Mean Flow Effects In The Nearly Inviscid
Faraday Waves
Author(s)
E. Martın & J.M. Vega
Abstract
We study the weakly nonlinear evolution of Faraday waves in a two dimensional
version of a vertically vibrating annular container. In the small viscosity limit, the
evolution of the surface waves is coupled to a non-oscillatory mean flow that develops
in the bulk of the container. A system of equations is derived for the coupled
slow evolution of the spatial phase of the surface wave and the streaming flow.
These equations are numerically integrated to show that the simplest reflection
symmetric steady state (the usual array of counter-rotating eddies below the surface
wave) becomes unstable for realistic values of the parameters. The new states
include limit cycles, steadily travelling waves (which are standing in a moving
reference frame), and some more complex attractors. We also consider the effect
of surface contamination, modelled byMarangoni elasticity with insoluble surfactant,
in promoting drift instabilities in spatially uniform standing Faraday waves. It
is seen that contamination enhances drift instabilities that lead to various steadily
propagating and (both standing and propagating) oscillatory patterns. In particular,
steadily propagating waves appear to be quite robust, as in the experiment by
Douady et al. (1989).
Keywords: Faraday instability, mean flow, weakly nonlinear analysis, Marangoni
elasticity.
1 Introduction
We consider the parametric excitation of waves at the free surface of a horizontal
liquid layer that is being vertically vibrated. If the forcing amplitude exceeds a
threshold value, the system exhibits surface waves that are named after
Keywords
Faraday instability, mean flow, weakly nonlinear analysis, Marangoni
elasticity.
Related Book
Other papers in this volume
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