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Two-frequency excitation of single-mode Faraday waves

Published online by Cambridge University Press:  09 January 2015

W. Batson ,
F. Zoueshtiagh  and
R. Narayanan
W. Batson*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32601, USA
F. Zoueshtiagh
Affiliation:
Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR CNRS 8520, University of Lille 1, Avenue Poincaré, 59652 Villeneuve d’Ascq, France
R. Narayanan
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32601, USA
*
†Email address for correspondence: [email protected]
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Abstract

The purpose of this work is to investigate, for the first time, excitation of Faraday waves in small containers using two commensurate frequencies. This spatial restriction, which is encountered at low frequencies, leads to a wave composed primarily of one spatial eigenmode of the container. When two frequencies are used, the mode resonates primarily with one frequency, while the role of the second is to alter the instability threshold and the resulting nonlinear dynamics. As the parameter space expands greatly as a result of the introduction of three new degrees of freedom, viz. the frequency, amplitude and phase of the new component, the linear theory is first used as a guide to highlight basic two-frequency phenomena. These predictions and nonlinear phenomena are then studied experimentally with the system of Batson, Zoueshtiagh & Narayanan (J. Fluid Mech., vol. 729, 2013, pp. 496–523), who studied single-frequency excitation of different modes in a cylindrical cell. The two-frequency experiments of this work focus on excitation of the fundamental axisymmetric mode, and are quantitatively compared to the model via a posteriori Fourier decomposition of the parametric input. In doing so, experimental dependence of the instability on the new degrees of freedom is demonstrated, in accordance with the model predictions. This is done for a variety of frequency ratios, and overall agreement between the observed and predicted onset conditions is identical to that already reported for the single-frequency experiment. For each frequency ratio, the nonlinear behaviour is experimentally characterized by bifurcation and time series data, which is shown to differ significantly from comparable single-frequency excitations. Finally, we present and discuss a wave in which both temporal frequencies are used to simultaneously excite different spatial modes.

JFM classification

Instability: Instability Instability: Nonlinear instability Instability: Parametric instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 538 - 571
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Copyright
© 2015 Cambridge University Press 

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Batson et al. supplementary movie

Simultaneous excitation of a (0,1) and a (1,1) mode with [l/m, f, A, χ]=[3/2, 2.55 Hz, 1.40 mm, 48.0◦].

Download Batson et al. supplementary movie(Video)
Video 8.8 MB