Baroclinic Instabilities of a Deep Fluid

Abstract

An analytical study is made of the baroclinic instability problem for a zonal wind U (z), by modifying the Eady model through relaxation of the shallow-layer approximation. The linearized perturbation equation is derived, including the mass-divergence effect in the continuity equation and the non-hydrostatic effect in the vertical momentum equation. When U (z) = constant, the non-hydrostatic effect decreases the effective propagation speeds of wave having short horizontal wavelengths. Assuming that the zonal current velocity profile is linear, two limiting cases are treated (i.e., the geostrophic-type instability limit and the symmetric-type instability limit). For the case of the geostrophic-type instability limit, the mass-divergence effect seems to reduce primarily the wave propagation speeds, while the unstable wave growth rates are decreased by both the mass-divergence and the non-hydrostatic effects. However, for the case of the symmetric-type instability limit, the mass-divergence effect is quite mild, but the non-hydrostatic effect strongly affects the unstable wave growth rates.