||The stability of a horizontally- and vertically-sheared surface jet is examined, with a focus on the vertical structure of the resultant eddies. Over a flat bottom, the instability is mixed baroclinic/barotropic, producing strong eddies at depth which are characteristically shifted downstream relative to the surface eddies. Baroclinic instability is suppressed over a large slope for retrograde jets (with a flow anti-parallel to topographic wave propagation), and to a lesser extent for prograde jets (with flow parallel to topographic wave propagation), as seen previously. In such cases, barotropic (lateral) instability dominates if the jet is sufficiently narrow. This yields surface eddies whose size is independent of the slope but proportional to the jet width. Deep eddies still form, forced by interfacial motion associated with the surface eddies, but they are weaker than under baroclinic instability and are vertically aligned with the surface eddies. A sinusoidal ridge acts similarly, suppressing baroclinic instability and favoring lateral instability in the upper layer.
A ridge with a 1 km wavelength and an amplitude of roughly 10 m is sufficient to suppress baroclinic instability. Surveys of bottom roughness from bathymetry acquired with shipboard multibeam echosounding reveal that such heights are common, beneath the Kuroshio, the Antarctic Circumpolar Current and, to a lesser extent, the Gulf Stream. Consistent with this, vorticity and velocity cross sections from a 1/50° HYCOM simulation suggest that Gulf Stream eddies are vertically aligned, as in the linear stability calculations with strong topography. Thus lateral instability may be more common than previously thought, due to topography hindering vertical energy transfer.