NUMERICAL SIMULATIONS OF UNIFORMLY STRATIFIED FLUID-FLOW OVER TOPOGRAPHY

We use a high-resolution spectral numerical scheme to solve the two-di mensional equations of motion for the flow of a uniformly stratified B oussinesq fluid over isolated bottom topography in a channel of finite depth. The focus is on topography of small to moderate amplitude and slope and for conditions such that the flow is near linear resonance o f either of the first two internal wave modes. The results are compare d with existing inviscid theories: the steady hydrostatic analysis of Long (1955), time-dependent linear long-wave theory, and the fully non linear, weakly dispersive resonant theory of Grimshaw & Yi (1991). For the latter, we use a spectral numerical technique, with improved accu racy over previously used methods, to solve the approximate evolution equation for the amplitude of the resonant mode. Also, we present some new results on the modal similarity of the solutions of Long and of G rimshaw & Yi. For flow conditions close to linear resonance, solutions of Grimshaw & Yi's evolution equation compare very well with our full y nonlinear numerical solutions, except for very steep topography. For flow conditions between the first two resonances, Long's steady solut ion is approached asymptotically in time when the slope of the topogra phy is sufficiently small. For steeper topography, the flow remains un steady. This unsteadiness is manifested very clearly as periodic oscil lations in the drag, which have been observed in previous numerical si mulations and tow-tank experiments. We explain these oscillations as m ainly due to the internal waves that according to linear theory persis t longest in the neighbourhood of the topography.