Three‐dimensional non‐geostrophic disturbances in a baroclinic zonal flow

Abstract

Abstract A study is made to determine the stability properties of a baroclinic zonal current on which small amplitude three‐dimensional non‐geostrophic disturbances are superimposed. The flow is assumed to be bounded to the north and south by rigid vertical walls and the Rossby number Ro is taken to be small compared to unity. It is then shown that if the perturbation quantities are expanded in power series in Ro the leading or zero order terms in the series correspond to the quasi‐geostrophic solution obtained by Eady (1949) and that the higher order terms represent the “non‐geostrophic” effects neglected by the latter. It is shown that to the second order in Ro the non‐geostrophic effects decrease the growth rates of those disturbances which are found to be unstable according to Eady's analysis but do not alter their speed of propagation. The results indicate, on the other hand, that to the same order of approximation the stable waves travel at a speed which is different from that given by Eady's solution. The modification of the perturbation wave structure by the non‐geostrophic effects is also investigated. It is found in particular that to the first order in Ro the latter produce a northward tilt with height in the ridge (or trough) lines of the meridional and vertical particle velocity fields away from the lateral boundaries.