波浪与泥质海床的相互作用
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摘要
泥质海岸的动力特性及其与海洋动力环境的相互作用是海岸及近海工程中有着重要理论意义和广泛应用价值的研究课题。本论文将海床上可运动、可变形的底泥作为单相非牛顿流体,从不可压缩流体运动的基本方程出发,建立了波浪作用下底泥运动的数值模型以及水体与底泥耦合运动的数值模型,并以此为基础分析了波浪与泥质底床的相互作用过程,相比于以往基于理论解析的研究方法具有更为广泛的应用前景。
底泥运动以不可压缩流体运动的连续方程和动量方程为基本方程,同时针对底泥复杂的非牛顿流变特性,引入了一个高度综合的粘弹塑性模型。该模型对应的流变方程能简化为常见的粘性模型、粘弹性模型、粘弹塑性模型。基本方程的数值求解由SMAC方法拓展而成,并针对大粘度底泥运动问题需要提高计算稳定性的事实,对动量方程的时间离散进行了改进。数值模型在平板起动流计算中的应用证明了其有效性。论文还通过对二维槽道进口段流动进行计算,分析了不同格式的稳定性和计算效率。
波浪作用下底泥运动的数值模型是将波浪作用简化为作用于泥层顶部的周期性波压,忽略了底泥动力相应对波浪的影响。论文采用不同的底泥流变模型,系统分析了底泥粘性、弹性、塑性在波浪作用下的底泥运动中对底泥运动速度的幅值、物质输移速度、能量耗散等的影响,还探讨了波高与底泥运动特征量之间的关系。
水体与底泥耦合运动模型中考虑了底泥对波浪的影响,以及水体紊动和域内存在多个运动界面的情况。模型中采用k-ε模型处理紊流,自由水面利用VOF方法追踪。泥层界面用泥沙物质守恒方程描述,并针对底泥分层的情况,利用ENO的思路结合Youngs界面重构技术特别构建了数值处理方法。耦合模型能很好地反映波浪与底泥的相互作用。模型应用于计算波浪在不同性质的泥床上的传播和变形过程,并与实验比较,在一定程度上明确了底泥流变模型的适用范围。论文还初步探讨了底泥呈层特性对波浪衰减的影响,以及复杂地形条件下底泥对波浪传播和变形的影响。
The dynamic interaction between waves and muddy seabed is studied. The mud is considered as a non-Newtonian fluid with complex rheological property including viscosity, elasticity, and plasticity. An extraordinarily generalized constitutive equation is proposed, which includes various existing models as special cases. The numerical method is based on the well-known SMAC method in modern CFD, but the discretization of the momentum equations is replaced by a weighted implicit scheme to achieve a better stability, which is definitely necessary when mud with very large viscosity is involved.
The response of muddy seabed to surface water waves is investigated based on the non-Newtonian fluid flow model established. The wave action is represented by periodic pressure acting on the surface of the seabed. The effects of the viscosity, the elasticity, and the plasticity of the mud on the motion of the seabed and its resulting mud transport are discussed. The relationship between wave height and the amplitude of the velocity, the rate of mass transport and energy dissipation is also clarified.
A fully coupled model is also developed to deal with the dynamic interaction between waves and the muddy seabed. The k-εturbulence model is used. The free water surface is treated by the VOF method, while the numerical method for tracing the moving water-mud interfaces and the interfaces between different mud layers is specially developed, which combines the essence of ENO and Youngs’reconstruction scheme. The coupled model is applied to the study of wave propagation over a mud layer under various conditions. It is demonstrated that the viscous model is fairly satisfactory for mud with low density, but the plastic feature of the mud plays an important role when the density of the mud is relatively large. The model is also employed to study the effects of the seabed stratification on wave motion. It is also shown to be applicable to problems with practical background.
