Large-scale motions in the ocean and the atmosphere case of stable stratification (ocean, stratosphere)

Characteristics of large-and meso-scale ocean flows ( 10 km < L < 6000 km ) : Thin layer of fluid: H << L Stable stratification Importance of Earths rotation T rot < T dyn Ro = = T rot / T dyn = U/2 L<1

Apparent forces in a rotating frame with = z

Navier-Stokes equations in a rotating frame with = z

Navier-Stokes equations in a rotating frame with = z

Navier-Stokes in a rotating frame with = z

Boussinesq approximation

Thin layer, stable stratification: hydrostatic approximation (L > 10 km)

Incompressible, hydrostatic fluid: primitive equations

Problem: A spherical Earth. Motion on a sphere: local tangent plane

Incompressible, inviscid fluid on a local Cartesian plane at midlatitudes

Problema: lapprossimazione geostrofica è diagnostica abbiamo bisogno di una approssimazione prognostica

Primitive equations on a local Cartesian plane at midlatitudes

Primitive equations on the beta plane

Primitive equations on the beta plane