SWAN-Mud: Engineering Model for Mud-Induced Wave Damping
Publication: Journal of Hydraulic Engineering
Volume 137, Issue 9
Abstract
This paper describes the implementation of a new dispersion relation and energy-dissipation equation obtained from a viscous two-layer model schematization in the state-of-the-art wave forecasting model SWAN to simulate wave damping in coastal areas by fluid mud deposits. This new dispersion relation is derived for a nonviscous, nonhydrostatic upper layer and a viscous, hydrostatic lower layer, covering most conditions encountered in nature. An algorithm is developed for a robust numerical solution of this new implicit dispersion relation through proper starting values in the iteration procedure. The implementation is tested against a series of analytical solutions and three schematic test cases. Next, four dispersion relations published in the literature are evaluated and compared with the new dispersion relation. The solution of the dispersion relations forms a multidimensional space. Comparison of the various model solutions through one-dimensional graphs can therefore become quite misleading, as shown in the discussion of a two-dimensional representation of the solution space, explaining for instance the variation in ambient conditions at which maximum wave damping is to be expected. The various models have been developed for a variety of conditions, such as shallow and deep water and shallow and thick mud layers; the various models agree well in their domain of applicability, but they show significant deviations when used outside their domain. Because the ambient and mud conditions may vary considerable in space and time at a particular site, the use of the new model is advocated because it covers most water depths and fluid mud thicknesses encountered in nature. The strength of the new SWAN-mud model lies in its large-scale applicability, assessing the two-dimensional evolution of wave fields in coastal areas. Therefore, the new implementation is evaluated with respect to the behavior of waves on a sloping seabed, representing real-world coasts. In all cases, the new SWAN-mud model behaves satisfactorily; a critical remaining issue, though, is the assessment of the relevant fluid mud parameters.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was partly carried out under the project “An operational sand-mud model for marine waters” for the U.S. Office of Naval Research, award No. ONRN00173-05-1-G026, and cofinanced by Deltares (formerly Delft Hydraulics) corporate funding and Delft University of Technology. The authors would like to thank Professor Andre Metrikine and Dr. Cees Kranenburg for valuable suggestions during the execution of this work; we are sad to announce that Dr. Kranenburg passed away and did not see the end result of our work. Finally, the authors are grateful to Dr. Elgar Steve for making available the original data of the Louisiana measurements (Elgar and Raubenheimer 2008), from which the full wave spectra of his data was retrieved. Part of this work was presented at the Chapman Conference on Physics of Wave-Mud Interactions, Amelia Island, Florida, November 2008.
References
Booij, N., Ris, R. C., and Holthuijsen, L. H. (1999). “A third-generation wave model for coastal regions. Part I: Model description and validation.” J. Geophys. Res., 104(C4), 7649–7666.
Calliari, L. J., et al. (2009). “Fine grain sediment transport and deposition in the Patos Lagoon-Cassino beach sedimentary system.” Cont. Shelf Res., 29(3), 515–529.
Chou, H.-T., Foda, M. A., and Hunt, J. R. (1993). “Rheological response of cohesive sediment to oscillatory forcing.” Nearshore and estuarine cohesive sediment transport, A. J. Mehta, ed., American Geophysical Union, Washington, DC, 126–147.
Dalrymple, R. A., and Liu, P. L. (1978). “Waves over soft mud beds: A two-layer fluid mud model.” J. Phys. Oceanogr., 8, 1121–1131.
De Wit, P. J. (1995). “Liquefaction of cohesive sediment by waves.” Ph.D. dissertation, Delft Univ. of Technology, Netherlands.
De Wit, P. J., and Kranenburg, C. (1996). “On the effects of a liquefied mud bed on wave and flow characteristics.” J. Hydraul. Res., 34(1), 3–18.
Elgar, S., and Raubenheimer, B. (2008). “Wave dissipation by muddy seafloors.” Geophys. Res. Lett., 35(7), L07611.
Fenton, J. D. (2006). A note on two approximations to the linear dispersion relation for surface gravity water waves, Universitat Karslruhe, Germany.
Gade, H. G. (1958). “Effects of a non-rigid, impermeable bottom on plane surface waves in shallow water.” J. Mar. Res., 16(2), 61–82.
Golden, S. P., Godwin, J. W., and Olal, A. D. (1982). “Dependence of the elastic properties of clay dispersions on the mode of interaction between the particles.” Trans. J. Br. Ceram. Soc., 81(3), 84–87.
Guo, J. (2002). “Simple and explicit solution of the wave dispersion relation.” Coastal Eng., 45, 71–74.
Jain, M., and Mehta, A. J. (2009). “Role of basic rheological models in determination of wave attenuation over muddy seabeds.” Cont. Shelf Res., 29(3), 642–651.
