Benjamin-Feir instability of wave packets at interface of liquid half-space and layer

TL;DR

This paper investigates the Benjamin-Feir instability of internal wave packets at the interface of a liquid half-space and layer, using a nonlinear model that accounts for surface tension and derives conditions for modulational stability.

Contribution

It introduces a low-dimensional nonlinear model incorporating surface tension to analyze wave packet stability at a liquid interface, identifying conditions for Benjamin-Feir instability.

Findings

Instability occurs within specific parameter ranges.

Surface tension significantly affects modulational stability.

Layer thickness and wavelength influence stability conditions.

Abstract

The propagation of internal waves in a hydrodynamic system comprising a solid bottom and an upper half-space is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interface using the method of multi-scale expansions. The evolution equation of the envelope of the wave packet takes the form of the Schrodinger equation. Conditions for the Benjamin-Feir stability of the solution of the evolution equation are identified for various physical and geometrical characteristics of the system. An estimation of the parameter range in which the instability occurs is performed. Significant influence on the modulational stability of the geometrical characteristics of the system and surface tension is observed in each system for relatively small liquid layer thicknesses and waves with a wavelength comparable to the layer thickness