The propagation of compact, surface-intensified vortices over a topographic slope on the beta-plane is studied in the framework of a two-layer model. A perturbation theory is derived for a circular vortex in the upper layer with the lower layer at rest as a basic state. An integral momentum balance for the upper layer is used to obtain expressions for the velocity of the vortex center assuming the flow is quasi-stationary to leading order. This approach allows the calculation of the lower-layer flow pattern as a function of the interface shape and the slope orientation. The essential part of the lower-layer flow pattern is elongated dipolar gyres generated by the cross-slope vortex drift which remains nearly the same as in the reduced-gravity approximation, although it is slightly modified when the slope is not constant. Therefore, the major effect of the lower-layer flow is an additional along-slope propagation which is proportional to the cross-slope speed and the ratio of the interface slope to the topographic slope. Both along-slope and cross-slope drift components are found to be also affected by the slope variation.
Sutyrin, Georgi. 2001. "Effects of topography on the beta-drift of a baroclinic vortex." Journal of Marine Research 59, (6). https://elischolar.library.yale.edu/journal_of_marine_research/2418