Parametric Subharmonic Instability of Internal Waves: Locally Confined Beams vs. Monochromatic Wavetrains (Workshop on Nonlinear Water Waves)

Abstract

Internal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions that amplify short-scale perturbations with frequency equal to one half of that ofthe underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves, as a potential mechanism for transferring energy from large-scale internal waves to small-scale mixing in oceans. However, the PSI found in stability analyses ofpurely monochromatic wavetrains may not be entirely relevant to ocean internal waves, as such highly idealized disturbances are not encountered in the field. Instead, tidally generated ocean internal waves are often in the form of beams—time-harmonic plane waves with general spatial profile—that propagate along a direction to the vertical determined by the wave frequency. Here, we present an asymptotic analysis of PSI of internal wave beams in an effort to understand how these more realistic disturbances differ, in regard to PSI, from monochromatic waves.