MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1118-1129.

MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

刘长根, 陶建华

Department of Mechanics, Tianjin University, Tianjin 300072, P.R.China

收稿日期:2003-04-05 修回日期:2004-06-15 出版日期:2004-10-18 发布日期:2004-10-18
通讯作者: TAO Jian-hua,Professor(Tel:+86-22-27404403;Fax:+86-22-27401647;E-mail:jhtao@tju.edu.cn) E-mail:jhtao@tju.edu.cn
基金资助:
the National "863" Project of China(2002AA639610);the National Natural Science Foundation of C1hina(598339330),LIU Hui Center for Applied Mathematics,Naikai University & Tianjin University

MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

LIU Chang-gen, TAO Jian-hua

Department of Mechanics, Tianjin University, Tianjin 300072, P.R.China

Received:2003-04-05 Revised:2004-06-15 Online:2004-10-18 Published:2004-10-18
Supported by:
the National "863" Project of China(2002AA639610);the National Natural Science Foundation of C1hina(598339330),LIU Hui Center for Applied Mathematics,Naikai University & Tianjin University

摘要/Abstract

摘要： A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.

关键词: Reynolds equation, VOF method, free surface, semi-circular breakwater, solitary wave

Abstract: A vertical 2-D numerical wave model was developed based on unsteady Reynolds equations. In this model, the k-epsilon models were used to close the Reynolds equations, and volume of fluid(VOF) method was used to reconstruct the free surface. The model was verified by experimental data. Then the model was used to simulate solitary wave interaction with submerged, alternative submerged and emerged semi-circular breakwaters. The process of velocity field, pressure field and the wave surface near the breakwaters was obtained. It is found that when the semi-circular breakwater is submerged, a large vortex will be generated at the bottom of the lee side wall of the breakwater; when the still water depth is equal to the radius of the semi-circular breakwater, a pair of large vortices will be generated near the shoreward wall of the semi-circular breakwater due to wave impacting, but the velocity near the bottom of the lee side wall of the breakwater is always relatively small. When the semi-circular breakwater is emerged, and solitary wave cannot overtop it, the solitary wave surface will run up and down secondarily during reflecting from the breakwater. It can be further used to estate the diffusing and transportation of the contamination and transportation of suspended sediment.

Key words: Reynolds equation, VOF method, free surface, semi-circular breakwater, solitary wave

中图分类号:

O351.2

刘长根;陶建华. MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1118-1129.

LIU Chang-gen;TAO Jian-hua. MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1118-1129.

参考文献

[1] XIE Shi-leng. Wave forces on semi-circular breakwaters when the breakwater is in submerged[J]. Journal of Technology on Port Engineering, 1998, 15(2): 1-5. (in Chinese)
[2] TAO Jian-hua, YUAN De-kui, LIU Chang-gen. Computation the wave height for designing the breakwaters in the second stage of the deep channel projection in the estuary of Yangtze River[R].Tanjin: Technical Report of Tianjin University, 2002. (in Chinese).
[3] WANG Hai-bing, LIU Zi-qi. Research on the section models of the semi-circular breakwaters used in Tianjin Port North Breakwater projection[R]. Tianjin: Tianjin Port and Harbour Research Institute, 1995. (in Chinese)
[4] JIA Dong-hua. Numerical model for the semi-circular breakwater[R]. Technical Report of the First Design Institute of Navigation Engineering, Ministry of Communication of China, 1999. (in Chinese)
[5] YUAN De-kui, TAO Jian-hua. Wave forces on submerged, alternately submerged, and emerged semicircular breakwaters[J]. Coastal Engineering, 2003,48 (2): 75-93.
[6] Hirt C W, Nichols B D. Volume of fluid (VOF) Method for the dynamics of free boundaries[J].Journal of Computational Physics, 1981,39(1):201-225.
[7] Youngs D L. Time-dependent multi-material flow with large fluid distortion[A]. In: Morton K W,Baineks M J Eds. Numerical Methods for Fluid Dynamics[C]. New York: Academic, 1982,273-285.
[8] ZHUANG Fei, LEE Jiin-Jin. A viscous rotational model for wave overtopping over marine structure[A]. In: Billy L Edge Ed. Proc 25 th Internat Conf Coastal Eng[C]. Florida: ASCE, 1996, 2178-2191.
[9] Launder B E, Spalding D B. The numerical computation of turbulent flows[J]. Computer Methods in Applied Mechanics and Engineering, 1974,3(1):269-289.
[10] Larsen Jesper, Dancy Henry. Open boundaries in short wave simulations-a new approach[J].Coastal Engineering, 1983,7(3):285-297.
[11] Ashgriz N,Poo JY. FLAIR(flux line-segment model for advection and interface reconstruction)[J].Journal of Computational Physics, 1991,93(2):449-468.
[12] Chorin A J. On the convergence of discrete approximations of the Navier-Stokes equations[J]. Math Comp, 1969,23(106): 341-353.
[13] LIN Peng-zhi, LIU Philip L-F. A numerical study of breaking waves in the surface zone[J]. J Fluid Mech, 1998,359 (6): 239-264.

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MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

MODELING THE INTERACTION OF SOLITARY WAVES AND SEMI-CIRCULAR BREAKWATERS BY USING UNSTEADY REYNOLDS EQUATIONS

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