In a rotating system in curved geometry the Coriolis parameter has a gradient which gives rise to the beta effect. This is the case for spherical geometry but not for planar geometry. Then there is one more step down to the 2D incompressible non-rotating Euler equation. The Navier-Stokes equations describe the motion in a 3D compressible viscous fluid. They serve as a model for the fluid dynamics aspects of the atmosphere and oceans in which many processes take place with various length and time scales.
Dissipation is determined by viscosity, and convection by conductivity.
The zero-order transport equations are the 3D Euler equations that describe the motion in a 3D compressible nonviscous fluid. These equations are studied in a rotating system under the action of gravity for a stably stratified fluid. The shallow-water equations describe the motion in a homogeneous incompressible hydrostatic fluid. The tidal equations describe the response of a stably stratified incompressible hydrostatic fluid under forcing. Forced tidal motion in the oceans is caused by the gravitational pull of the moon, in the atmospere by thermal forcing of the sun.