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 ${\omega }_0$ 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 $p=|m-n|$ 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 $p=|m-n|$ at frequency $2{\omega }_0$. A superharmonic wave field with a predominantly mode-$p=|m-n|$ structure is observed over a finite range of frequency ($\mathrm{\Delta }{\omega }_0\simeq 0.03N$) 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.

• Received 11 December 2019
• Accepted 7 July 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.074804