Time-dependent topographic meandering of a baroclinic current

Abstract

The effects of baroclinic instability of a broad ocean current, flowing in an ocean basin with a plane sloping bottom, on the path of the current are studied. The set of equations governing this path and its variation with depth are the vorticity equation and the heat equation. It is assumed that the vertical and horizontal temperature contrasts are comparable as suggested by observations of the Gulf Stream. When quasi-geostrophy is assumed in addition, this implies that the leading contribution to the heat equation does not contain the vertical advection of the basic stratification. This corresponds to the long-wave approximation of the usual baroclinic-instability problem. The heat equation determines the vertical variation of the path and when this is combined with the vorticity equation, the equation governing the path at one level is obtained. The path equation requires a specification of the direction and curvature at the inlet and these conditions are taken to be time-dependent. When these conditions contain frequencies for which the current is unstable, meanders in the path of the current increase in amplitude downstream of the inlet. When the path at the inlet changes suddenly from one parallel to the isobaths to one making a small angle with them, the region of instability in which the amplitude of the meanders increases, is confined to a restricted segment of the path, at soms distance from the inlet. This region becomes advected with the basic current, and its extent increases with time. The amplitude of the meanders in this region increases while their wavelength decreases in time because the shorter waves are unstabler. The increase in amplitude and decrease in wavelength in a restricted segment of the path could lead to eddy formation in a finite-amplitude model and may therefore suggest a mechanism for eddy formation in the Gulf Stream.