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Triadic resonance is one mechanism via which internal waves dissipate theirenergy, often at locations away from their generation sites. In this paper, weperform a combined theoretical and numerical study of triadic resonance ininternal wave modes in a finite-depth ocean with background rotation and anarbitrary stratification profile. The spatial evolution of the modal amplitudeswithin a resonant triad are first derived based on the requirement that thenonlinear solution at leading order cannot diverge. The amplitude evolutionequations are then numerically solved for two different cases: (i) modes 1 and2 at a specific frequency ({\omega_0}) in triadic resonance with the mode-1superharmonic wave (2{\omega_0}) in a uniform stratification, and (ii) aself-interacting mode-3 at a specific frequency {\omega_0} in triadic resonancewith the mode-2 (2{\omega_0}) in a nonuniform stratification representative ofthe ocean. Quantitative estimates of energy transfer rates within the resonanttriad show that superharmonic wave generation resulting from modal interactionsshould be an important consideration alongside other triadic resonances likeparametric subharmonic instability (PSI). Remarkably, in case (ii), theamplitude evolution equations suggest that any initial energy in mode-3 at{\omega_0} would get permanently transferred to mode-2 at frequency2{\omega_0}. Direct numerical simulations (DNS) are then performed to show thespontaneous generation of superharmonic internal waves resulting from modalinteractions in the aforementioned two cases, and quantitatively validate theinitial spatial evolution of the wave field predicted by the amplitudeevolution equations. DNS at off-resonant frequencies are used to identify therange of primary wave frequencies (around the resonant frequency) over whichspontaneous superharmonic wave generation occurs.

Spontaneous superharmonic internal wave generation by modal interactions in uniform and nonuniform stratifications