Experimental study on super-harmonic wave generation by resonant interaction between internal wave modes

We present an experimental study of resonant generation of super-harmonic internal waves as a result of interaction between horizontally propagating vertical internal wave modes m and n at frequency $\omega $ in a uniformly stratified finite-depth fluid. Theoretical studies have shown that modes m and n at frequency $\omega $ and mode-p $=$ \textbar m-n\textbar at frequency 2$\omega $ are in triadic resonance at specific values of $\omega $. To demonstrate the occurrence of this triadic resonance, a primary wave field of modes m and n at various $\omega $ is forced using a novel internal wave generator, and the spontaneous growth (or lack thereof) of the super-harmonic mode-p $=$ \textbar m-n\textbar at frequency 2$\omega $ is measured. A super-harmonic wave field with a predominantly mode-p $=$ \textbar m-n\textbar structure is observed over a finite range of frequency ($\Delta \omega \simeq $0.03N) around the resonant value, where N is the uniform buoyancy frequency. The observed spatial growth of the super-harmonic wave field is then quantitatively compared with the predictions from amplitude evolution equations at resonance at various forcing amplitudes, thereby validating this model.