【作者】 冯文静；

【导师】 张洪生；

【作者基本信息】 上海交通大学 ， 船舶与海洋结构物设计制造， 2007， 硕士

【摘要】 波浪在由深海向近岸传播的过程中,由于地形和水工建筑物等多种因素的影响,将发生浅水变形、折射、绕射、反射、破碎以及能量耗散等复杂的物理现象。Boussinesq型方程包含了非线性和色散性,能够模拟近岸水域中多种波浪传播变形的综合过程和现象。从势流理论出发,考虑缓变水深和定常背景水流的影响,假定水流沿水深方向均匀分布、沿水平方向缓慢变化,给出了一种新型的考虑波流相互作用的含有变换速度变量的新型Boussinesq型方程。本文所给出的方程的频散性精度和速度沿垂向分布的精度与任意水深层的选取有关。在不考虑水流的情况下,方程的相对速度与Airy波的相对运动速度平方比误差小于2%时,对应τ=?0 .2,其相对水深可达到6.37;对应τ=?0 .5,其相对水深可达到3.98(τ为任意水深层与静水深之比,为常数)。当时,保持与一阶Stokes波结果的相对误差小于5%,方程适用的最大相对水深μ可达1.0( Fr = u /gh,u为水流流速)。本文所给出的方程可用于研究强水流与波浪相互作用的强非线性问题。对一维形式的控制方程进行离散,其中空间导数项采用七点差分格式,时间积分采用五阶的Runge-Kutta-England格式,采用Shapiro的四更多还原

【Abstract】 As water waves propagate from deep to shallow water, the waves will take series of transformation including shoaling, refraction, diffraction, reflection, breaking and energy dissipation due to the effects of topography and various hydraulic structures. Having the properties of nonlinearity and dispersion, Boussinesq-type equations have been shown to provide an accurate description of wave transformation in coastal regions.With the water depth assumed to be slowly varying and the ambient current velocity supposed to be uniform over depth, a new type of Boussinesq equations including utility velocity for nonlinear wave propagation incorporating wave-current interactions is given. The linear dispersion properties of the new equations and the accuracy of wave celerity are both determined by the choice of water level which is under still water surface. In the absence of ambient current, A 2% error in the wave celerity is reached atμ= 6.37 for z? = ?0 .2h andμ= 3.98 for z? = ?0 .5h (where is an arbitrary water depth level, z?μis the ratio of depth to wave length). At Fr = ?0.1, the更多还原