Rossby Wave Frequency Change Induced by Small-Scale Topography

A homogenization technique is used to study the change in the frequency of planetary Rossby waves that results from their interaction with a small-scale two-dimensional topography. The frequency change is computed explicitly for a topography consisting of a random distribution of well-separated cylindrical seamounts; it corresponds to a phase-speed increase (decrease) when the flat-bottom Rossby wave frequency is larger (smaller) than a typical topographic frequency. The topography is also shown to lead to a finite damping of the Rossby waves, even in the limit of infinitesimally small Ekman friction.