Experimental study of internal gravity waves generated by supercritical topography

Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number similar to O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Omega), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Omega emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of D. G. Hurley and G. Keady [J. Fluid Mech. 351, 119 (1997)]. The width of the wave beams is determined by competition between forcing and viscous smoothing, and hydrodynamic screening of the steep part of the topography extends the cylinder's horizontal length scale. Beyond the weak forcing regime, harmonic waves of frequency n Omega (with integer n > 1 and n Omega < N, where N is the buoyancy frequency) are generated mainly by nonlinear interaction involving the overlapping fundamental waves. For moderate forcing we find that the intensity of the fundamental and second harmonic waves scales linearly and quadratically with A, respectively. (c) 2007 American Institute of Physics.