Indexed on: 16 Aug '18Published on: 16 Aug '18Published in: arXiv - Physics - Fluid Dynamics
In this paper, we derive a simplified mathematical model for calculating the energy exchange in a resonant triad formed by weakly nonlinear internal gravity waves in the presence of weakly non-uniform density stratification. Such triad interactions are one of the mechanisms by which high wavenumber internal waves lead to ocean turbulence and mixing. We assume each internal wave to have a slowly varying amplitude and a rapidly varying phase and derive the amplitude evolution equations using the method of multiple scales. Non-uniform stratification introduces wave detuning, which strongly affects the energy transfer process. This yields an apparently non-intuitive outcome - the energy transfer process between the constituent waves of a resonant triad in uniform density stratification is significantly different from the case when density stratification has a weak non-uniformity.