 Nonlinear Equatorial Kelvin Waves
16.7.1 Physics of the One-Dimensional Advection (ODA) equation16.7.2 Post-Breaking: Overturning, Taylor shock or "soliton clusters" . . . . . . . . . . . . . . . . . . . . . .
16.7.3 Viscous regularization of Kelvin fronts: Burgers' equationad matched asymptotic pertubation tery
16.8 Kelvin-Gravity Wave Shortwave Resonance: Curving Fronts and
Undulations
16.9 Kelvin solitary and cnoidal waves
16.10Corner Waves and the Cnoidal-Corner-Breaking Scenario
16.11Rossby Solitary Waves
16.12Antisymmetrc Latitudinal Modes & MKdV Eq
16.13Shear effects on nonlinear equatorial waves
16.14Equatorial Modons 16.15A KdV alternative: the Regularized Long Wave (RLW) equation
16.15.1The useful non-uniqueness of perturbation theory
16.15.2Eastward-traveling modons and other cryptozoa 16.16Phenomenology of the Korteweg-deVries Equation on an
unbounded domain
16.16.1Standard form/group invariance
16.16.2The KdV equation and longitudinal boundaries
16.16.3Calculating the Solitons Only
16.16.4Elastic soliton collisions
16.16.5Periodic BC 16.16.6The KdV cnoidal wave
16.17Soliton Myths and Amazements16.17.1Imbricate series & the Nonlinear Superposition Principle
16.17.2The Lemniscate Cnoidal Wave: Strong Overlap of theSoliton and Sine Wave Regimes
16.17.3Solitary waves are not special
16.17.4Why "Solitary Wave" is the most misleading term in
oceanography
16.17.5Scotomas and discovery: the Lonely Crowd
16.18Weakly nonlocal solitary waves .
16.18.1Background 16.18.2Initial Value Experiments
16.18.3Nonlinear Eigenvalue Solutions 16.19Tropical Instability Vortices
16.20The Missing Soliton Problem
17 Nonlinear Wavepackets and Nonlinear Schroedinger Equation
17.1 The Nonlinear Schroedinger Equation for Weakly Nonlinear
Wavepackets: Envelope Solitons, FPU Recurrence and Sideband
Instability
17.2 Linear Wavepackets
17.2.1 Perturbation Parameters 17.3 Derivation of the NLS Equation from the KdV Equation
17.3.1 NLS Dilation Group Invariance17.3.2 Defocusing
17.3.3 Focusing, envelope solitons and resonance17.3.4 Nonlinear plane wave
17.3.5 Envelope solitary wave
17.3.6 NLS cnoidal & dnoidal
17.3.7 N-soliton solutions
17.3.8 Breathers 17.3.9 Modulational ("sideband") instability, self-focusing and
FPU Recurrence17.4 KdV from NLS
17.4.1 The Landau constant: Poles and resonances17.5 Weakly Dispersive Waves
17.6 Numerical Experiments
17.7 Nonlinear Schroedinger equation (NLS) summary
17.8 Resonances: Triad, Second Harmonic & Long-Wave Short Wave
17.9 Second Harmonic Resonance17.9.1 Barotropic/baroclinic triads
17.10Long Wave/Short Wave Resonance
17.10.1Landau constant poles 17.11Triad Resonances: The General Case Continued)
17.11.1A Brief Catalog of Triad Concepts
17.11.2Rescalings
17.11.3The general explicit solutions
17.12Linearized Stability Theory 17.12.1Vacillation and Index Cycles
17.12.2Euler Equations and Football
17.12.3Lemniscate Case 17.12.4Instability & the Lemniscate Case
17.13Resonance Conditions: A Problem in Algebraic Geometry 17.13.1Selection Rules and Qualitative Properties
17.13.2Limitations of Triad Theory
17.14Solitary Waves in Numerical Models 17.15Gerstner Trochoidal Waves and Lagrangian Coordinate Descriptions of Nonlinear Waves
17.16Potential Vorticity Inversion
17.16.1A Proof That the Linearized Kelvin Wave Has Zero Potential Vorticity
17.17Coupled systems of KdV or RLW equations
A Hermite Functions
A.1 Normalized Hermite Functions: Definitions and Recursion
A.2 Raising and Lowering Operators
A.3 Integrals of Hermite Polynomials and Functions
A.4 Integrals of Products of Hermite Functions A.5 Higher Order and Symmetry-Preserving Recurrences
A.6 Unnormalized Hermite Polynomials
A.7 Zeros of Hermite Series A.8 Zeros of Hermite Functions
A.9 Gaussian Quadrature A.9.1 Gaussian Weighted
A.9.2 Unweighted Integrand
