Credits: 3 (3-0-0)
Description
(i) Fundamental concepts in geophysical fluid dynamics: equations of motion on a rotating planet, vorticity and circulation, conservation of potential vorticity, thermal wind, Taylor-Proudman theorem; Ertel-Rossby invariants; Ertel’s potential vorticity conservation theorem; consequences of geostrophic and hydrostatic approximation.
(ii) Shallow-water theory: derivation of shallow-water equations; derivation of vorticity equation; linearized form of shallow-water equations; plane waves in a layer of constant depth; dispersion diagrams of Kelvin and Poincaré waves. (iii) Rossby wave theory: mechanism of Rossby wave generation; inertial boundary currents; derivation of potential vorticity on beta-plane; quasigeostrophic scaling; Rossby waves in a zonal current; method of multiple scales for linear potential vorticity equation; reflection and radiation of Rossby waves; generation of Rossby waves by an initial disturbance; Quasigeostrophic normal modes in a closed basin; resonant interaction; energy and enstrophy conservation; upscale energy transfer. (iv) Friction effects in geophysical flows: Turbulent Reynolds stresses; Ekman layers in a homogeneous, incompressible rotating fluid; Ekman layer on a sloping surface; quasigeostrophic potential vorticity with friction and topography. (v) Instability theory: linear stability; normal modes; growth rates; baroclinic instability; Eady model and Charney model; instability in a two-layer model.