Reflection of internal wave beams from rough surfaces

Internal wave beams do not propagate long distances in the ocean, which has been attributed to nonuniform background density and other mechanisms. However, beams also reflect from solid and free surfaces shortly after generation, which reduces the energy in the reflected beams and may be an important mechanism in scattering this tidal energy. We use low Reynolds number tank experiments and numerical simulations to understand how the reflection coefficient: the ratio of the outgoing energy flux to the incoming energy flux through a surface near the reflection region, is affected by properties of the surface from which it reflects. We measure the velocity field using particle image velocimetry and determine the energy flux using the work of Lee et al. (Phys. Fluids, 26, 2014). The wave beams are separated using the Hilbert transform method of Mercier et al. (Phys. Fluids, 20, 2008) to calculate the contributions from the incoming wave beam and any harmonic waves. We find that sinusoidal topography with wavelengths less than the beam's dominant wavelength significantly reduces the reflection coefficient. We also find wave energy reflected backwards toward the source from sinusoidal topography. Our tank experiments are scaled to higher Reynolds numbers in matched numerical simulations. The simulations also show reduced reflection coefficients when the surface is roughened even when viscosity is reduced by an order of magnitude.