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Highly nonlinear standing water waves with small capillary effect

Published online by Cambridge University Press:  25 August 1998

WILLIAM W. SCHULTZ ,
JEAN-MARC VANDEN-BROECK ,
LEI JIANG  and
MARC PERLIN
WILLIAM W. SCHULTZ
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA
JEAN-MARC VANDEN-BROECK
Affiliation:
Department of Mathematics, University of Wisconsin Madison, WI 53706, USA Present address: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK.
LEI JIANG
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA Present address: Intel Corp. M/S RA1-305, 5200 NE Elam Young Parkway, Hillsboro, OR 97124, USA.
MARC PERLIN
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
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Abstract

We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 369 , 25 August 1998 , pp. 253 - 272
Copyright
© 1998 Cambridge University Press

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