Some stability properties of large-scale baroclinic flows with nonlinear zonal current profile

Abstract

The stability properties of a baroclinic zonal current with nonlinear velocity profile are investigated. The integral method is applied to the governing eigenvalue equation having the vertical velocity as the dependent variable. Expressed in terms of the Rossby number and the Richardson number, stability criteria, unstable regions in the complex c plane, and the upper bound of the unstable wave growth rate are found. Some differences in the results are noted between the present model and the quasi-geostrophic streamfunction model, particularly in connection with the effect of the velocity profile curvature term Uzz. It is conjectured in the present model that, depending on extreme behaviors of Uzz, the propagation speed of unstable waves can be greater than Umax or smaller than Umin. © 1977 Oceanographical Society of Japan.