Equations of Quasi-geostrophic Baroclinic Motion
As we mentioned above, in a moving baroclinic medium isobaric and isopycnic (or iso-density) surfaces usually do not match. Recall that in the case of an incompressible baroclinic fluid its density and pressure are independent quantities, while the density of the baroclinic gas depends not only on pressure, but on yet one more thermodynamical quantity, for instance on the potential temperature Θ, i.e., ρ=ρ(p,Θ). (I would like to emphasize yet again that for the sake of simplicity, the possibility of phase transitions in the medium is not considered here, so there are only two independent thermodynamical variables.) Denote by the index s equilibrium distributions of thermodynamical quantities, which describe the medium state in the absence of relative motions, and use them as the background characteristics of the medium, while its motion is a deviation from this background.