Harmonic generation by reflecting internal waves

Author :Bruce Rodenborn, D. Kiefer, H.P. Zhang, and Harry L. Swinney
Publication :Physics of Fluids
Volume :23
Number :026601
Year :2011

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. © 2011 American Institute of Physics.