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Shock trains on a planar beach

Published online by Cambridge University Press:  30 September 2011

Matteo Antuono
Matteo Antuono*
Affiliation:
CNR-INSEAN (The Italian Ship Model Basin), Via di Vallerano 139, 00128 Rome, Italy
*
†Email address for correspondence: matteoantuono@gmail.com
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Abstract

Following on from the author’s previous work, the propagation of trains of shock waves on a planar beach is studied in the framework of the nonlinear shallow water equations. The analysis is based on the use of a quasi-analytical solution valid for a shock wave which is fed by a constant Riemann invariant. The asymptotic behaviour of a train of such shock waves is inspected and novel approximate analytical solutions are provided. These are useful both for representing fundamental physical scenarios (e.g. propagation of saw-tooth spilling breakers in the surf zone) and for benchmarking wave-resolving and wave-averaged theoretical/numerical solutions. Finally, a study of the energy dissipation induced by the shock train is provided.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 583 - 606
Copyright
Copyright © Cambridge University Press 2011

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