[A-CG40] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

[ACG40-07] Resonant triad interactions among internal waves in stratified shear flow

★Invited Papers

*Anubhab Roy¹, Ramana Patibandla¹, Manikandan Mathur² (1.Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India, 2.Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, India)

Keywords:Internal waves, Resonant Triad Interaction, Weakly Nonlinear Analysis, Stratified Shear Flow

Triadic resonance interactions among discrete internal wave modes in a 2D, inviscid, finite-depth, stratified shear flow is studied. Motivated by the internal tides generated due to barotropic forcing over a topography, we consider the primary wave field to be a sum of countably infinite internal wave modes at a single frequency. The weakly nonlinear solution of this primary wave will comprise of a superharmonic term (twice the primary wave frequency) and a mean flow term (zero frequency). For a given interaction and for exponential background shear flow, we show the resonance locations in the parameter space of nondimensional frequency and Richardson number by tracking locii of the locations where the superharmonic term diverges. Assuming uniform stratification and in the absence of any shear flow, three conditions have to be satisfied for resonance: two wavenumber and a frequency condition. Using asymptotic theory, we show that even with a weak shear, the resonance condition on the vertical wavenumber need not be satisfied. Therefore, all those locations that satisfy horizontal wavenumber and frequency conditions but are non-resonant due to the absence of shear will become resonant with the presence of an arbitrarily weak shear. This will also result in self-interaction and resonances close to zero frequency. Our asymptotic theory can be extended to other inhomogeneities, such as non-uniform stratification, as well.