The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level. Analytically, we are limited to special choices of bottom topography, such as sinusoidal corrugations or an undulating continental slope, so long as the topographic restoring effect equals or exceeds that due to planetary curvature (the beta-effect). (Very slight topographic features, on the other hand, provide weak, resonant interactions between Rossby waves.)

Integral properties of the equations, and computer experiments reported elsewhere, verify the following results found in the analytical models: typical frequencies of oscillation are [lsim ]fδ, where f is the Coriolis frequency and δ measures the fractional height of the bottom bumps; an initially imposed flow pattern of large scale will rapidly shrink in scale over severe roughness (even the simplest analytical model shows this rapid change in spatial structure with time); and energy propagation can be severely reduced by roughness of the medium, the energy velocity being of order fδa, where a is the horizontal topographic scale (although in an exceptional case, the sinusoidal bottom, the group velocity remains finite for vanishingly small values of a).