A.10 Pointwise Bound on Normalized Hermite FunctionsA.11 Asymptotic Approximations
A.11.1 Interior Approximations
A.11.2 Airy Approximation Near the Turning Points
A.12 Convergence Theory
A.13 Abel-Euler Summability, Moore's Trick, and TaperingA.14 Alternative Implementation of Euler Acceleration
A.15 Tapering
A.16 Hermite Functions on a Finite Interval A.17 Hermite-Galerkin Numerical Models
A.18 Fourier Transform
A.19 Integral Representations
B Expansion of the Wind-Driven Flow in Vertical Modes
C Potential Vorticity and Y
C.1 Potential Vorticity
C.2 Potential Vorticity InversionC.3 Mass-Weighted Streamfunction
C.3.1 General Time-Varying Flows
C.3.2 Streamfunction for Steadily-Traveling Waves
C.4 Streakfunction
C.5 The Streamfunction for Small Amplitude Traveling Waves C.6 Other Nonlinear Conservation Laws
Glossary
Index
References
Approximation
4.7.1 The Method of Images
4.7.2 Dilated Images
4.7.3 Zonal Velocity
4.8 Forced Problems in the Long Wave Approximation
5 Coastally Trapped Waves and Ray-Tracing
5.1 Introduction
5.2 Coastally-Trapped Waves
5.3 Ray-Tracing for Coastal Waves
5.4 Ray-Tracing on the Equatorial Beta-plane
5.5 Coastal & Equatorial Kelvin Waves
5.6 Topographic and Rotational Rossby Waves and Potential Vorticity
6 Reflections and Boundaries
6.1 Introduction 6.2 Reflection of Midlatitude Rossby Waves from a Zonal Boundary
6.3 Reflection of Equatorial Waves from a Western Boundary 6.4 Reflection from an Eastern Boundary
6.5 The Meridional Geostrophy/Long Wave Approximation and Boundaries 6.6 Quasi-Normal Modes: Definition and Other Weakly Non-existent Phenomena
6.7 Quasi-Normal Modes in the Long Wave Approximation: Derivation
6.8 Quasi-Normal Modes in the Long Wave Approximation: Discussion
6.9 High Frequency Quasi-Free Equatorial Oscillations 6.10 Scattering & Reflection from Islands
7 Response of the Equatorial Ocean to Periodic Forcing7.1 Introduction
7.2 A Hierarchy of Models for Time-Periodic Forcing7.3 Description of the Model and the Problem
7.4 Numerical models: Reflections and "Ringing" 7.5 Atlantic versus Pacific
7.6 Summary
8 Impulsive Forcing and Spin-up
8.1 Introduction
8.2 The Reflection of the Switched-On Kelvin Wave
8.3 Spin-up of a Zonally-Bounded Ocean: Overview
8.4 The Interior (Yoshida) Solution
8.5 Inertial-Gravity Waves8.6 Western Boundary Response
8.7 Sverdrup Flow on the Equatorial Beta-Plane8.8 Spin-Up: General Considerations
8.9 Equatorial Spin-up: Details8.10 Equatorial Spin-up: Summary
9 Yoshida Jet and Theories of the Undercurrent
9.1 Introduction 9.2 Wind-Driven Circulation in an Unbounded Ocean: f-plane
9.3 The Yoshida Jet 9.4 An Interlude: Solving Inhomogeneous Differential Equations at Low Latitudes
9.4.1 Forced eigenoperators: Hermite series 9.4.2 Hutton-Euler Acceleration of Slowly Converging Hermite Series
9.4.3 Regularized Forcing
9.4.4 Bessel Function Explicit Solution for the Yoshida Jet
9.4.5 Rational Approximations: Two-Point Pade Approximantsand Rational Chebyshev Galerkin Methods
9.5 Unstratified Models of the Undercurrent 9.5.1 Theory of Fofonoff and Montgomery (1955)
9.5.2 Model of Stommel (1960) 9.5.3 Gill(1971) and Hidaka (1961)
10 Stratified Models of Mean Currents
10.1 Introduction
10.2 Modal Decompositions for Linear, Stratified Flow 10.3 Different Balances of Forces
10.3.1 Bjerknes Balance 10.4 Forced Baroclinic Flow
10.4.1 Other Balances10.5 The Sensitivity of the Undercurrent to Parameters
10.6 Observations of the Tsuchiya Jets
10.7 Alternate Methods for Vertical Structure with Viscosity
10.8 McPhaden's Model of the EUC and SSCC's: Results
10.9 A Critique of Linear Models of the Continuously-Stratified Ocean
11 Waves and Beams in the Continuously Stratified Ocean
11.1 Introduction 11.1.1 Equatorial beams: A Theoretical Inevitability
