Mixed Topographic-Planetary Waves in a Stratified Ocean on a Background Flow

The work presents the development of Rhines' theory for mixed topographic-planetary waves in a stratified ocean on a background current. The vertical anisotropy of baroclinic Rossby waves has been established depending on the slopes of the topography. If for positive slopes (water shallowing to the north) the baroclinic mode node shifts downward, then for negative slopes the frequency and phase velocity decrease and the vertical node shifts upward. Estimates of frequency variability for vertical modes at a negative bottom slope were obtained. For weak changes in bottom topography in the long-wave limit, an analytical asymptotic expression of the dispersion relation for the surface mode is constructed for positive and negative slopes. The dispersion curves in one-dimensional and two-dimensional cases were analyzed numerically. It is shown that the range of influence of topography on baroclinic waves reaches maximum deviations of the order of 50% in the long-wave part of the spectrum.