It is shown that (i) internal gravity waves propagating along a horizontal density gradient in a uniformly rotating ocean can exist for a range of slightly smaller frequencies than is possible in the absence of such a gradient, (ii) such waves exhibit a phase difference from top to bottom, and (iii) they exchange energy with the geostrophic current, which balances the density-induced pressure gradient....
Healey, David, and Paul H. LeBlond. 1969. "Internal wave propagation normal to a geostrophic current." Journal of Marine Research 27, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1145