Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T04:17:31.889Z Has data issue: false hasContentIssue false
  • English
  • Français

On long-wave propagation over a fluid-mud seabed

Published online by Cambridge University Press:  02 May 2007

PHILIP L.-F. LIU  and
I-CHI CHAN
PHILIP L.-F. LIU
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
I-CHI CHAN
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Using the Boussinesq approximation, a set of depth-integrated wave equations for long-wave propagation over a mud bed is derived. The wave motions above the mud bed are assumed to be irrotational and the mud bed is modelled as a highly viscous fluid. The pressure and velocity are required to be continuous across the water–mud interface. The resulting governing equations are differential–integral equations in terms of the depth-integrated horizontal velocity and the free-surface displacement. The effects of the mud bed appear in the continuity equation in the form of a time integral of weighted divergence of the depth-averaged velocity. Damping rates for periodic waves and solitary waves are calculated. For the solitary wave case, the velocity profiles in the water column and the mud bed at different phases are discussed. The effects of the viscous boundary layer above the mud–water interface are also examined.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 579 , 25 May 2007 , pp. 467 - 480
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Dalrymple, R. A. & Liu, P. L.-F. 1978 Waves over soft muds: a two layer model. J. Phys. Oceanogr. 8, 1121–1131.2.0.CO;2>CrossRefGoogle Scholar
Gade, H. G. 1958 Effects of a non-rigid, impermeable bottom on plane surface waves in shallow water. J. Mar. Res. 16, 61–82.Google Scholar
Healy, T., Wang, Y., & Healy, H.-J. 2002 Muddy Coasts of the World: Processes, Deposits and Function. Elsevier.Google Scholar
Liu, P. L.-F. 1973 Damping of water waves over porous bed. J. Hydraul. Div., ASCE 99, 2263–2271.Google Scholar
Liu, P. L.-F. & Orfila, A. 2004 Viscous effects on transient long-wave propagation. J. Fluid Mech. 520, 83–92 (and corrigendum 537, 2005, 443).Google Scholar
Liu, P. L.-F., Simarro, G., VanDever, J., & Orfila, A. 2006 Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank. Coastal Engng. 53 (2/3), 181–190.CrossRefGoogle Scholar
Liu, P. L-F., Park, Y. S. & Cowen, E. A. 2007 Boundary layer flow and bed shear stress under a solitary wave, J. Fluid Mech. 574, 449–463.CrossRefGoogle Scholar
MacPherson, H. 1980 The attenuation of water waves over a non-rigid bed. J. Fluid Mech. 97, 721–742.CrossRefGoogle Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005 Theory and Applications of Ocean Surface Waves. World Scientific.Google Scholar
Ng, C.-O. 2000 Water waves over a muddy bed: a two-layer Stokes' boundary layer model. Coastal Engng. 40, 221–242.Google Scholar
Ott, E. & Sudan, R. N. 1970 Damping of solitary waves. Phys. Fluids 13, 1432.CrossRefGoogle Scholar
Peregrine, D. H. 1972 Equations for water waves and the approximations behind them. In Waves on Beaches and the Resulting Sediment Transport (ed. Meyer, R. E.), pp. 95–121. AcademicCrossRefGoogle Scholar
Wen, J. & Liu, P. L.-F. 1998 Effects of seafloor conditions on water wave damping, in Free-Surface Flows with Viscosity (ed. Tyvand, P. A.). Computational Mechanics Publications.Google Scholar
Yamamoto, T., Koning, H. L., Sellmeigher, H. & Hijum, E. V. 1978 On the response of poro-elastic bed to water waves. J. Fluid Mech. 87, 193–206.CrossRefGoogle Scholar