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In this paper, using multiple scale analysis we derive a generalizedmathematical model for amplitude evolution, and for calculating the energyexchange in resonant and near-resonant global triads consisting of weaklynonlinear internal gravity wave packets in weakly non-uniform densitystratifications in an unbounded domain in the presence of viscous androtational effects. Such triad interactions are one of the mechanisms by whichhigh wavenumber internal waves lead to ocean turbulence and mixing viaparametric subharmonic instability. Non-uniform stratification introducesdetuning - mismatch in the vertical wavenumber triad condition, which maystrongly affect the energy transfer process. We investigate in detail howfactors like wave-packets' width, group speeds, nonlinear couplingcoefficients, detuning, and viscosity affect energy transfer in weakly varyingstratification. We find limitations of the well-known 'pump-wave approximation'and derive a non-dimensional number, which can be evaluated from initialconditions, that can predict the maximum energy transferred from the primarywave during the later stages. Two additional non-dimensional numbers, based onvarious factors affecting energy transfer between near-resonant wave-packetshave also been defined. Moreover, we identify the optimal backgroundstratification in a medium of varying stratification for the primary wave toform a triad with no detuning so that the energy transfer is maximum. Finally,we show that even a small change in the background stratification can cause asignificant difference in the energy transfer process between the wave-packetswhen they have the same order of magnitude of energy.

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