Internal waves in the oceans play critical roles in the large scale transport processes, and will interact with surface waves in producing complex wave patterns and dynamics. Triad resonance can occur among three components of internal waves in stratified fluids when the angular frequencies and wave numbers satisfy special constraints. The effect of damping and amplification on the evolution of coupled triads are illustrated via numerical simulations. Different combinations of damping and amplification in parent and sibling waves are applied to capture the nonlinear physics, which can lead to different types of energy transfer among interaction components.


Internal waves are ubiquitous in the oceans which are being modelled by stratified fluids. These waves serve as an important role in fluid mixing and energy redistribution in the ocean (Sutherland, 2010; Wunsch & Ferrari, 2004). An intriguing question arising in this topic is how the energy dissipated from large scales to small scales. Different kinds of dissipation routes have been proposed, including the interaction of internal waves and mean flow, the effect of oceanic bottom topography and continental structures (MacKinnon et al, 2017). In terms of nonlinear wave-wave interactions, parametric subharmonic instability (PSI) is considered as one possible dissipation mechanism of the internal waves. The energy will flow from the primary wave to a pair of subharmonic waves of half the frequency (Staquet & Sommeria, 2002). Although observational evidence of energy transfer through PSI has been gathered in the ocean, such dissipation mechanism was still not precisely understood (Alford et al, 2007; MacKinnon et al, 2013). Here we consider a more general interaction framework among three waves known as triad resonance, in which the frequencies of the subharmonic waves are not required to be less than the frequency of the primary wave. The occurrence condition for such resonance is that the wavenumber and angular frequency satisfy special constraints.

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