On the baroclinic instability of nonplanar flows

Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow andvice versa. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.