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Short and long waves over a muddy seabed

Published online by Cambridge University Press:  15 January 2010

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: [email protected]

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.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Coussot, P. 1997 Mud Flow Rheology and Dynamics. Bakema.Google Scholar
Dalrymple, R. & Liu, P. L.-F. 1978 Waves over soft muds: a two-layer fluid model. J. Phys. Oceanogr. 8 (6), 11211131.2.0.CO;2>CrossRefGoogle Scholar
Foda, M. A., Hunt, J. R. & Chou, H. T. 1993 A nonlinear model for the fluidization of marine mud by waves. J. Geophys. Res 98, 70397047.CrossRefGoogle Scholar
Hsiao, S. V. & Shemdin, O. H. 1980 Interaction of ocean wave with a soft bottom. J. Phys. Oceanogr. 10, 605610.2.0.CO;2>CrossRefGoogle Scholar
Huang, Z., Huhe, A. & Zhang, Y. 1992 An experimental study of the properties of fluid mud in Xishu, Lianyungang. Tech Rep. IMCAS STR-92019. Institute of Mechanics, Chinese Academy of Sciences. In Chinese.Google Scholar
Huhe, A. & Huang, Z. H. 1994 An experimental study of fluid mud rheology – mud properties in Hangzhou Bay navigation channel. Part II. Beijing. Rep. No. 1. Institute of Mechanics, Chinese Academy of Sciences, pp. 34–56. In Chinese.Google Scholar
Jiang, F. & Mehta, A. J. 1995 Mudbanks of the southwest coast of India. Part IV. Mud viscoelastic properties. J. Coastal Res. 11 (3), 918926.Google Scholar
Liu, K. F. & Mei, C. 1989 Effects of wave-induced friction on a muddy seabed modelled as a Bingham-plastic fluid. J. Coastal Res. 5 (4), 777789.Google Scholar
Liu, P. L.-F. & Chan, I.-C. 2007 On long-wave propagation over a fluid-mud seabed. J. Fluid Mech. 579, 467480.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves, a physical discussion with applications. Deep-Sea Res. 11, 529562.Google Scholar
Maa, J. P.-Y. & Mehta, A. J. 1988 Soft mud properties: Voigt model. J. Waterways Port Coastal Ocean Engng 114 (6), 765770.CrossRefGoogle Scholar
MacPherson, H. 1980 The attenuation of water waves over a non-rigid bed. J. Fluid Mech. 97, 721742.CrossRefGoogle Scholar
Malvern, L. E. 1969 Introduction to the Mechanics of a Continuous Medium. Prentice Hall.Google Scholar
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.Google Scholar
Ng, C. 2000 Water waves over a muddy bed: a two-layer Stokes' boundary layer model. J. Coastal Engng 40, 221242CrossRefGoogle Scholar
Ng, C. & Zhang, X. 2007 Mass transport in water waves over a thin layer of soft viscoelastic mud. J. Fluid Mech. 573, 105130.CrossRefGoogle Scholar
Piedra-Cueva, I. 1993 On the response of a muddy bottom to surface water waves. J. Hydraul. Res. 31, 681695.CrossRefGoogle Scholar
Shibayama, T., Okuno, M. & Sato, S. 1990 Mass transport rate in muddy layer due to wave action. In Proceedings of the 22nd Coastal Engineering Conference (ed. B. L. Edge), pp. 3037–3049. ASCE.Google Scholar
Soltanpour, M., Shibayama, T. & Noma, T. 2003 Cross-shore mud transport and beach deformation mode. J. Coastal Engng 45, 363386.CrossRefGoogle Scholar
Wan, Z. H. & Wang, Z. Y. 1994 Hyperconcentrated Flow. Balkema.CrossRefGoogle Scholar
de Wit, P. J & Kranenburg, C. 1997 On the liquefaction and erosion of mud due to waves and current. In Proceedings of INTERCOH '94 (ed. Watts, J., Burt, N. & Parker, R.), pp. 331–340.Google Scholar
Zhang, X. & Ng, C. O. 2006 On the oscillatory and mean motions due to waves in a thin viscoelastic layer. Wave Mot. 43, 387405.CrossRefGoogle Scholar