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Potential energy in steep and breaking waves

Published online by Cambridge University Press:  26 April 2006

William W. Schultz ,
Jin Huh  and
Owen M. Griffin
William W. Schultz
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan 48109-2125, USA
Jin Huh
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan 48109-2125, USA Present address: Korea Atomic Energy Institute, Taejon, Korea
Owen M. Griffin
Affiliation:
Remote Sensing Division, Naval Research Laboratory, Washington, DC 20375-5000, USA
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Abstract

We find that the RMS wave height (square root of the potential energy) rather than peak-to-peak wave height is a better experimental and analytic criterion for determining when a regular, two-dimensional deep-water wave will break. A spectral algorithm for two-dimensional potential flow is developed and used to compare breaking onset criteria for energy input from (i) converging sidewalls, (ii) a submerged disturbance, and (iii) wave focusing. We also find that wave-breaking criteria (potential energy or the more classical peak-to-peak wave height) are a function of the rate of energy input. Large plunging waves occur when energy input rates are large. As energy input rates become smaller there is a smooth transition to smaller spilling waves. The various energy input methods show similar breaking trends in the limit as the energy input rate becomes small - waves break when the potential energy becomes approximately 52 % of the energy for the most energetic Stokes wave, with the formation of a singularity immediately before the crest. The effects of wave modulation and reflection are briefly discussed and shown not to affect the potential energy breaking criterion significantly. The experimental scatter of the RMS wave height is shown to be half that of wave steepness during incipient breaking in wave packets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 201 - 228
Copyright
© 1994 Cambridge University Press

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