A Comparison of Hydrostatic and Nonhydrostatic Wave-CISK

Abstract

Most conventional wave-CISK models have been used in the study of circulations with aspect ratios less than one, and as a result have been hydrostatic. In general, the most unstable waves in the models are the small-scale high frequency ones. For these waves the hydrostatic assumption is invalid. It therefore seems appropriate to consider a model in which the high aspect ratio waves are treated correctly, i.e., a nonhydrostatic one. In this paper, a comparison between a hydrostatic and a nonhydrostatic wave-CISK model is made. In the hydrostatic model, there is no coupling of the horizontal and vertical scales of the waves and this results in its lack of scale selection. The nonhydrostatic model has an explicit coupling in it and this leads to a preferred scale for the growth of the waves. For all the cases considered, the most unstable wave has an aspect ratio of order one.