Experimental study on superharmonic wave generation by resonant interaction between internal wave modes

We present an experimental study of resonant generation of superharmonic internal waves as a result of interaction between horizontally propagating vertical internal wave modes m and n at frequency ω0 in a uniformly stratified finite-depth fluid. Thorpe [J. Fluid Mech. 24, 737 (1966)JFLSA70022-112010.1017/S002211206600096X] has shown theoretically that modes m and n at frequency ω0 and mode p=|m-n| at frequency 2ω0 are in triadic resonance at specific values of ω0. We demonstrate the occurrence of this triadic resonance by forcing a primary wave field of modes m and n at various ω0 using a novel internal wave generator, and observing the spontaneous growth (or lack thereof) of the superharmonic mode p=|m-n| at frequency 2ω0. A superharmonic wave field with a predominantly mode-p=|m-n| structure is observed over a finite range of frequency (Δω0≃0.03N) around the resonant value, where N is the uniform buoyancy frequency. The spatial growth of the superharmonic wave field is then quantitatively measured, to subsequently compare with the predictions from amplitude evolution equations at resonance at various forcing amplitudes, thereby validating this model. It is furthermore shown that a large-scale spatial evolution of the wave field is more suited to describe our experiments than the slow temporal evolution approach. The paper concludes with a brief discussion of viscous effects