Symmetric instability of stratified geostrophic flow.

Abstract

The disturbances considered are two-dimensional with axes aligned along the flow direction. Diffusive processes enter the stability problem through the Ekman number, E, and the Prandtl number Pr. The analysis is valid for general vertical stable stratification, characterized by S = N2/f2, where N is the Brunt- Vaisala frequency and f the (constant) Coriolis parameter. When E is small, the horizontal scale of the marginally stable disturbance is proportional to H(1 + Pr S)1/2 E 1/3, where H is the distance between the bounding planes. Large values of E stabilize the system. For given viscosity, and S = 0, the system is destabilized by increasing Pr, while for S more than 1 destabilization occurs if Pr is not equal to 1.- from Author