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 Monsoon1.4 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 conditions2.3 Separation of Variables
2.4 Lamb's Parameter and all 2.5 Vertical Modes and Layer Models .
2.6 Nondimensionalization
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sp; Kelvin, Yanai, Rossby and Gravity Waves3.1 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 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 Hough-Hermite Applications
3.10 Initialization Through Hough-Hermite Expansion
3.11 Energy Relationships
3.12&nbs
p; The Equatorial Beta-Plane as the Thin Limit of the NonlinearShallow Water Equations on the Sphere
4 The "Long Wave" Approximation & Geostrophy4.1 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 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-
Tracing5.1 Introduction5.2 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 Boundaries6.1 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 Phenomena6.7 Quasi-Normal Modes in the Long Wa
ve Approximation: Derivation6.8 Quasi-Normal Modes in the Long Wave Approximation: Discussion6.9 High Frequency Quasi-Free Equatorial Oscillations
6.10 Scattering & Reflection from Islands
7 Response of the Equatorial Ocean to Periodic Forcing
7.1 Introduction7.2 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 Pacific7.6 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: Overv
iew8.4 The Interior (Yoshida) Solution8.5 Inertial-Gravity Waves
8.6 Western Boundary Response8.7 Sverdrup Flow on the Equatorial Beta-Plane
8.8 Spin-Up: General Cons
