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Surface wave pattern formation in a cylindrical container

Published online by Cambridge University Press:  09 March 2021

X. Shao ,
P. Wilson ,
J.R. Saylor  and
J.B. Bostwick Open the ORCID record for J.B. Bostwick [Opens in a new window]
X. Shao
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
P. Wilson
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
J.R. Saylor
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
J.B. Bostwick*
Affiliation:
Department of Mechanical Engineering, Clemson University, Clemson, SC29634, USA
*
†Email address for correspondence: jbostwi@clemson.edu
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Abstract

Surface waves are excited by mechanical vibration of a cylindrical container having an air/water interface pinned at the rim, and the dynamics of pattern formation is analysed from both an experimental and theoretical perspective. The wave conforms to the geometry of the container and its spatial structure is described by the mode number pair ($n,\ell$) that is identified by long exposure time white light imaging. A laser light system is used to detect the surface wave frequency, which exhibits either a (i) harmonic response for low driving amplitude edge waves or (ii) sub-harmonic response for driving amplitude above the Faraday wave threshold. The first 50 resonant modes are discovered. Control of the meniscus geometry is used to great effect. Specifically, when flat, edge waves are suppressed and only Faraday waves are observed. For a concave meniscus, edge waves are observed and, at higher amplitudes, Faraday waves appear as well, leading to complicated mode mixing. Theoretical predictions for the natural frequency of surface oscillations for an inviscid liquid in a cylindrical container with a pinned contact line are made using the Rayleigh–Ritz procedure and are in excellent agreement with experimental results.

JFM classification

Waves/Free-surface Flows: Faraday waves Instability: Parametric instability Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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