Internal gravity waves are propagating disturbances in stably stratified fluids. They are ubiquitous in the atmosphere and ocean, transport significant momentum and energy, with cascades of nonlinear interactions resulting in turbulence and dissipation. In the atmosphere, internal-wave-driven processes are sometimes attributed to clear air turbulence (CAT), and hence represent a hazard to aircraft. In the ocean, internal waves are an important consideration for submarine detection and offshore structures. More fundamentally, mechanisms that drive internal wave dissipation in the ocean are of paramount importance in understanding the global energy budget, state of the ocean and its spatio-temporal variability, and in improving the parametrization of internal wave driven mixing in general circulation models. In this thesis, we study one possible mechanism, namely triadic resonance, via which internal waves can transfer energy to other frequencies and spatial scales, and subsequently lead to turbulence and dissipation.

A theoretical framework to identify internal wave resonant triads in finite-depth uniform and nonuniform stratifications with background rotation is developed. The energy transfer rates within an internal wave resonant triad are then calculated based on the method of
multiple scales, by deriving the amplitude evolution equations for a finite-depth arbitrary stratification in the presence of background rotation. This theoretical framework developed could potentially model how the energy in a linearly forced internal wave field such as the internal tides or near-inertial internal waves could get redistributed to other frequencies and wavenumbers as the waves propagate away from their generation location. Quantitative estimates of energy transfer rates within representative resonant triads show that
superharmonic wave excitation resulting from modal interactions should be an important consideration alongside other triadic resonances like the parametric subharmonic instability.

Numerical simulations and laboratory experiments are performed for representative resonant triads to (i) demonstrate the spontaneous excitation of the theoretically predicted superharmonic internal wave due to resonant interaction between internal wave modes, (ii) quantitatively validate the initial spatial growth of the superharmonic wave estimated from the amplitude evolution equations, and (iii) investigate off-resonance superharmonic excitation, i.e. to identify the range of primary wave frequencies (around the resonant frequency) over which spontaneous superharmonic wave excitation occurs.