Baroclinic Instability over a Slope. Part II: Finite-Amplitude Theory

Abstract

Baroclinic instability of a circular current is modified by the presence of a unidirectional bottom slope.An analytical theory is developed for the slightly unstable flow regime over a weak slope. The presence of theslope creates azimuthal sidebands n? to the basic azimuthal wavenumber n, of the instability. The interaction of the sidebands with the slope causes a decrease in the stability of the flow compared with that inthe case with a flat bottom. The interaction of the sidebands with the primary baroclinic wave produces atime-independent asymmetric current. In addition, the basic wave self-interaction produces a time-independent current which flows up the slope and generates asymmetric vorticity. This latter effect is predominant when the Rossby radius of deformation is much smaller than the radius of the basic current.