Stability of a Flow Over Bottom Topography: A General Condition and a Linear Analysis in a Two‐Layer Quasi‐Geostrophic Model With a Possible Application to a Kuroshio Meander

Abstract

AbstractThe stability of a two‐layer quasi‐geostrophic flow over bottom topography is examined by combining a method of obtaining a sufficient condition for stability and a linear stability analysis. First, using a conserved quantity called pseudoenergy that is proportional to the square of the disturbance amplitude, a sufficient condition for stability is derived for the simplest steady background field in which the potential vorticity and the stream function are proportional to each other. The theoretically obtained condition enables us to judge the stability of various background fields by explicitly taking into account the limitation imposed on the scale of the disturbance by the domain size and/or boundary conditions. Applying the stability condition to a special case of a sinusoidal background flow and topography then shows that the stable range extends to the area where the currents flow with shallower water on their right in both the upper and lower layers. The stable range is broadened as the disturbance becomes limited to smaller horizontal scales. A linear stability analysis shows that this broadening is mainly due to the suppression of barotropic instability that works effectively at large scales. Finally, a numerical simulation is performed with a realistic situation of a Kuroshio meander over a seamount south of Japan in mind. The results suggest that the theory is useful to identify a stable flow with negative‐definite pseudoenergy, which can be achieved under realistic ocean conditions where the scale of the disturbance is moderately restricted by a basin bounded by prominent topographic features.