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 co o in a uniformly stratified finite-depth fluid. Thorpe [J. Fluid Mech. 24, 737 (1966)] has shown theoretically that modes m and n at frequency omega(0) and mode p = vertical bar m - n vertical bar at frequency 2 omega(0) are in triadic resonance at specific values of omega(0). We demonstrate the occurrence of this triadic resonance by forcing a primary wave field of modes m and n at various omega(0) using a novel internal wave generator, and observing the spontaneous growth (or lack thereof) of the superharmonic mode p = vertical bar m - n vertical bar at frequency 2 omega(0). A superharmonic wave field with a predominantly mode-p = vertical bar m - n vertical bar structure is observed over a finite range of frequency (Delta omega(0) similar or equal to 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.