1. Governing Equations
(a) Rotation and stratification
Rossby, Froude and Burger numbers
Buoyancy force and radiative-convective equilibrium
(b) Thermodynamics and the equation of state
(c) The exact primitive equations
(d) The primitive equations with the traditional and hydrostatic approximations
(e) The continuity equation and the anelastic and Boussineq approximations
(f) Some remarks on the ocean and atmosphere
2. Potential Vorticity
(a) Early developments of Kelvin and Bjerknes
(b) Ertel’s derivation
(c) Haynes and McIntyre’s theorem (Impermeability theorem)
3. Quasi-geostrophic Dynamis
(a) Governing equations
(b) Quasi-equilibrium dynamics
(c) Secondary circulation equation
(d) Non-acceleration theorem and the EP flux
4. Vertical Normal Modes of a Continuous Stratified Fluid
(a) Governing equations and boundary conditions
(b) Vertical transform and divergent barotropic primitive equations (shallow water equations)
(c) Barotropic (external) and baroclinic (internal) models
5. Divergent Barotropic Primitive Equations
(a) Linearization and nondimensionalization
(b) Eigenvalues and eigenfunctions on f plane and on equatorial Beta-plane
(c) Topography, Rossby, and vortex Rossby waves
(d) Geostrophic adjustment
(e) Potential vorticity principle, invertibility principle and the final geostrophically balanced state
6. Nondivergent Barotropic Equations
(a) From the divergent barotropic to the nondivergent barotropic model
(b) Barotropic instability
(c) Emergence of coherent structures in two-dimensional turbulence
(d) The binary vortex interactions
(e) Two-dimensional turbulence on the sphere: the Rhine’s barrier
(f) Two-dimensional turbulence and three-dimensional turbulence
7. Large-Scale Ocean Circulation
(a) Current without friction; geostrophic flow
(b) Current with friction; wind-driven circulation
(c) Sverdrup balance
(d) Westward intensification
Stommel’s contribution
Munk’s solution
Boundary-layer approach
(e) Thermohaline effect and abyssal circulation
8. Boundary Dynamics
(a) Boundary perturbation methods
(b) Ekman layer
(c) Ekman and Reynold numbers
(d) Marine stratocumulus and the mixed layer model
9. Typhoon Dynamics
(a) Ooyama’s cooperative intensification theory
(b) Balanced vortex theory and secondary circulation equation
(c) Track dynamics and the beta-gyre
(d) Vortex axisymmetrization and merger
(e) Asymmertric eye dynamics
10. Large-Scale Motion Near the Equator
(a) Buoyant convection and trimodal characteristics
(b) Dynamical adjustment of the trade wind inversion layer
(c) Heat induced tropical circulations
(d) Pooling of synoptic vorticity in the tropics
(e) ITCZ breakdown