Instabilities of finite-amplitude internal wave beams

Yohei Onuki, Kyushu University, Research Institute for Applied Mechanics, Kasuga, Japan and Yuki Tanaka, The University to Tokyo, Department of Earth and Planetary Science, Graduate School of Science, Tokyo, Japan
Abstract:
Beam-like internal waves are commonly generated by tides in the ocean but their dissipation processes that cause vertical mixing remain poorly understood. Previous studies examined small-amplitude beams to find that parametric subharmonic instability (PSI) induces latitude-dependent wave dissipation. Using a novel approach based on Floquet theory, this study analyzes the stability of finite-amplitude beams over a wide range of parameters. If beam amplitude is small, PSI is indeed the principal mode under the condition f/σ≤0.5, where f is the Coriolis parameter and σ is the beam frequency, and the growth rate is maximum when equality holds. However, as beam amplitude is increased, instability arises even when f/σ>0.5, but the location of maximum instability shifts toward lower f/σ; thus, the latitudinal dependence of instability is significantly altered. Furthermore, the resulting energy spectrum is strongly Doppler shifted to higher frequencies, which therefore distinguishes this configuration from the common cases of PSI.