底泥运动以不可压缩流体运动的连续方程和动量方程为基本方程,同时针对底泥复杂的非牛顿流变特性,引入了一个高度综合的粘弹塑性模型。该模型对应的流变方程能简化为常见的粘性模型、粘弹性模型、粘弹塑性模型。基本方程的数值求解由SMAC方法拓展而成,并针对大粘度底泥运动问题需要提高计算稳定性的事实,对动量方程的时间离散进行了改进。数值模型在平板起动流计算中的应用证明了其有效性。论文还通过对二维槽道进口段流动进行计算,分析了不同格式的稳定性和计算效率。
波浪作用下底泥运动的数值模型是将波浪作用简化为作用于泥层顶部的周期性波压,忽略了底泥动力相应对波浪的影响。论文采用不同的底泥流变模型,系统分析了底泥粘性、弹性、塑性在波浪作用下的底泥运动中对底泥运动速度的幅值、物质输移速度、能量耗散等的影响,还探讨了波高与底泥运动特征量之间的关系。
水体与底泥耦合运动模型中考虑了底泥对波浪的影响,以及水体紊动和域内存在多个运动界面的情况。模型中采用k-ε模型处理紊流,自由水面利用VOF方法追踪。泥层界面用泥沙物质守恒方程描述,并针对底泥分层的情况,利用ENO的思路结合Youngs界面重构技术特别构建了数值处理方法。耦合模型能很好地反映波浪与底泥的相互作用。模型应用于计算波浪在不同性质的泥床上的传播和变形过程,并与实验比较,在一定程度上明确了底泥流变模型的适用范围。论文还初步探讨了底泥呈层特性对波浪衰减的影响,以及复杂地形条件下底泥对波浪传播和变形的影响。
The dynamic interaction between waves and muddy seabed is studied. The mud is considered as a non-Newtonian fluid with complex rheological property including viscosity, elasticity, and plasticity. An extraordinarily generalized constitutive equation is proposed, which includes various existing models as special cases. The numerical method is based on the well-known SMAC method in modern CFD, but the discretization of the momentum equations is replaced by a weighted implicit scheme to achieve a better stability, which is definitely necessary when mud with very large viscosity is involved.
The response of muddy seabed to surface water waves is investigated based on the non-Newtonian fluid flow model established. The wave action is represented by periodic pressure acting on the surface of the seabed. The effects of the viscosity, the elasticity, and the plasticity of the mud on the motion of the seabed and its resulting mud transport are discussed. The relationship between wave height and the amplitude of the velocity, the rate of mass transport and energy dissipation is also clarified.
A fully coupled model is also developed to deal with the dynamic interaction between waves and the muddy seabed. The k-εturbulence model is used. The free water surface is treated by the VOF method, while the numerical method for tracing the moving water-mud interfaces and the interfaces between different mud layers is specially developed, which combines the essence of ENO and Youngs’reconstruction scheme. The coupled model is applied to the study of wave propagation over a mud layer under various conditions. It is demonstrated that the viscous model is fairly satisfactory for mud with low density, but the plastic feature of the mud plays an important role when the density of the mud is relatively large. The model is also employed to study the effects of the seabed stratification on wave motion. It is also shown to be applicable to problems with practical background.
引文
白玉川,胡世雄,金玉石. (2001).泥质床面上波浪衰减规律的研究.水利学报(11): 56-61.
曹祖德. (1990).日本熊本港的淤积分析.港口工程(3): 28-36.
韩式方. (2000).非牛顿流体本构方程和计算解析理论.北京:科学出版社.
练继建,赵子丹. (1994).波流作用下底泥的响应.水动力学研究与进展A辑, 9(4): 460-468.
练继建,赵子丹. (1995).波流与淤泥质海床的相互作用.泥沙研究(3): 40-50.
练继建,赵子丹,张庆河. (1999).波流作用下底泥输移的非线性粘弹性体模型.科学通报, 44(4): 445-448.
钱宁,万兆惠. (2003).泥沙运动力学.北京:科学出版社.
