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Nonlinear long waves over a muddy beach

Published online by Cambridge University Press:  08 February 2013

Erell-Isis Garnier ,
Zhenhua Huang  and
Chiang C. Mei
Erell-Isis Garnier
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Zhenhua Huang
Affiliation:
School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

We analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Waves/Free-surface Flows: Surface gravity waves Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 371 - 397
Copyright
©2013 Cambridge University Press

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