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Experimental evidence of stable wave patterns on deep water*

Published online by Cambridge University Press:  16 August 2010

DIANE M. HENDERSON ,
HARVEY SEGUR  and
JOHN D. CARTER
DIANE M. HENDERSON*
Affiliation:
Department of Mathematics, Penn State University, University Park, PA 16803, USA
HARVEY SEGUR
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
JOHN D. CARTER
Affiliation:
Mathematics Department, Seattle University, Seattle, WA 98122, USA
*
†Email address for correspondence: dmh@math.psu.edu
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Abstract

Recent predictions from competing theoretical models have disagreed about the stability/instability of bi-periodic patterns of surface waves on deep water. We present laboratory experiments to address this controversy. Growth rates of modulational perturbations are compared to predictions from: (i) inviscid coupled nonlinear Schrödinger (NLS) equations, according to which the patterns are unstable and (ii) dissipative coupled NLS equations, according to which they are linearly stable. For bi-periodic wave patterns of small amplitude and nearly permanent form, we find that the dissipative model predicts the experimental observations more accurately. Hence, our experiments support the claim that these bi-periodic wave patterns are linearly stable in the presence of damping. For bi-periodic wave patterns of large enough amplitude or subject to large enough perturbations, both models fail to predict accurately the observed behaviour, which includes frequency downshifting.

JFM classification

Waves/Free-surface Flows: Surface gravity waves

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 247 - 278
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

*

With an appendix by Abhijit Chaudhuri and Erin Byrne

References

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