王以谋,范顺庭,王兴德. (1995).黄河口“烂泥”波浪特性的分析.海洋科学(6): 42-46.
吴其晔,巫静安. (2002).高分子材料流变学.高等教育出版社.
吴永胜,王兆印,胡世雄. (2003).淤泥对波浪衰减作用的数值模拟.水利学报(7): 22-29.
严恺. (2002).海岸工程.北京:海洋出版社.
张庆河. (1994).规则波、不规则波与淤泥质底床的相互作用[博士学位论文].水资源与港湾工程系,天津大学.
张庆河,赵子丹. (1997).波浪作用下的底泥质量输移.天津大学学报, 30(3): 274-280.
张庆河,王殿志,赵子丹. (2002).扰动淤泥和沉积淤泥的流变特性研究.水利学报(6): 77-82.
赵子丹. (1982).波浪作用下的浮泥输送.海洋通报(6): 65-74.
赵子丹,李贺春,郭美谊. (1993).不规则波在浮泥床面上传播的实验研究.海洋通报(4).
赵子丹,张庆河. (1993).泥床上的波浪衰减--伪塑性体模型.海洋通报, 12(6): 1-7.
赵子丹,练继建. (1994).波浪在淤泥质床面上传播时波要素的变化.天津大学学报, 27(5): 521-528.
赵子丹,刘同利. (1997).淤泥流变参数的确定.海洋通报, 16(5): 71-78.
赵子丹,张庆河. (1997a).不规则波在淤泥质底床上的传播.水利学报(4): 35-41.
赵子丹,张庆河. (1997b).规则波与淤泥质底床的相互作用--波浪衰减.水利学报(4): 26-34.
中国海洋学会. (1998).漫长的中国海岸.郑州:大象出版社.
Amsden A A, Harlow F H. (1970). The SMAC method: a numerical technique for calculating incompressible fluid flows. Rep. No. LA-4370, Los Alamos Sci. Lab.
An N N. (1993). Mud mass transport under wave and current. Department of Civil Engineering, Yokohama National University.
Beji S, Battjes J A. (1993). Experimental investigation of wave propagation over a bar. Coastal Engineering, 19: 151-162.
Beji S, Battjes J A. (1994). Numerical simulation of nonlinear wave propagation over a bar. Coastal Engineering, 23: 1-16.
Brorsen M, Larsen J. (1987). Source generation of nonlinear gravity waves with the boundary integral equation method. Coastal Engineering, 11(2): 93-113.
Dalrymple R A, Liu P L-F. (1978). Waves over soft muds: A two-layer fluid model. Journal of Physical Oceangraphy, 8: 1121-1131.
Gade H G. (1958). Effect of nonrigid, impermeable bottom on plane surface waves in shallow water. Journal of Marine Research, 16(2): 61-82.
Gobbi M F, Kirby J T. (1999). Wave evolution over submerged sills: tests of a high-order Boussinesq model. Coastal Engineering, 37: 57-96.
Hall K, Oveisy A. (2007). Wave evolution on fluid mud bottom. Coastal Sediments '07 - Proceedings of 6th International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, New Orleans, LA, United States.
Huang L, Ng C-O, Chwang A T. (2006). A Fourier-Chebyshev collocation method for the mass transport in a layer of power-law fluid mud. Computer Methods in Applied Mechanics and Engineering, 195: 1136-1153.
Jiang F. (1993). Bottom Mud Transport due to Water Waves [D]. Coastal and Oceanographic Engineering Department, University of Florida.
Jiang L, Zhao Z. (1989). Viscous damping of solitary waves over fluid-mud seabeds. Journal of Waterway, Port, Coastal, and Ocean Engineering, 115(3): 345-362.
Jiang L, Kioka W, Ishida A. (1990). Viscous damping of cnoidal waves over fluid-mud seabed. Journal of Waterway, Port, Coastal, and Ocean Engineering, 116(4): 470-491.
