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A stationary potential-flow approximation for a breaking-wave crest

Published online by Cambridge University Press:  26 April 2006

Alastair D. Jenkins
Alastair D. Jenkins
Affiliation:
The IBM Environmental Sciences and Solutions Centre, Bergen, Norway Present address: Nansen Environmental and Remote Sensing Center, Edvard Griegs vei 3a, N-5037 Solheimsviken, Bergen, Norway
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Abstract

The flow in a breaking-wave crest is represented by a complex velocity potential on a Riemann surface, satisfying the Bernoulli condition on two free boundaries. The flow is assumed to be stationary in the reference frame which moves with the wave crest, and at large distances approximates Stokes corner flow in the main part of the fluid and a parabolic descending flow in the jet. The interaction of the jet with the rest of the fluid is neglected.

The solution is obtained by means of a conformal transformation from a bounded, teardrop-shaped domain, using a Faber polynomial expansion. The Bernoulli condition is applied at a number of discrete points on the boundaries, and the resulting nonlinear equations for the expansion coefficients are solved iteratively. The resulting surface form is similar to that obtained by laboratory experiments and time-dependent numerical simulations of waves up to the point of breaking, with a stagnation point at the top of the crest, an overturning loop with major axis $\ap 8g^{-\frac{1}{3}}\Psi^{\frac{2}{3}}$, and a maximum acceleration of ≈ 5.4 g, where g is the gravitational acceleration and ψ is the flux in the jet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 335 - 347
Copyright
© 1994 Cambridge University Press

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