河流海岸系统综合水动力学模型研究
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摘要
波浪、潮流、波生流、河川径流等是河口海岸地区重要的水动力学现象。这些水动力学现象具有不同的时空尺度,但又相互作用、相互影响。建立一个实用的统一理论对这些现象及其相互作用进行描述是非常必要的,也是富有挑战性的。
本论文将能精确地反映海域内波动流场的非线性和频散特性、可以应用到潮汐、风暴潮等对河口产生重要影响的近岸水动力模型和能够模拟河道内洪水演进等非恒定流问题的河道水动力学模型进行耦合,结合二维模型和一维模型各自的优势,建立了一个河流海岸系统综合水动力学模型。
近岸水动力学模型基于改进的Boussinesq方程。模型中采用了Kennedy等人建议的[1]波浪破碎模型。数学模型的数值求解在交错网格上进行,时间步进采用ADI格式,离散后的方程组用追赶法求解。验证和应用的结果表明,基于Boussinesq方程的近岸水动力学模型具有强大的功能和良好的精度。不仅能够描述近岸波浪传播、变形乃至破碎等现象,同时也能描述波生流现象。
河流水动力学模型基于Saint-Venant方程。数值方法采用了Preissman格式。验证和应用的结果表明,河道水动力学模型不仅能够精确地描述河道内孤立波的传播及碰撞,对于钱塘江涌潮的描述也具有非常高的精度。论文利用流量和水位的连续条件,实现了近岸水动力学模型及河道水
动力学模型的耦合求解,建立了河流海岸综合水动力学模型。综合水动模型用于研究长江口及口内感潮河道径流与潮流的相互作用,涨潮及落潮过程中水流运动的基本规律。计算得到的各测站水位、流速及流向与观测资料吻合良好。
An integrated model for the study of river, estuarine, and coastal hydrodynamics is developed. The model consists of a two-dimensional component for coastal hydrodynamics and a one-dimensional component for river channel flows.
The two-dimensional model for coastal hydrodynamics is based on the extended Boussinesq equations. A simple but effective model is introduced to represent the energy dissipation due to wave breaking and seabed friction. The model is applied to the computation of wave transformation and breaking over a submerged shoal, and of wave transformation around a detached breakwater. In both cases, the computational results are in good agreement with experimental data. The model is also shown to be valid for wave-induced currents. The excellent performance of the model is demonstrated as applied to the simulation of the rip current generated by waves propagating over a plane beach with two longshore bars separated by a narrow channel.
The Saint-Venant equations are used as the governing equations of river hydrodynamics. They are also solved by the finite difference method. The model is verified by an analytic solution for the propagation and collision of solitary waves. It is also used to the computation of the tidal bore in Qiantang River, and the computational results are shown to agree well with measured data.
The integrated model is used to study the interaction between the river flow and the tidal flow in the estuary of Yangtze River. The computational results are demonstrated to be in good agreement with the measured data.
本论文将能精确地反映海域内波动流场的非线性和频散特性、可以应用到潮汐、风暴潮等对河口产生重要影响的近岸水动力模型和能够模拟河道内洪水演进等非恒定流问题的河道水动力学模型进行耦合,结合二维模型和一维模型各自的优势,建立了一个河流海岸系统综合水动力学模型。
近岸水动力学模型基于改进的Boussinesq方程。模型中采用了Kennedy等人建议的[1]波浪破碎模型。数学模型的数值求解在交错网格上进行,时间步进采用ADI格式,离散后的方程组用追赶法求解。验证和应用的结果表明,基于Boussinesq方程的近岸水动力学模型具有强大的功能和良好的精度。不仅能够描述近岸波浪传播、变形乃至破碎等现象,同时也能描述波生流现象。
河流水动力学模型基于Saint-Venant方程。数值方法采用了Preissman格式。验证和应用的结果表明,河道水动力学模型不仅能够精确地描述河道内孤立波的传播及碰撞,对于钱塘江涌潮的描述也具有非常高的精度。论文利用流量和水位的连续条件,实现了近岸水动力学模型及河道水
动力学模型的耦合求解,建立了河流海岸综合水动力学模型。综合水动模型用于研究长江口及口内感潮河道径流与潮流的相互作用,涨潮及落潮过程中水流运动的基本规律。计算得到的各测站水位、流速及流向与观测资料吻合良好。
An integrated model for the study of river, estuarine, and coastal hydrodynamics is developed. The model consists of a two-dimensional component for coastal hydrodynamics and a one-dimensional component for river channel flows.
The two-dimensional model for coastal hydrodynamics is based on the extended Boussinesq equations. A simple but effective model is introduced to represent the energy dissipation due to wave breaking and seabed friction. The model is applied to the computation of wave transformation and breaking over a submerged shoal, and of wave transformation around a detached breakwater. In both cases, the computational results are in good agreement with experimental data. The model is also shown to be valid for wave-induced currents. The excellent performance of the model is demonstrated as applied to the simulation of the rip current generated by waves propagating over a plane beach with two longshore bars separated by a narrow channel.
