Stability properties of an arbitrarily oriented mean flow

Abstract

The linear properties of eddies growing in a mean flow that is oriented in any horizontal direction are analyzed. The mean flow only varies with height. The growth rate, phase speed and structure of the waves change dramatically with different orientations of the mean flow and the waves. These properties are related to the vertical profile of the mean total interior potential vorticity gradient, Ǭ. Ǭ is largest for those orientations where the Coriolis terms are most positive; it is smallest when those terms are most negative. When Ǭ is maximized; the growth rates are largest, the propagation speed is least, the upper level eddy amplitude is enhanced and the sharpest vertical tilts of the trough and ridge axes occur at lower levels. The opposite properties result when Ǭ is minimized. Limiting the horizontal extent of the wave (by using side-wall boundaries) causes cross-flow asymmetry in the wave structure and induces horizontal tilts to the wave axes.