Measuring the Reflection Coefficient When Internal Wave Beams Reflect from Rough Surfaces

Internal waves may be important in the redistribution of tidal energy within the ocean and cause the erosion of continental shelves to the critical angle of tidally generated waves. We analyze this problem using the reflection coefficient of internal waves defined as the ratio of outgoing propagating energy to the incoming wave beam energy. Our experiments use particle image velocimetry to determine the velocity field of internal wave beams, and the Hilbert Transform method created by Mercier et al. (Phys. Fluids, 2008) to select for wave beams based on frequency and propagation direction. The energy flux of the internal waves is derived from the velocity field using the method of Lee et al. (Phys. Fluids, 2014). Our experiments focus on determining the dependence of the reflection coefficient on different types of boundaries: a smooth boundary with angles ranging from horizontal to critical, and various horizontal boundaries with sinusoidal roughness. We compare our results to the theory of Baines et al. (J. Fluid Mech, 1971) for internal waves and find good agreement. We have found that a rough boundary greatly alters the values of the reflection coefficient, which may have implications for internal wave beams in the ocean.