The effect of bottom topography on the speed of long extratropical planetary waves

This paper examines how slowly varying topography induces changes in all as pects 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 arbit rary 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 s peed. Increases occur on the western and equatorward sides of hills. Focusi ng of ray trajectories and caustics are common features of the solutions. D espite a bias between slowdown and speedup, on average there is little spee dup except in high latitudes (where long-wave theory is less applicable). C alculations are performed for five main ocean basins, assuming waves are ge nerated at the eastern coastline, using smoothed topography. These calculat ions confirm the above findings: there are significant local effects on wav e speed, but these largely cancel over the basin scale. Thus, topographic e ffects cannot explain recent observations, which demonstrate long planetary waves propagating about twice as fast as linear theory. The presence of me an flow, which induces changes to the planetary vorticity gradient, remains the prime candidate for the observed speedup.