Jiang Q. (1996). Study on Rheological Properties and Mass Transport of Soft Mud under Water Waves [D]. Department of Civil Engineering, Tokyo University.
Lee S-C, Mehta A J. (1997). Problems in characterizing dynamics of mud shore profiles. Journal of Hydraulic Engineering, 123(4): 351-361.
Liu P L-F, Chan I-C. (2007). A note on the effects of a thin visco-elastic mud layer on small amplitude water-wave propagation. Coastal Engineering, 54: 233-247.
Longuet-Higgins M S. (1953). Mass transport in water waves. Philosophical transactions of the Royal Society of London.Series A,Mathematical and Physical Sciences, 245(903): 535-581.
Maa P-Y. (1986 ). Erosion of soft muds by waves [D]. Civil Engineering, University of Florida. Maa P-Y, Mehta A J. (1988). Soft mud properties: Voigt model. Journal of Waterway, Port, Coastal, and Ocean Engineering, 114(6).
Maa P-Y, Mehta A J. (1990). Soft mud response to water waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 116(5): 634-650.
Macpherson H. (1980). The attenuation of water waves over a non-rigid bed. Journal of Fluid Mechanics, 97(4): 721-742.
Mallard W W, Dalrymple R A. (1977). Water waves propagating over a deformable bottom. Proceeding 9th Offshore Technology Conference, Houston, 141-146.
Mathew J. (1992). Wave-mud interaction in mudbanks. Cochin Univerisity of Science and Technology.
Mehta A J, Lee S-C, Li Y. (1994). Fluid Mud and Water Waves: A Brief Review of Interactive Processes and Simple Modeling Approaches. Florida.
Mei C C, Liu K-F. (1987). A Bingham-plastic model for a muddy seabed under long waves. Journal of Geophysical Research, 92( C13): 14581-14594.
Ng C-O. (2000). Water waves over a muddy bed: a two-layer Stokes' boundary layer model. Coastal Engineering, 40: 221-242.
Sakakiyama T, Bijker E W. (1989). Mass transport velocity in mud layer due to progressive waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 115(5): 614-633.
Shen D. (1993). Study on Mud Mass Transport and Topography Change of Muddy Bottom due to Waves [D]. Department of Civil Engineering, Tokyo University.
Shibayama T, Okuno M, Sato S. (1990). Mud transport rate in mud layer due to wave action. Proceeding 22nd International Conference on Coatal Engineering, 3037-3049.
Soltanpour M. (1999). Two Dimensional Modeling of Mud Profile Processes [D]. Department of Civil Engineering, Yokohama National University.
Soltanpour M, Haghshenas S A, Shibayama T. (2007a). Time dependent mud fluidization and irregular wave transformation on muddy profiles. Coastal Sediments '07 - Proceedings of 6th International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, New Orleans, LA, United States.
Soltanpour M, Shibayama T, Masuya Y. (2007b). Irregular wave attenuation and mud mass transport. Coastal Engineering Journal, 49(2): 127-147.
Tome M F, Mangiavacchi N, Cuminato J A, Castelo A, McKee S. (2002). A finite difference technique for simulating unsteady viscoelastic free surface flows. Journal of Non-Newtonian Fluid Mechanics, 106: 61-106.
Trien H N (1991). Study on Mud Transport in Coastal Waters [D]. Department of Civil Engineering, University of Tokyo.
Trien H N, Isobe M, Kobayashi T, Watanabe A. (1990). An experimental study on rheological properties of mud in the coastal waters. Proceeding of Coastal Engineering, JSCE, 225-229.
Tsuruya H, Nakano S, Takahama J. (1987). Investigation between surface waves and amultilayered mud bed. Report of the Port and Harbor Research Institute, Ministry of Transport, Japan
Tubman M W, Suhayada J N. (1976). Wave action and bottom movements in fine sediments. Proceedings of 15th International Conference on Coastal Engineering., 1168-1183.
