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

Abstract

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

2010 MSC Number:

O351.2

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

TrendMD

References

[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.

[1]	Dalin TAN, Xu WANG, Jinlong DUAN, Jifu ZHOU. Linear analysis of the dynamic response of a riser subject to internal solitary waves [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 1023-1034.
[2]	Weiguo ZHANG, Siyu HONG, Xingqian LING, Wenxia LI. Influence of dissipation on solitary wave solution to generalized Boussinesq equation [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(3): 477-498.
[3]	Zhihui ZHANG, Liguo CHEN, Ruigang ZHANG, Liangui YANG, Quansheng LIU. Dynamics of Rossby solitary waves with time-dependent mean flow via Euler eigenvalue model [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1615-1630.
[4]	M. ISHAQ, Hang XU. Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(8): 1139-1156.
[5]	Dalin TAN, Jifu ZHOU, Xu WANG, Zhan WANG. Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 421-434.
[6]	H. SAGHI;M. J. KETABDARI;S. BOOSHI. Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1179-1190.
[7]	Jing-sun YAO;Cheng OU-YANG;Li-hua CHEN;Jia-qi MO. Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1583-1594.
[8]	ZHANG Shan-yuan;LIU Zhi-fang. Three kinds of nonlinear dispersive waves in elastic rods with finite deformation [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(7): 909-917 .
[9]	LI Ji-bin. Exact traveling wave solutions for an integrable nonlinear evolution equation given by M. Wadati [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(4): 437-440 .
[10]	FENG Da-he;LI Ji-bin. Bifurcations of travelling wave solutions for Jaulent-Miodek equations [J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 999-1005 .
[11]	YUAN Yu-bo;PU Dong-mei;LI Shu-min. BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS [J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(6): 811-822 .
[12]	WU Zheng-ren;CHENG You-liang;WANG Song-ling;LÜYu-kun. EFFECTS OF VARYING BOTTOM ON NONLINEAR SURFACE WAVES [J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(3): 409-416 .
[13]	XU Gui-qiong;LI Zhi-bin. EXPLICIT SOLUTIONS TO THE COUPLED KdV EQUATIONS WITH VARIABLE COEFFICIENTS [J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(1): 101-107 .
[14]	MA Chen-ming . INTERNAL RESONANT INTERACTIONS OF THREE FREE SURFACE-WAVES IN A CIRCULAR CYLINDRICAL BASIN [J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(12): 1411-1420.
[15]	ZHANG Ren;WANG Ji-guang;YU Zhi-hao;JIANG Quan-rong. ROSSBY INERTIA GRAVITY SOLITARY WAVE AND THE REMOTE CORRELATION BETWEEN THE EAST-AND THE WEST-PACIFIC SUBTROPICAL HIGH [J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(7): 794-803.