The stability of zonal jets in a rough-bottomed ocean on the barotropic beta plane

The author considers the stability of a barotropic jet on the beta plane, u sing the model of a "rough-bottomed ocean" (i.e., assuming that the horizon tal scale of bottom irregularities is much smaller than the width of the je t). An equation is derived, which governs disturbances in a sheared flow ov er one-dimensional bottom topography. such that the isobaths are parallel t o the streamlines. Interestingly, this equation looks similar to the equati on for internal waves in a vertically stratified current, with the density stratification term being the same as the topography term. It appears that the two effects work in a similar way, that is, to return the particle to t he level (isobath) where it "belongs" (determined by its density or potenti al vorticity). Using the derived equation, the author obtains a criterion o f stability based on comparison of the mean-square height of bottom irregul arities with the maximum shear of the current. It is argued that the influe nce of topography is a stabilizing one, and it turns out that "realistic" c urrents can be stabilized by relatively low bottom irregularities (30-70 m) . This conclusion is supported by numerical calculation of the growth rate of instability for jets with a Gaussian profile.