The effect of small-scale topography on oceanic Rossby waves is investigated using a barotropic quasi-geostrophic model with Ekman friction and viscous dissipation. A multiple-scale analysis of the quasi-geostrophic equation including a two-dimensional periodic topography is developed under the assumption that the slope of the topography is much larger than the ratio of the ocean depth to the earth's radius. The analysis yields an evolution equation for the large-scale Rossby waves in which the effect of the small-scale topography is accounted for by a new dissipative term. When the spatial scale of the waves is of the same order as the radius of deformation, this term represents an additional vorticity damping that depends on the history of the large-scale flow; when the spatial scale of the wave is much larger than the radius of deformation the new term reduces to a standard Ekman friction. The enhancement of the dissipation associated with the new term is analysed for simple topographies using numerical and analytical calculations. Particular attention is paid to the limits of small Ekman friction and weak history dependence. The differences between the effect of the potential-vorticity gradient caused by the small-scale topography and that which may be caused by a small-scale flow are emphasised.
Close window or click on previous window to return to the Conference Program.
12th Conference on Atmospheric and Oceanic Fluid Dynamics