Harmonic generation by reflecting internal waves

The generation of internal gravity waves by tidal flow over topography is an important oceanic process that redistributes tidal energy in the ocean. Internal waves reflect from boundaries, creating harmonics and mixing. We use laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from our experiments and simulations agree well but differ markedly from theoretical predictions by S. A. Thorpe ["On the reflection of a train of finite amplitude waves from a uniform slope," J. Fluid Mech. 178, 279 (1987)] and A. Tabaei et al. ["Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217 (2005)], except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the Dauxois-Young amplitude parameter value is only 0.01), we find that the ratio of the reflected wave number to the incoming wave number is very different from the prediction of weakly nonlinear theory. Further, we observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with our results from experiments and numerical simulations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3553294]