Hysteretic Faraday Waves

TL;DR

This paper investigates the subcritical bifurcation of Faraday waves at a fluid interface, combining numerical, theoretical, and phenomenological modeling to understand hysteresis phenomena in shallow fluid layers.

Contribution

It introduces a simple phenomenological model to describe the subcritical bifurcation and hysteresis of Faraday waves in shallow fluid layers, supported by numerical analysis.

Findings

Identification of subcritical bifurcation behavior

Development of a phenomenological model for hysteresis

Numerical validation of the stress balance explanation

Abstract

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate towards highly nonlinear ones, with twice their amplitude. We propose a simple phenomenological model which can describe the observed bifurcation. We relate this hysteresis with the change of shear stress using a simple stress balance, in agreement with numerical results.