Internal Wave Turbulence in Large Aspect Ratio Domains

Abstract

Continuous stratification profoundly impacts the onset of hydrodynamical instabilities due to a unique dispersion relation. According to this relation, wave beams and wave energy propagate perpendicular to the phase velocity. It has been also observed that the dynamics of wave beams (webs of rays) in closed domains differ considerably from conventional ray tracing. In a general case, an attracting trajectory exists for the wave beams, referred to as wave attractors. These trajectories evolve due to the focusing/defocusing of wave packets upon reflection from the walls [1]. Owing to the high concentration of wave energy along these attracting paths, they are particularly susceptible to instabilities and serve as a source for the propagation of secondary waves. In our previous works, we demonstrated that if the aspect ratio of the motion is of the order of one, the transitions to turbulence can be effectively described using a laboratory toy-box model [2]. In such a laboratory model, turbulence originates from cascades of triadic resonances. This model represents one important case of natural flows. Another case involves large aspect ratio domains, where the horizontal scale is much larger than the vertical, yet buoyancy effects cannot be neglected. Previously, we described the peculiarities of linear regimes of large aspect ratio wave attractors and their instabilities at multiples of half the forcing frequency. Now, we present a full scenario of weak (not reaching overturning) instabilities, encompassing superharmonic and subharmonic frequencies at half the forcing frequency, along with cascades of triadic resonance instabilities in each half-harmonic frequency interval.