Wells J T, Kemp G P. (1986). Interaction of surface waves and cohesive sediments: field observations and geologic significance. A. J. Mehta. Estuarine Cohesive Sediment Transport. Berlin: Springer-Verlag, 43-65.
Winterwerp J C, Graaff R F d, Groeneweg J, Luijendijk A P. (2007). Modelling of wave damping at Guyana mud coast. Coastal Engineering, 54(3): 249-261.
Yamamoto T. (1982). On the response of a Coulomb-damped poroelastic bed to water waves. Marine Geotechnology, 5(2): 93-130.
Yamamoto T, Takahashi S. (1985). Wave damping by soil motion. Journal of Waterway, Port, Coastal, and Ocean Engineering, 111(1): 62-77.
Zhang D, Ng C-O. (2006). A numerical study on wave-mud interaction. China Ocean Engineering, 20(3): 383-394.
Zhang Q, Wai O W H, Lee J H W. (2003). Wave attenuation over mud bed: A pseudo-plastic model. Journal of Hydrodynamics, 15(6): 32-38.
Zhang X, Ng C-O. (2006a). On the oscillatory and mean motions due to waves in a thin viscoelastic layer. Wave Motion, 43(5): 387-405.
Zhang X, Ng C-O. (2006b). Mud-wave interaction: A viscoelastic model. China Ocean Engineering, 20(1): 15-26.
Zhao Z, Lian J, Shi J. (2006). Interactions among waves, current, and mud: Numerical and laboratory studies. Advances in Water Resources, 29(11): 1731-1744.
曹祖德. (1990).日本熊本港的淤积分析.港口工程(3): 28-36.
韩式方. (2000).非牛顿流体本构方程和计算解析理论.北京:科学出版社.
练继建,赵子丹. (1994).波流作用下底泥的响应.水动力学研究与进展A辑, 9(4): 460-468.
练继建,赵子丹. (1995).波流与淤泥质海床的相互作用.泥沙研究(3): 40-50.
练继建,赵子丹,张庆河. (1999).波流作用下底泥输移的非线性粘弹性体模型.科学通报, 44(4): 445-448.
钱宁,万兆惠. (2003).泥沙运动力学.北京:科学出版社.
王以谋,范顺庭,王兴德. (1995).黄河口“烂泥”波浪特性的分析.海洋科学(6): 42-46.
吴其晔,巫静安. (2002).高分子材料流变学.高等教育出版社.
吴永胜,王兆印,胡世雄. (2003).淤泥对波浪衰减作用的数值模拟.水利学报(7): 22-29.
严恺. (2002).海岸工程.北京:海洋出版社.
张庆河. (1994).规则波、不规则波与淤泥质底床的相互作用[博士学位论文].水资源与港湾工程系,天津大学.
张庆河,赵子丹. (1997).波浪作用下的底泥质量输移.天津大学学报, 30(3): 274-280.
张庆河,王殿志,赵子丹. (2002).扰动淤泥和沉积淤泥的流变特性研究.水利学报(6): 77-82.
赵子丹. (1982).波浪作用下的浮泥输送.海洋通报(6): 65-74.
赵子丹,李贺春,郭美谊. (1993).不规则波在浮泥床面上传播的实验研究.海洋通报(4).
赵子丹,张庆河. (1993).泥床上的波浪衰减--伪塑性体模型.海洋通报, 12(6): 1-7.
赵子丹,练继建. (1994).波浪在淤泥质床面上传播时波要素的变化.天津大学学报, 27(5): 521-528.
赵子丹,刘同利. (1997).淤泥流变参数的确定.海洋通报, 16(5): 71-78.
赵子丹,张庆河. (1997a).不规则波在淤泥质底床上的传播.水利学报(4): 35-41.
