The Generalization of Semigeostrophic Theory to the β-Plane
Published Web Locationhttps://doi.org/10.1175/1520-0469(1990)047<1714:TGOSTT>2.0.CO;2
We develop here the isentropic–geostrophic coordinate version of semigeostrophic theory on a midlatitude β-plane. This approach results in a simple mathematical form in which the horizontal ageostrophic velocities are implicit and the entire dynamics reduces to a predictive equation for the potential pseudodensity and an invertibility relation. Linearized versions of the theory lead to a generalized Charney–Stern theorem for combined barotropic–baroclinic instability and to Rossby wave solutions with a meridional structure different from that in quasi-geostrophic theory.