Determining reflection coefficients when internal waves reflect from solid boundaries

Instabilities and other nonlinear processes may cause local dissipation of internal wave beams when they reflect from solid boundaries. We analyze this problem using the reflection coefficient, the ratio of the outgoing propagating energy to the incoming wave beam energy: R≡Eout /Ein. We have developed a method to independently measure losses due to viscous decay, boundary dissipation and harmonic generation when calculating R. We use a 2D pseudo-spectral and a 2D finite volume code to solve the Navier-Stokes equations in the Boussinesq limit, along with low Reynolds number experiments to find values of R for different conditions. We compare results from no-slip boundaries, free-slip boundaries, rough surfaces, and from turning depths. The reflection coefficient for a turning depth in the numerical simulations is similar to that of a free slip boundary and so provides a mechanism to create a quasi-free-slip boundary in experiments. We apply our method to a sloping boundary to evaluate the different mechanisms that cause decay of the reflected wave beam. We find that R is minimized when the wave beam and slope angle are the same, as is common on continental slopes in the ocean.