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Short and long waves over a muddy seabed



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.


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Coussot, P. 1997 Mud Flow Rheology and Dynamics. Bakema.
Dalrymple, R. & Liu, P. L.-F. 1978 Waves over soft muds: a two-layer fluid model. J. Phys. Oceanogr. 8 (6), 11211131.
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.
Hsiao, S. V. & Shemdin, O. H. 1980 Interaction of ocean wave with a soft bottom. J. Phys. Oceanogr. 10, 605610.
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.
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.
Jiang, F. & Mehta, A. J. 1995 Mudbanks of the southwest coast of India. Part IV. Mud viscoelastic properties. J. Coastal Res. 11 (3), 918926.
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.
Liu, P. L.-F. & Chan, I.-C. 2007 On long-wave propagation over a fluid-mud seabed. J. Fluid Mech. 579, 467480.
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves, a physical discussion with applications. Deep-Sea Res. 11, 529562.
Maa, J. P.-Y. & Mehta, A. J. 1988 Soft mud properties: Voigt model. J. Waterways Port Coastal Ocean Engng 114 (6), 765770.
MacPherson, H. 1980 The attenuation of water waves over a non-rigid bed. J. Fluid Mech. 97, 721742.
Malvern, L. E. 1969 Introduction to the Mechanics of a Continuous Medium. Prentice Hall.
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.
Ng, C. 2000 Water waves over a muddy bed: a two-layer Stokes' boundary layer model. J. Coastal Engng 40, 221242
Ng, C. & Zhang, X. 2007 Mass transport in water waves over a thin layer of soft viscoelastic mud. J. Fluid Mech. 573, 105130.
Piedra-Cueva, I. 1993 On the response of a muddy bottom to surface water waves. J. Hydraul. Res. 31, 681695.
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.
Soltanpour, M., Shibayama, T. & Noma, T. 2003 Cross-shore mud transport and beach deformation mode. J. Coastal Engng 45, 363386.
Wan, Z. H. & Wang, Z. Y. 1994 Hyperconcentrated Flow. Balkema.
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.
Zhang, X. & Ng, C. O. 2006 On the oscillatory and mean motions due to waves in a thin viscoelastic layer. Wave Mot. 43, 387405.
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