Nonlinear long waves over a muddy beach
Mei, Chiang C.
Date of Issue2013
School of Civil and Environmental Engineering
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.
Journal of fluid mechanics
© 2013 Cambridge University Press. This paper was published in Journal of Fluid Mechanics and is made available as an electronic reprint (preprint) with permission of Cambridge University Press. The paper can be found at the following official DOI: [http://dx.doi.org/10.1017/jfm.2012.617]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.