The Effect of Bottom Topography on the Speed of Long Extratropical Planetary Waves

Abstract

This paper examines how slowly varying topography induces changes in all aspects of long planetary wave propagation, including phase speed and surface signature, through steering effects. The approach introduces a method for the exact solution of the vertical topographic eigenvalue problem for arbitrary realistic stratification and ray theory in the horizontal. It is shown that, for observed stratifications, first internal mode topographic waves have phase speeds between about 0.4 and twice the local flat-bottom phase speed. Increases occur on the western and equatorward sides of hills. Focusing of ray trajectories and caustics are common features of the solutions. Despite a bias between slowdown and speedup, on average there is little speedup except in high latitudes (where long-wave theory is less applicable). Calculations are performed for five main ocean basins, assuming waves are generated at the eastern coastline, using smoothed topography. These calculations confirm the above findings: there are significant local effects on wave speed, but these largely cancel over the basin scale. Thus, topographic effects cannot explain recent observations, which demonstrate long planetary waves propagating about twice as fast as linear theory. The presence of mean flow, which induces changes to the planetary vorticity gradient, remains the prime candidate for the observed speedup.