Forcing function control of Faraday wave instabilities in viscous shallow fluids

Cristián Huepe*, Yu Ding, Paul Umbanhowar, Mary Silber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We investigate the relationship between the linear surface wave instabilities of a shallow viscous fluid layer and the shape of the periodic, parametric-forcing function (describing the vertical acceleration of the fluid container) that excites them. We find numerically that the envelope of the resonance tongues can only develop multiple minima when the forcing function has more than two local extrema per cycle. With this insight, we construct a multi-frequency forcing function that generates at onset a nontrivial harmonic instability which is distinct from a subharmonic response to any of its frequency components. We measure the corresponding surface patterns experimentally and verify that small changes in the forcing waveform cause a transition, through a bicritical point, from the predicted harmonic short-wavelength pattern to a much larger standard subharmonic pattern. Using a formulation valid in the lubrication regime (thin viscous fluid layer) and a Wentzel-Kramers-Brillouin (WKB) method to find its analytic solutions, we explore the origin of the observed relation between the forcing function shape and the resonance tongue structure. In particular, we show that for square and triangular forcing functions the envelope of these tongues has only one minimum, as in the usual sinusoidal case.

Original languageEnglish (US)
Article number016310
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume73
Issue number1
DOIs
StatePublished - Jan 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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