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Solving the nonlinear shallow-water equations in physical space

Published online by Cambridge University Press:  23 December 2009

M. ANTUONO  and
M. BROCCHINI
M. ANTUONO*
Affiliation:
INSEAN (The Italian Ship Model Basin), via di Vallerano 139, 00128 Rome, Italy
M. BROCCHINI
Affiliation:
Dipartimento ISAC, Università Politecnica delle Marche, via Brecce Bianche 12, 60131 Ancona, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The boundary value problem for the nonlinear shallow-water equations with a beach source term is solved by direct use of physical variables, so that solutions are more easily inspected than those obtained by means of hodograph transformations. Beyond an overall description of the near-shoreline flows in terms of the nonlinear shallow-water equations, significant results are provided by means of a perturbation approach which enables much of the information on the flow to be retained. For sample waves of interest (periodic and solitary), first-order solutions of the shoreline motion and of the near-shoreline flows are computed, illustrated and successfully compared with the equivalent ones obtained through a hodograph transformation method previously developed by the authors. Wave–wave interaction, both at the seaward boundary and within the domain, is also accurately described. Analytical conditions for wave breaking within the domain are provided. These, compared with the authors' hodograph model, show that the first-order condition of the present model is comparable to the second-order condition of that model.

JFM classification

Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 207 - 232
Copyright
Copyright © Cambridge University Press 2009

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References

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