Reflection coefficients for reflecting internal wave beams

Tidally generated internal waves beams do not propagate far from the generation site and instabilities and other nonlinear processes may be the cause of this local dissipation of higher wave modes, but we find that the reflection coefficient, R≡Eout /Ein, for internal wave beams is always less than unity and approaches zero when the boundary angle matches the wave beam angle indicating that internal wave reflection may be an equally important dissipation mechanism for tidally generated wave beams. 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 focus on beam angles where the only propagating modes are in the incoming and fundamental reflection (θ > 30^◦) to minimize nonlinear effects. We measure the decay rate due to viscous dissipation to separate its effects from the energy loss upon reflection. We also reduce the viscosity by two orders of magnitude, and even under these conditions, R falls off rapidly as the boundary angle increases indicating that high energy loss may be expected for many oceanic conditions.