Internal waves in the ocean are well-recognized to play an important role in the global energy budget. Triadic resonance is one mechanism via which these internal waves transfer their energy to other spatial and temporal scales before dissipation, at locations blue both near and away from their generation sites. In this paper, we perform a combined theoretical and numerical study of triadic resonance in internal wave modes in a finite-depth ocean with an arbitrary stratification profile. Considering internal waves generated at spatially localized regions, the spatial evolution of the modal amplitudes within a resonant triad are derived based on the method of multiple scales. Two representative cases are considered: (i) modes 1 and 2 at a specific frequency ${\omega }_0$ in triadic resonance with the mode-1 superharmonic wave (frequency $2{\omega }_0$) in a uniform stratification, and (ii) a self-interacting mode-3 at a specific frequency ${\omega }_0$ in triadic resonance with the mode-2 at frequency $2{\omega }_0$ in an ocean-like nonuniform stratification. In case (ii), any initial energy in mode-3 at frequency ${\omega }_0$ gets permanently transferred to mode-2 at frequency 2${\omega }_0$. Numerical simulations are performed to show the spontaneous excitation of superharmonic internal waves resulting from modal interactions in the aforementioned cases, and quantitatively validate the initial spatial evolution of the wave field predicted by the amplitude evolution equations. Furthermore, numerical simulations at off-resonant frequencies are used to identify the range of primary wave frequencies (around the resonant frequency) over which spontaneous superharmonic wave excitation occurs. Quantitative estimates of energy transfer rates within the resonant triads considered show that superharmonic wave excitation resulting from modal interactions should be an important consideration alongside other triadic resonances like parametric subharmonic instability (PSI). We conclude by giving estimates of the relative importance of superharmonic wave excitation in the ocean, and provide motivation for future studies.