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.

The 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. Plain Language Summary: An oceanic flow passing over bottom topography is sometimes stable and persistent, while it sometimes becomes unstable and generates meanders and eddies. The stability of a flow is strongly affected by the existence of bottom topography as well as by the possible scale of the generated disturbance, which is often prescribed by the size of an ocean basin within which the disturbance is confined. This study presents a new criterion that can predict the stability of a flow over bottom topography, taking into account the possible scale of the disturbance. The theoretically obtained stability condition predicts that a current is more stabilized when it flows with shallower water on the right, and as the disturbance is limited to smaller scales. Furthermore, an idealized numerical simulation shows that the condition can successfully predict that a flow similar to the large meander path of the Kuroshio passing over a seamount is stable, whereas a flow similar to the straight path of the Kuroshio becomes unstable when it passes over the seamount. This result is consistent with recently revealed path variability of the Kuroshio south of Japan. Key Points: A stability condition of a two‐layer quasi‐geostrophic flow is derived that takes into account the possible spatial scale of the disturbanceThe condition predicts that a flow with shallower water on the right becomes more stable as the disturbance is limited to smaller scalesThe condition successfully judges the stability of a flow similar to the large meander and straight paths of the Kuroshio over a seamount [ABSTRACT FROM AUTHOR]