5. Quasi-Geostrophic Models of Continuously Stratified Flows

The transition from layered flows to continuously stratified flows requires the use of thermodynamic equations basically because, in the latter models, neither horizontal current is depth or height independent nor density fluid is a constant. Thus, vertical integration of the incompressibility equation is no longer fit for explicitly yielding the vertical velocity field, and the latter must be inferred on the basis of further assumptions about large-scale geophysical flows. These assumptions concern the resort to the thermodynamic equations already expounded in Sec. 2.4.2. In particular, in the core of the oceanic water body, sea water density is conserved up to a high degree of approximation, so that (2.588) applies there; on the other hand, near the ground, the atmosphere undergoes thermal forcing because of the long-wave radiation emitted by the Earth and the greenhouse effect, so that (2.589) applies in the troposphere. In Chap. 5, the adiabatic quasi-geostrophic circulation on two typical ocean scales will be developed together with the analysis of steady, quasi-geostrophic atmospheric waves under the effect of a spatially modulated thermal forcing. Moreover, the effect of bathymetry on ocean currents and of topography on adiabatic winds are also taken into account in some typical cases.