Non-Geostrophic and Non-Hydrostatic Stability of a Baroclinic Fluid

Abstract

Non-geostrophic and non-hydrostatic effects on the stability of Eady's baroclinic model are studied in the range of small Richardson numbers (Ri). The latitudinal as well as the longitudinal variations of wave perturbations are included. There are two growth rate maxima, one is that of the ordinary baroclinic instability on the l (latitudinal wave number)=0 axis, and the other is that of a symmetric instability on the k (longitudinal wave number)=0 axis and |ι|→∞ when Ri<1.There appears an unstable mode destabilized by the inertial effect. The non-hydrostatic effect supresses the appearance of Helmholtz type instability in the range of positive Ri. There is little difference between eigenvalues in the case (k, ι) and (k, -ι), but the structure of perturbations in the two cases differs greatly with the increase of |l| . The effect of the β-term is also studied under non-geostrophic and non-hydrostatic conditions.