赵子丹,张庆河. (1997b).规则波与淤泥质底床的相互作用--波浪衰减.水利学报(4): 26-34.
中国海洋学会. (1998).漫长的中国海岸.郑州:大象出版社.
Amsden A A, Harlow F H. (1970). The SMAC method: a numerical technique for calculating incompressible fluid flows. Rep. No. LA-4370, Los Alamos Sci. Lab.
An N N. (1993). Mud mass transport under wave and current. Department of Civil Engineering, Yokohama National University.
Beji S, Battjes J A. (1993). Experimental investigation of wave propagation over a bar. Coastal Engineering, 19: 151-162.
Beji S, Battjes J A. (1994). Numerical simulation of nonlinear wave propagation over a bar. Coastal Engineering, 23: 1-16.
Brorsen M, Larsen J. (1987). Source generation of nonlinear gravity waves with the boundary integral equation method. Coastal Engineering, 11(2): 93-113.
Dalrymple R A, Liu P L-F. (1978). Waves over soft muds: A two-layer fluid model. Journal of Physical Oceangraphy, 8: 1121-1131.
Gade H G. (1958). Effect of nonrigid, impermeable bottom on plane surface waves in shallow water. Journal of Marine Research, 16(2): 61-82.
Gobbi M F, Kirby J T. (1999). Wave evolution over submerged sills: tests of a high-order Boussinesq model. Coastal Engineering, 37: 57-96.
Hall K, Oveisy A. (2007). Wave evolution on fluid mud bottom. Coastal Sediments '07 - Proceedings of 6th International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, New Orleans, LA, United States.
Huang L, Ng C-O, Chwang A T. (2006). A Fourier-Chebyshev collocation method for the mass transport in a layer of power-law fluid mud. Computer Methods in Applied Mechanics and Engineering, 195: 1136-1153.
Jiang F. (1993). Bottom Mud Transport due to Water Waves [D]. Coastal and Oceanographic Engineering Department, University of Florida.
Jiang L, Zhao Z. (1989). Viscous damping of solitary waves over fluid-mud seabeds. Journal of Waterway, Port, Coastal, and Ocean Engineering, 115(3): 345-362.
Jiang L, Kioka W, Ishida A. (1990). Viscous damping of cnoidal waves over fluid-mud seabed. Journal of Waterway, Port, Coastal, and Ocean Engineering, 116(4): 470-491.
Jiang Q. (1996). Study on Rheological Properties and Mass Transport of Soft Mud under Water Waves [D]. Department of Civil Engineering, Tokyo University.
Lee S-C, Mehta A J. (1997). Problems in characterizing dynamics of mud shore profiles. Journal of Hydraulic Engineering, 123(4): 351-361.
Liu P L-F, Chan I-C. (2007). A note on the effects of a thin visco-elastic mud layer on small amplitude water-wave propagation. Coastal Engineering, 54: 233-247.
Longuet-Higgins M S. (1953). Mass transport in water waves. Philosophical transactions of the Royal Society of London.Series A,Mathematical and Physical Sciences, 245(903): 535-581.
Maa P-Y. (1986 ). Erosion of soft muds by waves [D]. Civil Engineering, University of Florida. Maa P-Y, Mehta A J. (1988). Soft mud properties: Voigt model. Journal of Waterway, Port, Coastal, and Ocean Engineering, 114(6).
Maa P-Y, Mehta A J. (1990). Soft mud response to water waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 116(5): 634-650.
Macpherson H. (1980). The attenuation of water waves over a non-rigid bed. Journal of Fluid Mechanics, 97(4): 721-742.
Mallard W W, Dalrymple R A. (1977). Water waves propagating over a deformable bottom. Proceeding 9th Offshore Technology Conference, Houston, 141-146.
Mathew J. (1992). Wave-mud interaction in mudbanks. Cochin Univerisity of Science and Technology.
Mehta A J, Lee S-C, Li Y. (1994). Fluid Mud and Water Waves: A Brief Review of Interactive Processes and Simple Modeling Approaches. Florida.
