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Water wave overwash of a step

Published online by Cambridge University Press:  29 January 2018

D. M. Skene*
Affiliation:
School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
L. G. Bennetts
Affiliation:
School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
M. Wright
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, MI 48109, USA
M. H. Meylan
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia
K. J. Maki
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, MI 48109, USA
*
Email address for correspondence: david.skene@adelaide.edu.au

Abstract

Water wave overwash of a step by small steepness, regular incident waves is analysed using a computational fluid dynamics (CFD) model and a mathematical model, in two spatial dimensions. The CFD model is based on the two-phase, incompressible Navier–Stokes equations, and the mathematical model is based on the coupled potential-flow and nonlinear shallow-water theories. The CFD model is shown to predict vortices, breaking and overturning in the region where overwash is generated, and that the overwash develops into fast-travelling bores. The mathematical model is shown to predict bore heights and velocities that agree with the CFD model, despite neglecting the complicated dynamics where the overwash is generated. Evidence is provided to explain the agreement in terms of the underlying agreement of mass and energy fluxes.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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