Triadic resonances in internal wave modes with background shear
| When |
Jun 17, 2022
from 11:00 to 12:00 |
|---|---|
| Where | R116 |
| Attendees |
Ramana Patibandla |
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Internal wave modes are small-amplitude normal mode solutions in a stably stratified fluid. In a 2D, uniformly stratified fluid with no background velocity, they are modeled by a countably infinite of discrete modes, sinusoidal in horizontal and vertical directions. The presence of a background shear flow modifies the vertical structure of these modes and differentiates between forward and backward traveling internal wave modes. Triadic resonance is one of the mechanisms leading to instability in the internal wave modes. Two internal wave modes ('m' and 'n') could lead to an increase in the amplitude of the third mode ('q') when all the three modes satisfy certain resonance conditions. In the absence of a background shear flow, the triad of waves should satisfy a frequency condition, a horizontal wavenumber condition, and a vertical wavenumber condition for resonance. With the presence of even a weak background shear, the vertical wavenumber condition is modified and could be trivially satisfied.
In this talk, I will start by explaining the weakly nonlinear solution associated with the primary internal wave field. Assuming that the secondary wave field is at twice the frequency of the primary wave field, I will explain the resonance conditions to be satisfied in a uniformly stratified fluid with no background flow. Introducing weak shear as a small parameter, I will explain how the presence of an arbitrarily weak background shear flow could make the vertical resonance condition trivially satisfied. Later, I will explain the implications: the possibility of self-interaction and resonances that occur at the seemingly trivial limit of ω ≈ 0, both of which are not possible in the no shear limit. I will conclude my talk by showing the number of new resonances that are activated with the inclusion of shear.