Mei C C, Liu K-F. (1987). A Bingham-plastic model for a muddy seabed under long waves. Journal of Geophysical Research, 92( C13): 14581-14594.
Ng C-O. (2000). Water waves over a muddy bed: a two-layer Stokes' boundary layer model. Coastal Engineering, 40: 221-242.
Sakakiyama T, Bijker E W. (1989). Mass transport velocity in mud layer due to progressive waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 115(5): 614-633.
Shen D. (1993). Study on Mud Mass Transport and Topography Change of Muddy Bottom due to Waves [D]. Department of Civil Engineering, Tokyo University.
Shibayama T, Okuno M, Sato S. (1990). Mud transport rate in mud layer due to wave action. Proceeding 22nd International Conference on Coatal Engineering, 3037-3049.
Soltanpour M. (1999). Two Dimensional Modeling of Mud Profile Processes [D]. Department of Civil Engineering, Yokohama National University.
Soltanpour M, Haghshenas S A, Shibayama T. (2007a). Time dependent mud fluidization and irregular wave transformation on muddy profiles. Coastal Sediments '07 - Proceedings of 6th International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, New Orleans, LA, United States.
Soltanpour M, Shibayama T, Masuya Y. (2007b). Irregular wave attenuation and mud mass transport. Coastal Engineering Journal, 49(2): 127-147.
Tome M F, Mangiavacchi N, Cuminato J A, Castelo A, McKee S. (2002). A finite difference technique for simulating unsteady viscoelastic free surface flows. Journal of Non-Newtonian Fluid Mechanics, 106: 61-106.
Trien H N (1991). Study on Mud Transport in Coastal Waters [D]. Department of Civil Engineering, University of Tokyo.
Trien H N, Isobe M, Kobayashi T, Watanabe A. (1990). An experimental study on rheological properties of mud in the coastal waters. Proceeding of Coastal Engineering, JSCE, 225-229.
Tsuruya H, Nakano S, Takahama J. (1987). Investigation between surface waves and amultilayered mud bed. Report of the Port and Harbor Research Institute, Ministry of Transport, Japan
Tubman M W, Suhayada J N. (1976). Wave action and bottom movements in fine sediments. Proceedings of 15th International Conference on Coastal Engineering., 1168-1183.
Wells J T, Kemp G P. (1986). Interaction of surface waves and cohesive sediments: field observations and geologic significance. A. J. Mehta. Estuarine Cohesive Sediment Transport. Berlin: Springer-Verlag, 43-65.
Winterwerp J C, Graaff R F d, Groeneweg J, Luijendijk A P. (2007). Modelling of wave damping at Guyana mud coast. Coastal Engineering, 54(3): 249-261.
Yamamoto T. (1982). On the response of a Coulomb-damped poroelastic bed to water waves. Marine Geotechnology, 5(2): 93-130.
Yamamoto T, Takahashi S. (1985). Wave damping by soil motion. Journal of Waterway, Port, Coastal, and Ocean Engineering, 111(1): 62-77.
Zhang D, Ng C-O. (2006). A numerical study on wave-mud interaction. China Ocean Engineering, 20(3): 383-394.
Zhang Q, Wai O W H, Lee J H W. (2003). Wave attenuation over mud bed: A pseudo-plastic model. Journal of Hydrodynamics, 15(6): 32-38.
Zhang X, Ng C-O. (2006a). On the oscillatory and mean motions due to waves in a thin viscoelastic layer. Wave Motion, 43(5): 387-405.
Zhang X, Ng C-O. (2006b). Mud-wave interaction: A viscoelastic model. China Ocean Engineering, 20(1): 15-26.
Zhao Z, Lian J, Shi J. (2006). Interactions among waves, current, and mud: Numerical and laboratory studies. Advances in Water Resources, 29(11): 1731-1744.