The stochastic mode of the Faraday instability of shallow fluid layers
Department of Applied Mathematics, University of Waterloo - Waterloo, ON, Canada, N2L 3G1
Received: 10 February 2014
Accepted: 29 April 2014
The instability of a vertically oscillated layer of fluid is a classical problem whose history dates back to Faraday in the 19th century. We consider the stability of a shallow layer for which the oscillation, as expressed through the effective gravitational acceleration, is a random function of time. Using both theoretical linear stability analysis and high-resolution numerical simulations, including both individual realizations and ensemble calculations, of the nonlinear system of equations, we find that two different stochastic modes of instability exist. Both modes find their expression in finite amplitude oscillations of the free surface that exhibit sharp crests and broad troughs, or in other words, that resemble the classical Stokes wave. We demonstrate that a necessary condition for the first type of instability is snapshot, or instantaneous, instability. The subdominant instability resembles classical parametric resonance that can exist in a harmonically oscillated layer of fluid, and occurs even when the flow is always snapshot stable (or the gravitational acceleration is non-negative).
PACS: 47.35.Bb – Gravity waves / 47.15.Fe – Stability of laminar flows / 47.15.K- – Inviscid laminar flows
© EPLA, 2014