Symmetric instability of stratified geostrophic flow

The linear stability of a stably stratified geostrophic current between parallel horizontal planes has been investigated theoretically. 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/f ², where N is the Brunt-Väisälä frequency and f the (constant) Coriolis parameter. When E is small, the horizontal scale of the marginally stable disturbance is ∝ H(1 + Pr S)^½ E ^⅓, where H is the distance between the bounding planes. Large values ofE stabilize the system. For given viscosity, and S = 0, the system is destabilized by increasing Pr, while for S ≫ 1 destabilization occurs if Pr ≠ 1.