Comparison of the effect of horizontal vibrations on interfacial waves in a two-layer system of inviscid liquids to effective gravity inversion

TL;DR

This paper investigates how high-frequency horizontal vibrations influence interfacial waves in a two-layer immiscible liquid system, revealing conditions under which vibrations can mimic gravity effects and potentially invert gravity's influence.

Contribution

The study derives nonlinear equations for interfacial waves under vibrations in two- and three-dimensional flows, using long-wavelength approximation, and compares vibrational effects to gravity in shallow water models.

Findings

Vibrations can effectively invert gravity effects on interfacial waves.

Derived equations are integrable and analogous to Boussinesq equations.

Vibrational influence depends on frequency and amplitude.

Abstract

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.