11.1.2 Slinky Physics and Impedance Mismatch, or How WaterCn Be As Reflective As Silvered Glass
11.1.3 Shallow Barriers to Downward Beams 11.1.4 Equatorial methodology
11.2 Alternate Form of the Vertical Structure Equation
11.3 The Thermocline as a Mirror
11.4 The Mirror-Thermocline Concept: A Critique
11.5 The Zonal Wavenumber Condition for Strong Excitation of a Mode
11.6 Kelvin Beams: Background
11.7 Equatorial Kelvin Beams: Results
12 Stable Waves in Shear12.1 Introduction
12.2 U (y): Pure Latitudinal Shear12.3 Waves in Two-Dimensional Shear
12.4 Vertical Shear and the Method of Multiple Scales
13 Inertial Instability and Deep Equatorial Jets13.1 Introduction: Stratospheric Pancakes & Equatorial Deep Jets
13.2.1 Linear Inertial Instability
13.3 Centrifugal Instability: Rayleigh's Parcel Argument
13.4 Equatorial Gamma-Plane Approximation
13.5 Dynamical Equator
13.6 Gamma-plane Instability
13.7 Mixed Kelvin-Inertial Instability 13.8 Summary
14 Kelvin Wave Instability
14.1 Proxies and the Optical Theorem
14.2 Six Ways to Calculate Kelvin Instability
14.2.1 Power Series for the Eigenvalue
14.2.2 Hermite-Padé Approximants
14.2.3 Numerical
14.3 Instability for the Equatorial Kelvin Wave In the Small Wavenumber Limit
14.3.1 Beyond-All-Orders Rossby Wave Instability
14.3.2 Beyond-All-Orders Kelvin Wave Instability in Weak Shear in the Long Wave Approximation
14.4 Kelvin Instability in Shear: the General Case
15 Nonmodal Instability
15.1 Introduction15.2 Couette and Poiseuille Flow & Subcritical Bifurcation
15.3 The Fundamental Orr
15.4 Interpretation: the "Venetian Blind Effect"
15.5 Refinements to the Orr Solution
15.6 The "Checkerboard" and Bessel Solution
15.6.1 The "Checkerboard" Solution
15.7 The Dandelion Strategy
15.8 Three-Dimensional Transients
15.9 ODE Models & Nonnormal Matrices 15.10Nonmodal Instability in the Tropics
15.11Summary
16 Nonlinear Equatorial Waves
16.1 Introduction
16.2 Weakly Nonlinear Multiple Scale Perturbation Theory
16.2.1 Reduction From Three Space Dimensions to One
16.2.2 Three Dimensions & Baroclinic Modes
16.3 Solitary and Cnoidal Waves
16.4 Dispersion and Waves
16.4.1 Derivation of the Group Velocity Through the Method of Multiple Scales 16.5 Integrability, Chaos and the Inverse Scattering method
16.6 Low Order Spectral Truncation (LOST) 16.7 Nonlinear Equatorial Kelvin Waves
16.7.1 Physics of the One-Dimensional Advection (ODA) equation16.7.2 Post-Breaking: Overturning, Taylor shock or "soliton clusters" . . . . . . . . . . . . . . . . . . . . . .
16.7.3 Viscous regularization of Kelvin fronts: Burgers' equationad matched asymptotic pertubation tery
16.8 Kelvin-Gravity Wave Shortwave Resonance: Curving Fronts and
Undulations
16.9 Kelvin solitary and cnoidal waves
16.10Corner Waves and the Cnoidal-Corner-Breaking Scenario
16.11Rossby Solitary Waves
16.12Antisymmetrc Latitudinal Modes & MKdV Eq
16.13Shear effects on nonlinear equatorial waves
16.14Equatorial Modons 16.15A KdV alternative: the Regularized Long Wave (RLW) equation
16.15.1The useful non-uniqueness of perturbation theory
16.15.2Eastward-traveling modons and other cryptozoa 16.16Phenomenology of the Korteweg-deVries Equation on an
unbounded domain
16.16.1Standard form/group invariance
16.16.2The KdV equation and longitudinal boundaries
16.16.3Calculating the Solitons Only
16.16.4Elastic soliton collisions
16.16.5Periodic BC 16.16.6The KdV cnoidal wave
16.17Soliton Myths and Amazements16.17.1Imbricate series & the Nonlinear Superposition Principle
16.17.2The Lemniscate Cnoidal Wave: Strong Overlap of theSoliton and Sine Wave Regimes
16.17.3Solitary waves are not special
16.17.4Why "Solitary Wave" is the most misleading term in
oceanography
16.17.5Scotomas and discovery: the Lonely Crowd
16.18Weakly nonlocal solitary waves .
