【摘要】 将两个不同的、考虑波流相互作用和能量耗散项的、依赖时间变化的双曲型缓坡方程分别化为一组等价的控制方程组,具体分析了底摩阻项对相对频率和波数矢的影响,从而选择了合适的数学模型．将所选择的缓坡方程化为依赖时间变化的抛物型方程,并用ADI法进行数值求解,建立了缓变水深水域非均匀水流中波浪传播的数值模拟模型．通过和波流共线的解析解的比较,说明数值解和解析解相一致．结合Arthur(1950)水流这一经典算例,定量地讨论了考虑联合折射-绕射作用后的波数和仅考虑折射作用的波数的差别及其对波高分布的影响．在基本同样的条件下,本文的数值解与他人的计算结果一致．更多还原

【Abstract】 By transforming two time dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into equivalent equations, respectively, the effects of dissipation on intrinsic frequency and wave number are analyzed to choose the suitable mathematical model, in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, a time dependent parabolic equation is obtained from the time dependent hyperbolic mild slope equation for a suitable mathematical model, and solved by using the alternating direction implicit method. A numerical model is built for wave propagation and transformation on non-uniform currents in water of slowly varying topography. Comparisons are made between the numerical solutions and the theoretical solutions for the case of collinear waves and current, and a good agreement is found. Based on the interactions between incident wave and current on a sloping beach (Arthur, 1950), the differences of wave number vector between refraction and combined refraction-diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on the numerical results are shown.更多还原