  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. We find limitations of the well-known 'pump-wave approximation'
and derive a non-dimensional number, which can be evaluated from initial
conditions, that can predict the maximum energy transferred from the primary
wave during the later stages. Two additional non-dimensional numbers, based on
various factors affecting energy transfer between near-resonant wave-packets
have also been defined. Moreover, we identify the optimal background
stratification in a medium of varying stratification for the primary wave to
form 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 a
significant difference in the energy transfer process between the wave-packets
when they have the same order of magnitude of energy.
