The vertical structure of eddies in a horizontally- and vertically-sheared surface jet is examined, using a two layer system with a sloping bottom. Baroclinic instability occurs over weak slopes, as seen in previous studies, producing strong eddies at depth which are characteristically shifted downstream from the surface eddies. Instability is suppressed over large positive slopes (such that the flow is parallel to the direction of topographic wave propagation) but persists over negative slopes. The growth rates are suppressed with a negative slope and the eddy scale decreases with slope inclination. However, if the surface jet is narrow enough (less than than roughly four deformation radii), barotropic (lateral) instability occurs in the upper layer. This produces surface eddies whose size is independent of the bottom slope. Then the deep eddies are much weaker and are aligned with the surface eddies, so that the meridional heat fluxes are nearly zero. Adding a sinusoidal ridge to the slope further reduces baroclinic instability, favoring lateral instability in the upper layer. With modest topographic amplitudes of only 5-10 m, lateral instability dominates for all slopes.
Seismic surveys of the ocean bottom suggest that such topographic amplitudes occur routinely beneath the Gulf Stream, Kuroshio and the Antarctic Circumpolar Current. As such, these currents may be more prone to lateral than baroclinic instability. Consistent with this, slices of the vertical vorticity from a 1/50th of a degree HYCOM simulation of the North Atlantic reveal cyclones beneath Gulf Stream troughs which are much weaker than and largely aligned with the near-surface eddies.