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Short and long waves over a muddy seabed

Published online by Cambridge University Press:  15 January 2010

CHIANG C. MEI ,
MIKHAEL KROTOV ,
ZHENHUA HUANG  and
AODE HUHE
CHIANG C. MEI*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
MIKHAEL KROTOV
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology Cambridge, MA 02139, USA
ZHENHUA HUANG
Affiliation:
Department of Civil and Environmental Engineering, Nanyang Technological University, 50, Nanyang Avenue 639798, Singapore
AODE HUHE
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Haidian District 100080, Beijing, China
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 33 - 58
Copyright
Copyright © Cambridge University Press 2010

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References

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