The Saint-Venant equations are used as the governing equations of river hydrodynamics. They are also solved by the finite difference method. The model is verified by an analytic solution for the propagation and collision of solitary waves. It is also used to the computation of the tidal bore in Qiantang River, and the computational results are shown to agree well with measured data.
The integrated model is used to study the interaction between the river flow and the tidal flow in the estuary of Yangtze River. The computational results are demonstrated to be in good agreement with the measured data.
引文
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[2]恽才兴.长江河口近期演变基本规律.北京:海洋出版社, 2004.
[3]谷汉斌,孙精石,郑宝友等.近岸波浪数学模型的发展.水道港口, 2004, 25(02): 78-83.
[4]李孟国,蒋德才.关于波浪缓坡方程的研究.海洋通报, 1999, 18(04): 70-92.
[5]陶建华.水波的数值模拟.天津:天津大学出版社, 2005.
[6]李孟国,王正林,蒋德才.关于波浪Boussinesq方程的研究.青岛海洋大学学报(自然科学版), 2002, 32(03): 345-354.
[7] Boussinesq J. Theory of wave and swells propagated in long horizontal rectangular canal and imparting to the liquid contained in this canal. Journal of Mathematiques Pures et Appliquees, 1872, 17(2): 55-108.
[8] Peregrine D H. Long waves on a beach. Journal of Fluid Mechanics, 1967, 27(4): 815-827.
[9] Witting J M. A Unified Model for the Evolution of Nonlinear Water Waves. Journal of Computational Physics, 1984, 56: 203-236.
[10] Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering, 1993, 119(6): 618-638.
[11] Madsen P A, Murray R, Sorensen O R. A new form of Boussinesq equations with improved linear dispersion characteristics. Coastal Engineering, 1991, 15: 371-388.
[12] Abbott M B, McCowan A D, Warren I R. Accuracy of short wave numerical models. Journal of Hydraulic Engineering, 1984, 110(10): 1287-1301.
[13] Madsen P A, Sorensen O R. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly varying bathymetry. Coastal Engineering, 1992, 18: 183-204.
[14]张永刚.波浪折射-绕射及反射的数值模拟. [博士]大连理工大学,大连, 1995.
[15]林建国,邱大洪,邹志利.新型Boussinesq方程的进一步改善.海洋学报,1998, 20(2): 113-129.
[16] Wei G, Kirby J T, Grilli S T, et al. A fully nonlinear Boussinesq model for surface waves. PartⅠ. Highly nonlinear unsteady waves. Journal of Fluid Mechanics, 1995, 294: 71-92.
[17] Gobbi M F, Kirby J T. A Fourth Order Boussinesq-Type Wave Model. Presented at Proceedings of the 25th International Coastal Engineering Conference. New York, 1996.
[18] Gobbi M F, Kirby J T, Wei G. A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4. Journal of Fluid Mechanics, 2000, 405: 181-210.
[19] Zou Z L. High order Boussinesq equations. Ocean Engineering, 1999, 26: 767-792.
[20]邹志利.高阶Boussinesq水波方程.中国科学(E辑), 1997, 27(5): 460-473.
[21] Zou Z L. A new form of higher order Boussinesq equations. Ocean Engineering, 2000, 27: 557-575.
[22]邹志利.高阶Boussinesq水波方程的改进.中国科学(E辑), 1999, 29(1): 87-96.
[23] Longuet-Higgins M S, Stewart R W. radiation stresses in water waves: a physical discussion with application. Deep Sea Research, 1964, 11(5): 529-562.
[24]郑金海,严以新.波浪辐射应力理论的应用和研究进展.水利水电科技进展, 1999, 19(06): 5-7.
[25] Chen Q, Dalrymple R A, Kirby J T, et al. Boussinesq modeling of a rip current system. Journal of Geophysical Research, 1999, 104: 20617-20637.
[26]陶建华.波浪在岸滩上的爬高和破碎的数学模拟.海洋学报(中文版), 1984, 15(01): 107-118.
[27] Haller M C, Dalrymple R A, Svendsen I A. Modeling rip currents and nearshore circulation. Presented at Ocean Wave Measurement and Analysis, VA., 1997.
[28] Chen Q, Kirby J T, Dalrymple R A, et al. Boussinesq modeling of longshore currents. Journal of Geophysical Research, 2003, 108(C11): 26-1—26-18.
[29] Visser P J. Laboratory measurements of uniform longshore currents. Coastal Engineering, 1991, 15: 563-593.
[30]李绍武.近海、近岸地区波浪变形及波生流系统数学模型理论与应用. [博士]横滨国立大学,日本, 1997.
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