Jaramillo, S., Sheremet, A., Allison, M. A., Reed, A. H., and Holland, K. T. (2009). “Wave-mud interactions over the muddy Atchafalaya subaqueous clinoform, Louisiana, United States: Wave-supported sediment transport.” J. Geophys. Res., 114, C04002.
Jiang, F. (1993). “Bottom mud mass transport due to water waves.” Ph.D. thesis, Univ. of Florida, Gainesville, FL.
Jiang, L., and Zhao, Z. (1989). “Viscous damping of solitary waves over fluid-mud beds.” J. Waterway, Port, Coastal, Ocean Eng., 115(3), 345–362.
Kaihatu, J. M., Sheremet, A., and Holland, K. T. (2007). “A model for the propagation of nonlinear surface waves over viscous muds.” Coastal Eng., 54, 752–764.
Kranenburg, W. (2008). “Modeling wave damping by fluid mud.” M.Sc. thesis, Delft Univ. of Technology, Netherlands.
Liu, K., and Mei, C. C. (1989). “Effects of wave-induced friction on a muddy seabed modeled as a Bingham-plastic fluid.” J. Coastal Res., 5(4), 777–789.
Liu, P. L.-F. (1973). “Damping of water waves over porous bed.” J. Hydraul. Div., 99(12), 2263–2271.
Maa, P.-Y. (1986). “Erosion of soft mud beds by waves.” Ph.D. dissertation, Coastal and Oceanographic Engineering Dept., Univ. of Florida, Gainesville, FL.
Maa, P.-Y., and Mehta, A. J. (1990). “Soft mud response to water waves.” J. Waterway, Port, Coastal, Ocean Eng., 116(5), 634–650.
MacPherson, H. (1980). “The attenuation of water wave over a non-rigid bed.” J. Fluid Mech., 97(4), 721–742.
Mehta, A. J. (1996). “Interaction between fluid mud and water waves.” Environmental hydraulics, V. P. Singh and W. H. Hager, eds., Kluwer Academic, Netherlands, 153–187.
Mehta, A. J., Williams, D. J. A., Williams, P. R., and Feng, J. (1995). “Tracking dynamic changes in mud bed due to waves.” J. Hydraul. Eng., 121(6), 504–506.
Mei, C. C., and Liu, K. F. (1987). “A Bingham plastic model for a muddy seabed under long waves.” J. Geophys. Res., 92(C13), 14581–14594.
Ng, C.-O. (2000). “Water waves over a muddy bed: A two layer Stokes’ boundary layer model.” Coastal Eng., 40, 221–242.
Ris, R. C., Booij, N., and Holthuijsen, L. H. (1999). “A third-generation wave model for coastal regions. Part II: Verification.” J. Geophys. Res., 104(C4), 7667–7681.
Rodriguez, H. N. (2000). “Mud bottom evolution at open coasts.” Ph.D. thesis, Univ. of Florida, Gainesville, FL.
Rodriguez, H. N., and Mehta, A. J. (2001). “Modeling muddy coast response to waves.” J. Coastal Res., SI27, 137–148.
Rogers, W. E., and Holland, K. T. (2009). “A study of dissipation of wind-waves by mud at Cassino Beach, Brazil: Prediction and inversion.” Cont. Shelf Res., 29(3), 676–690.
Sakakiyama, T., and Bijker, E. W. (1989). “Mass transport velocity in mud layer due to progressive water waves.” J. Waterway, Port, Coastal, Ocean Eng., 115(5), 614–633.
Soltanpour, M., Shibayama, T., and Noma, T. (2003). “Cross-shore mud transport and beach deformation model.” Coastal Eng. J., 45(3), 363–386.
Spierenburg, S. E. J. (1987). “Seabed response to water waves.” Ph.D. dissertation, Delft Univ. of Technology, Netherlands.
Verbeek, H., and Cornelisse, J. M. (1997). “Erosion and liquefaction of natural mud under surface waves.” Cohesive sediments, N. Burt, R. Parker, and J. Watts, eds., Wiley, New York, 353–364.
Winterwerp, J. C., de Graaff, R., Groeneweg, J., and Luijendijk, A. (2007). “Modelling of wave damping at Guyana mud coast.” Coastal Eng., 54(3), 249–261.
Yamamoto, T., Koning, H. L., Sellmeijer, H., and Van Hijum, E. (1978). “On the response of the poro-elastic bed to water wave.” J. Fluid Mech., 87(1), 193–206.
Yamamoto, T., and Takahashi, S. (1985). “Wave damping by soil motion.” J. Waterway, Port, Coastal, Ocean Eng., 111(1), 62–77.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 137 • Issue 9 • September 2011
Pages: 959 - 975
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jun 15, 2010
Accepted: Nov 30, 2010
Published online: Jan 28, 2011
Published in print: Sep 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.