Barotropic instability of flow along a trench

Abstract

The linear stability of a laterally sheared barotropic flow along a trench is analyzed. The depth and mean flow profiles used in the model are piecewise constant and piecewise linear, respectively. As a consequence the stream function and dispersion relation describing the perturbation field can be written in terms of elementary functions. The dispersion relation, being a quartic in the wave frequency, yields four neutral wave modes: two shear waves, a shelf wave and a trench wave. An instability arises when two shear wave dispersion curves coalesce or when one of the shear wave curves coalesces with either a shelf or a trench wave dispersion curve. Further, because of the quartic nature of the dispersion relation, the stability diagrams can have overlapping regions of instability in Rossby number—wavenumber space.

The model is applied to the Alaskan Stream off Kodiak Island, where infrared satellite images reveal the presence of wavelike temperature fronts with scales of either 90–100 km or 30–40km. It is suggested that the larger scale waves may originate from one of the types of barotropically unstable waves discussed in this paper.