Stratified Flow over Topography: Wave Generation and Boundary Layer Separation

Linear theory and Long's model for stratified flow over topography both assume free-slip lower boundary conditions and so neglect the possibility of boundary-layer separation either between successive hill crests or in the lee of a range of hills. Numerical simulations do not yet have sufficient resolution to capture the fine-scale features of separated flow and turbulence while also capturing the large-scale dynamics associated with internal waves. However, using a computer-assisted schlieren technique, internal waves characteristics, including their amplitudes, may be measured non-intrusively in laboratory experiments.

Here we report upon laboratory experiments that focus upon periodic finite-amplitude hills which are representative of the Earth's major mountain ranges as well as the fractured crevasses of the ocean floor. The topographic shapes are selected to encompass varying degrees of roughness, from smoothly-varying sinusoidal hills to steeper triangular and rectangular hills.

For low flow speeds, U (and hence low values of the excitation frequency), the internal wave frequencies are consistent with those predicted by linear theory. However, when the excitation frequency exceeds the buoyancy frequency, N, internal waves are still excited and their frequencies are found to be an approximately constant fraction of N. In all experiments the wave amplitudes are much smaller than predicted because, through boundary-layer separation, fluid is trapped in the valleys between hills effectively reducing the peak-to-peak hill height, H. This is true even if NH/U is moderately less than 1.

For rough triangular and rectangular topographies, turbulent structures emerge even at low towing speeds. Here we find that internal waves are generated by the nonlinear interactions between the flow, lee waves and turbulence far in the lee.