Energy Dissipation and Boundary Flows in Reflecting Internal Waves

Theoretical analysis of internal wave reflection from a sloping boundary is typically analyzed using linear or a weakly nonlinear inviscid theory (Dauxois and Young, J. Fluid Mech., 390, 1999; Tabaei et al., J. Fluid Mech. 526, 2005). We previously used kinetic energy density to determine the intensity of the fundamental reflection and harmonic waves. Our experiments and simulation data did not match theory (Rodenborn et al. Phys., Fluids, 23, 2011). However, a later paper by Dettner et al. showed that using integrated kinetic energy density is not a good measure of radiated internal wave power (Phys., Fluids, 25, 2013). We reanalyze the reflection problem using an algorithm by Lee et al., which determines the energy flux of internal waves using experimental velocity field measurements. We compare the energy flow into and out of a surface above the reflection region and find high rates of energy dissipation that peak at the critical angle where the dissipation rate is O(90%) for all conditions studied. The reflecting waves create intense boundary flows but little radiated wave power, which may help explain the eroding of continental slopes to the local angle of tidally generated internal waves (Cacchione et al., Science 296, 2002).