Harmonic Generation of Internal Waves Reflected from a Slope

Internal wave reflection from a uniform sloping boundary is often analyzed using linear or a weakly nonlinear inviscid theory.\footnote{T. Dauxois and W.R. Young, J. Fluid Mech. {\bf390}, 271-295 (1999)} Under these assumptions for a linearly stratified fluid, Thorpe\footnote{S. A. Thorpe, J. Fluid Mech., {\bf178}, 279-302 (1987)} and Tabaei et al.\footnote{A. Tabaei, T. R. Akylas and K. G. Lamb, J. Fluid Mech. {\bf526}, 217-243 (2005)} derived predictions for the boundary angle where second harmonic generation should be most intense. We previously conducted experiments and simulations that found the angle that maximizes second harmonic generation is given instead by an empirical geometric relationship between the wave beam and boundary angles.\footnote{B. E. Rodenborn, D. Kiefer, H. P. Zhang, and H. L. Swinney. Phys. Fluids, 23(2), 2011.} We used integrated kinetic energy as a measure of beam intensity, but the method of Lee et al.\footnote{Frank M. Lee, M. S. Paoletti, H. L. Swinney, P. J. Morrison. arXiv:1401.2484.} determines the energy flux of the second harmonic wave in the experiments. We compare results using this new method to weakly nonlinear theories and our empirical prediction.