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On beach cusp formation

Published online by Cambridge University Press:  01 February 2008

NICHOLAS DODD ,
ADAM M. STOKER ,
DANIEL CALVETE  and
ANURAK SRIARIYAWAT
NICHOLAS DODD
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
ADAM M. STOKER
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
DANIEL CALVETE
Affiliation:
Dept. de Fisica Aplicada, Univeristat Politecnica de Catalunya, Barcelona, Spain
ANURAK SRIARIYAWAT
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
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Abstract

A system of shallow water equations and a bed evolution equation are used to examine the evolution of perturbations on an erodible, initially plane beach subject to normal wave incidence. Both a permeable (under Darcy's law) and an impermeable beach are considered. It is found that alongshore-periodic morphological features reminiscent of swash beach cusps form after a number of incident wave periods on both beaches. On the permeable (impermeable) beach these patterns are accretional (erosional). In both cases flow is ‘horn divergent’. Spacings of the cusps are consistent with observations, and are close to those provided by a standing synchronous linear edge wave. An analysis of the processes leading to bed change is presented. Two physical mechanisms are identified: concentration gradient and flow divergence, which are dominant in the lower and upper swash respectively, and their difference over a wave cycle leads to erosion or deposition on an impermeable beach. Infiltration enters this balance in the upper swash. A bed wave of elevation is shown to advance up the beach at the tip of the uprush, with a smaller wave of depression on the backwash. It is found that cusp horns can grow by a positive feedback mechanism stemming from decreased (increased) backwash on positive (negative) bed perturbations.

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Type
Papers
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Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 145 - 169
Copyright
Copyright © Cambridge University Press 2008

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