文档介绍：A Dissertation Submitted to the Shanghai Jiao Tong University for Master Degree NUMERICAL SIMULATION OF NONLINEAR WAVE-WAVE INTERACTION Candidate: Wei -Yuan Wang Supervisor: Hong-Sheng Zhang Major: Harbor, Coastal and Offshore Engineering School of Naval Architecture, Ocean and Civil Engineering Shanghai Jiao Tong University February, 2010 i 非线性波波相互作用的数值模拟摘要人们对河口海岸水域波浪传播过程中的多种现象都已进行了大量研究,相对来说,对其中的非线性相互作用的研究还不太充分。Stokes波理论多适合研究等水深的、相对水深比较大的水域中的波浪传播变形规律。对变水深水域中非线性波相互作用的研究,却还不多见,而研究河口海岸水域波浪的非线性相互作用具有十分重要的意义。例如,由两个不同频率的波浪组成的波列产生的差频效应与和频效应,对于防波堤的稳定、岸滩上泥沙的输运和港口中系泊船舶的运动都具有非常重要的影响;在斜坡地形上,两个波数相近、波向不同的自由波还会激发出边缘波。还有,约束波又会把能量传给自由波,从而发生三波共振,而这一现象对海岸建筑物和船舶锚链的设计非常重要。Boussinesq型方程是非线性方程,是模拟近岸水域中非线性波传播的强有力工具。因此,本文利用新型Boussinesq型方程波浪模型研究非线性波波相互作用的问题。首先,本文完善了基于新型Boussinesq型方程所建立的非线性波传播的数值模拟模型,使计算程序能长时间地稳定地运行,从而,使得模型能够更有效地模拟波列(包括单频波)的传播。其次,数值模拟等水深水域双频波的传播,将计算得到的波面数值解与理论解进行比较,发现二者相当吻合,从而说明完ii 善后的数值模型能够正确模拟双频波在等水深水域的传播变形,并讨论了非线性波波相互作用。再次,在变水深水域,利用物理模型实验验证完善后的数值模型。通过与物理模型实验值的比较,说明模型能够正确地模拟单频波和双频波在变水深水域中的传播变形。最后,数值模拟了双频波与强逆流的相互作用。数值模拟结果表明,高频波被水流阻塞,而低频波未被阻塞。关键词:新型Boussinesq型方程,双频波,非线性,波波相互作用,水流 iii NUMERICAL SIMULATION OF NONLINEAR WAVE-WAVE INTERACTIONABSTRACT We have done extensive research about a variety of phenomena in the process of wave propagation in the estuary and coastal zone, parison, the research about nonlinear wave-wave interaction is not enough. Stokes wave theory is suitable for investigating wave propagation in water with constant depth and large relative depth. Research of nonlinear wave-wave interaction in water with variable depth is rare. It is tremendously significant for studying nonlinear wave-wave interaction in the estuary and coastal zone. For example, the sum-frequency effect and difference-frequency effect caused by wave train formed by two waves with different frequencies play an important role in the stabilization of the breakwater, sediment transport on the beach and the movement of mooring ships. On the topography with a slope, two free waves with clos