Wall-damped Faraday waves in horizontally oscillating two-layer fluid flows

TL;DR

This study experimentally investigates the onset of Faraday waves in a two-layer fluid system under horizontal oscillations, revealing a damping mechanism governed by wall boundary layers and providing a theoretical model that matches experimental results.

Contribution

The paper introduces a new understanding of Faraday wave onset in two-layer fluids driven horizontally, modeling damping via a weakly-damped Mathieu equation and validating it experimentally.

Findings

Onset of subharmonic waves is controlled by wall boundary layer damping.

Critical acceleration scales with viscosity and frequency as predicted by the model.

Model predictions agree with experimental data across various parameters.

Abstract

We study experimentally the onset of Faraday waves near the endwalls of rectangular vessel containing two stably-stratified fluid layers, subject to horizontal oscillations. These subharmonic waves (SWs) are excited, because the horizontal inertial forcing drives a harmonic propagating wave which displaces the interface in the vertical direction at the endwalls. We find that the onset of SWs is regulated by a balance between capillary and viscous forces, where the rate of damping is set by the Stokes layer thickness at the wall rather than the wavelength of the SWs. We model the onset of SWs with a weakly-damped Mathieu equation and find that the dimensional critical acceleration scales as $\nu_m^{1/2} \omega^{3/2}$, where $\nu_m$ is the mean viscosity and $\omega$ is the frequency of forcing, in excellent agreement with the experiment over a wide range of parameters.