Long extratropical planetary wave propagation in the presence of slowly varying mean flow and bottom topography. Part I: the local problem

One of the most successful theories to date to explain why observed planetary waves propagate westwards faster than linear flat-bottom theory predicts has been to include the effect of background baroclinic mean flow, which modifies the potential vorticity waveguide in which the waves propagate. (Barotropic flows are almost everywhere too small to explain the observed differences.) That theory accounted for most, but not all, of the observed wave speeds. A later attempt to examine the effect of the sloping bottom on these waves (without the mean flow effect) did not find any overall speed-up. This paper combines these two effects, assuming long (geostrophic) waves and slowly varying mean flow and topography, and computes group velocities at each point in the global ocean. These velocities turn out to be largely independent of the orientation of the wavevector. A second speed-up of the waves is found (over that for mean flow only). Almost no eastward-oriented group velocities are found, so that features which appear to propagate in the same sense as a subtropical gyre would have to be coupled with the atmosphere or be density-compensated in some manner.