16.18.1Background 16.18.2Initial Value Experiments
16.18.3Nonlinear Eigenvalue Solutions 16.19Tropical Instability Vortices
16.20The Missing Soliton Problem
17 Nonlinear Wavepackets and Nonlinear Schroedinger Equation
17.1 The Nonlinear Schroedinger Equation for Weakly Nonlinear
Wavepackets: Envelope Solitons, FPU Recurrence and Sideband
Instability
17.2 Linear Wavepackets
17.2.1 Perturbation Parameters 17.3 Derivation of the NLS Equation from the KdV Equation
17.3.1 NLS Dilation Group Invariance17.3.2 Defocusing
17.3.3 Focusing, envelope solitons and resonance17.3.4 Nonlinear plane wave
17.3.5 Envelope solitary wave
17.3.6 NLS cnoidal & dnoidal
17.3.7 N-soliton solutions
17.3.8 Breathers 17.3.9 Modulational ("sideband") instability, self-focusing and
FPU Recurrence17.4 KdV from NLS
17.4.1 The Landau constant: Poles and resonances17.5 Weakly Dispersive Waves
17.6 Numerical Experiments
17.7 Nonlinear Schroedinger equation (NLS) summary
17.8 Resonances: Triad, Second Harmonic & Long-Wave Short Wave
17.9 Second Harmonic Resonance17.9.1 Barotropic/baroclinic triads
17.10Long Wave/Short Wave Resonance
17.10.1Landau constant poles 17.11Triad Resonances: The General Case Continued)
17.11.1A Brief Catalog of Triad Concepts
17.11.2Rescalings
17.11.3The general explicit solutions
17.12Linearized Stability Theory 17.12.1Vacillation and Index Cycles
17.12.2Euler Equations and Football
17.12.3Lemniscate Case 17.12.4Instability & the Lemniscate Case
17.13Resonance Conditions: A Problem in Algebraic Geometry 17.13.1Selection Rules and Qualitative Properties
17.13.2Limitations of Triad Theory
17.14Solitary Waves in Numerical Models 17.15Gerstner Trochoidal Waves and Lagrangian Coordinate Descriptions of Nonlinear Waves
17.16Potential Vorticity Inversion
17.16.1A Proof That the Linearized Kelvin Wave Has Zero Potential Vorticity
17.17Coupled systems of KdV or RLW equations
A Hermite Functions
A.1 Normalized Hermite Functions: Definitions and Recursion
A.2 Raising and Lowering Operators
A.3 Integrals of Hermite Polynomials and Functions
A.4 Integrals of Products of Hermite Functions A.5 Higher Order and Symmetry-Preserving Recurrences
A.6 Unnormalized Hermite Polynomials
A.7 Zeros of Hermite Series A.8 Zeros of Hermite Functions
A.9 Gaussian Quadrature A.9.1 Gaussian Weighted
A.9.2 Unweighted Integrand
A.10 Pointwise Bound on Normalized Hermite FunctionsA.11 Asymptotic Approximations
A.11.1 Interior Approximations
A.11.2 Airy Approximation Near the Turning Points
A.12 Convergence Theory
A.13 Abel-Euler Summability, Moore's Trick, and TaperingA.14 Alternative Implementation of Euler Acceleration
A.15 Tapering
A.16 Hermite Functions on a Finite Interval A.17 Hermite-Galerkin Numerical Models
A.18 Fourier Transform
A.19 Integral Representations
B Expansion of the Wind-Driven Flow in Vertical Modes
C Potential Vorticity and Y
C.1 Potential Vorticity
C.2 Potential Vorticity InversionC.3 Mass-Weighted Streamfunction
C.3.1 General Time-Varying Flows
C.3.2 Streamfunction for Steadily-Traveling Waves
C.4 Streakfunction
C.5 The Streamfunction for Small Amplitude Traveling Waves C.6 Other Nonlinear Conservation Laws
Glossary
Index
References
... weniger
Bibliographische Angaben
- Autor: John P. Boyd
- 2017, 1st ed. 2018, XXIV, 517 Seiten, 27 farbige Abbildungen, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3662554747
- ISBN-13: 9783662554746
- Erscheinungsdatum: 06.10.2017
Sprache:
Englisch
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