Finite-size effects in parametric subharmonic instability

TL;DR

This paper investigates how the finite width of wave beams influences parametric subharmonic instability in stratified fluids, combining experimental, numerical, and theoretical approaches to enhance understanding of energy transfer in oceanic internal waves.

Contribution

It introduces a new energy balance theory accounting for finite beam width effects, validated by experiments and simulations, advancing knowledge of internal wave dynamics.

Findings

Finite beam width affects secondary wave energy transfer.

The new theory aligns well with experimental and numerical data.

Insights applicable to ocean internal wave energy transfer.

Abstract

The parametric subharmonic instability in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared to numerical and experimental results. Because of the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant.