Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. Part I: Unbounded domain

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In this paper, using multiple scale analysis we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal gravity wave packets in weakly non-uniform density stratifications in an unbounded domain in the presence of viscous and rotational effects.

• Such triad interactions are one of the mechanisms by which high wavenumber internal waves lead to ocean turbulence and mixing via parametric subharmonic instability.
• Non-uniform stratification introduces detuning - mismatch in the vertical wavenumber triad condition, which may strongly affect the energy transfer process.
• We investigate in detail how factors like wave-packets' width, group speeds, nonlinear coupling coefficients, detuning, and viscosity affect energy transfer in weakly varying stratification.