Nonlinear internal wave penetration via parametric subharmonic instability

TL;DR

This study demonstrates how nonlinear parametric subharmonic instability enables internal waves to transfer energy across stratified layers, overcoming linear evanescence barriers, with about 10% of energy flux penetrating into the lower layer.

Contribution

It reveals that parametric subharmonic instability facilitates energy transfer in internal waves, a process not captured by linear theory, through laboratory experiments.

Findings

Approximately 10% of primary wave energy penetrates the lower layer.

Parametric subharmonic instability transfers energy to subharmonic waves.

Nonlinear interactions enable wave energy penetration despite linear evanescence.

Abstract

We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.