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Square patterns and secondary instabilities in driven capillary waves

Published online by Cambridge University Press:  26 April 2006

S. T. Milner
S. T. Milner
Affiliation:
AT&T Bell Laboratories, Murray Hill, NJ 07974, USA
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Abstract

Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from travelling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 81 - 100
Copyright
© 1991 Cambridge University Press

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