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

• Published in: Dynamics of atmospheres and oceans Vol. 91; p. 101159
• Main Authors: Varma, Dheeraj, Chalamalla, Vamsi K., Mathur, Manikandan
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2020
• Subjects: Geophysical fluid dynamics; Internal waves; Nonlinear wave interactions; Stratified flows; Nonlinear wave interactions; Geophysical fluid dynamics; Stratified flows; Internal waves
• ISSN: 0377-0265; 1872-6879
• DOI: 10.1016/j.dynatmoce.2020.101159

•Derivation of the amplitude evolution equations for any resonant triad containing internal wave modes in finite-depth fluid with an arbitrary stratification profile.•Demonstration of spontaneous superharmonic internal wave excitation by self-interaction of individual mode in ocean-like nonuniform stratification, followed by validation of theoretical predictions.•Identification of frequency bandwidth around the resonant frequency where superharmonic excitation would be significant.•At and around superharmonic resonance, superharmonic excitation dominates subharmonic resonances.
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 ω0 in triadic resonance with the mode-1 superharmonic wave (frequency 2ω0) in a uniform stratification, and (ii) a self-interacting mode-3 at a specific frequency ω0 in triadic resonance with the mode-2 at frequency 2ω0 in an ocean-like nonuniform stratification. In case (ii), any initial energy in mode-3 at frequency ω0 gets permanently transferred to mode-2 at frequency 2ω0. 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.