Note: Intro -- Preface -- References -- Contents -- Symbols & -- Notation -- 1 An Observational Overview of the Equatorial Ocean -- 1.1 The Thermocline: The Tropical Ocean as a Two-Layer Model -- 1.2 Equatorial Currents -- 1.3 The Somali Current and the Monsoon -- 1.4 Deep Internal Jets -- 1.5 The El Niño/Southern Oscillation (ENSO) -- 1.6 Upwelling in the Gulf of Guinea -- 1.7 Seasonal Variations of the Thermocline -- 1.8 Summary -- References -- 2 Basic Equations and Normal Modes -- 2.1 Model -- 2.2 Boundary Conditions -- 2.3 Separation of Variables -- 2.4 Lamb's Parameter, Equivalent Depths, Kelvin Phase Speeds and All that -- 2.5 Vertical Modes and Layer Models -- 2.6 Nondimensionalization -- References -- 3 Kelvin, Yanai, Rossby and Gravity Waves -- 3.1 Latitudinal Wave Modes: An Overview -- 3.2 Latitudinal Wave Modes: Structure and Spatial Symmetries -- 3.3 Dispersion Relations: Exact and Approximate Frequencies -- 3.4 Analytic Approximations to Equatorial Wave Frequencies -- 3.4.1 Explicit Formulas -- 3.4.2 Long Wave Series -- 3.5 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 Applications of the Hough-Hermite Basis: Linear Initial-Value Problems -- 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 -- References -- 4 The ``Long Wave'' Approximation & -- Geostrophy -- 4.1 Introduction -- 4.2 Quasi-Geostrophy -- 4.3 The ``Meridional Geostrophy'', ``Low Frequency'' or ``Long Wave'' Approximation -- 4.4 Boundary Conditions -- 4.5 Frequency Separation of Slow [Rossby/Kelvin] and Fast [Gravity] Waves. , 4.6 Initial Value Problems in an Unbounded Ocean, Linearized About a State of Rest, in the Long Wave Approximation -- 4.7 Reflection from an 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 -- References -- 5 The Equator as Wall: 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 and Equatorial Kelvin Waves -- 5.6 Topographic and Rotational Rossby Waves and Potential Vorticity -- References -- 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 and Reflection from Islands -- References -- 7 Response of the Equatorial Ocean to Periodic Forcing -- 7.1 Introduction -- 7.2 A Hierarchy of Models for Time-Periodic Forcing -- 7.3 Description of the Model and the Problem -- 7.4 Numerical Models: Reflections and ``Ringing'' -- 7.5 Atlantic Versus Pacific -- 7.6 Summary -- References -- 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 Waves -- 8.6 Western Boundary Response. , 8.7 Sverdrup Flow on the Equatorial Beta-Plane -- 8.8 Spin-Up: General Considerations -- 8.9 Equatorial Spin-Up: Details -- 8.10 Equatorial Spin-Up: Summary -- References -- 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 Padé Approximants and 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) -- References -- 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 in the ``Bjerknes'' Approximation -- 10.4.1 Other Balances -- 10.5 The Sensitivity of the Undercurrent to Parameters -- 10.6 Observations of Subsurface Countercurrents (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, Wind-Driven Ocean -- References -- 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 Water Can 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 -- References -- 12 Stable Linearized Waves in a Shear Flow -- 12.1 Introduction -- 12.2 U(y): Pure Latitudinal Shear -- 12.3 Neutral Waves in Flow Varying with Both Latitude -- 12.4 Vertical Shear and the Method of Multiple Scales -- References -- 13 Inertial Instability, Pancakes and Deep Internal Jets -- 13.1 Introduction: Stratospheric Pancakes and Equatorial Deep Jets -- 13.2 Particle Argument -- 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 -- References -- 14 Kelvin Wave Instability: Critical Latitudes and Exponentially Small Effects -- 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 Methods -- 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 -- References -- 15 Nonmodal Instability -- 15.1 Introduction -- 15.2 Couette and Poiseuille Flow and Subcritical Bifurcation -- 15.3 The Fundamental Orr Solution -- 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 and Nonnormal Matrices -- 15.10 Nonmodal Instability in the Tropics -- 15.11 Summary -- References -- 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 and 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) Equation: ut + c ux + b u u x =0 -- 16.7.2 Post-Breaking: Overturning, Taylor Shock or ``Soliton Clusters''? -- 16.7.3 Viscous Regularization of Kelvin Fronts: Burgers' Equation And Matched Asymptotic Perturbation Theory -- 16.8 Kelvin-Gravity Wave Shortwave Resonance: Curving Fronts and Undulations -- 16.9 Kelvin Solitary and Cnoidal Waves -- 16.10 Corner Waves and the Cnoidal-Corner-Breaking Scenario -- 16.11 Rossby Solitary Waves -- 16.12 Antisymmetric Latitudinal Modes and the Modified Korteweg-deVries (MKdV) Equation -- 16.13 Shear Effects on Nonlinear Equatorial Waves -- 16.14 Equatorial Modons -- 16.15 A KdV Alternative: The Regularized Long Wave (RLW) Equation -- 16.15.1 The Useful Non-uniqueness of Perturbation Theory -- 16.15.2 Eastward-Traveling Modons and Other Cryptozoa -- 16.16 Phenomenology of the Korteweg-deVries Equation on an Unbounded Domain -- 16.16.1 Standard Form/Group Invariance -- 16.16.2 The KdV Equation and Longitudinal Boundaries -- 16.16.3 Calculating the Solitons Only -- 16.16.4 Elastic Soliton Collisions -- 16.16.5 Periodic BC -- 16.16.6 The KdV Cnoidal Wave. , 16.17 Soliton Myths and Amazements.