Topographic eddies in a stratified ocean

The generation of topographic eddies and wave wakes over low seamounts in vertically and horizontally sheared zonal currents is studied on the $f$- and $\beta$-plane within the context of the baroclinic quasigeostrophic model. Water stratification and the vertical shear in velocity are shown to result in the joint effect of baroclinicity and a current velocity shift ('JEBACS'), which essentially transforms the manifestation of $\beta$-effect on the $\beta$-plane and can bring about pseudo $\beta$-effect on the $f$-plane. Similar to the $\beta$-effect, 'JEBACS' plays an important part in the generation of above- mountain topographic eddies and wave wakes. The spectrum of the Sturm–Liouville operator for vertical modes can have negative eigenvalues in the beginning of the spectrum not only on the $\beta$-plane but also on the $f$-plane. The negative eigenvalues in the spectrum result in the appearance of wave modes in the respective Helmholtz operator. The wave modes account for wave wakes behind seamounts. Captured Rossby waves, which always appear in any homogeneous eastward flow behind a seamount on the $\beta$-plane, may not appear in flows with vertical shear in velocity, even though these flows are also directed eastward. In this context, it was shown that the use of averaged velocities with the aim to derive the conclusion regarding the generation of waves that form the wave wake can be incorrect in the case of flows with vertical shift. This is an important distinction of the flows with velocity shift from homogenous flow in the case of flows around seamounts. Another important type of stratified shear currents is represented by two-layer flows with differently directed flows in different layers. The notion of eastern or western flows makes no sense in this case. Nevertheless, wave modes also form in such flows. The topographic eddy in such two-layer flows has the form of an eddy lens concentrated near the interface between layers. In one layer, the wave wake may be located upstream of the mountain, rather than downstream of it.