Nonlinear effects in reflecting and colliding internal wave beams

Abstract

Using small-amplitude expansions, we discuss nonlinear effects in the reflection from a sloping wall of a time-harmonic (frequency to the horizontal. Depending on the flow geometry, higher-harmonic beams can be found on the opposite side of the vertical from the primary reflected beam. Using the same approach, we also discuss collisions of two beams propagating in different directions. Nonlinear interactions in the vicinity of the collision region induce secondary beams with frequencies equal to the sum and difference of those of the colliding beams. The predictions of the steady-state theory are illustrated by specific examples and compared against unsteady numerical simulations.