综合考虑多种变形因素的近岸多向不规则波传播数学模型-I.模型的建立

根据线性波动的叠加原理和波浪方向谱理论,作者在综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射的近岸规则波传播基本方程的基础上,推导出了综合考虑多种变形因素的近岸多向不规则波传播变形的基本方程。使用有限差分作为数值方法,给出了波浪破碎和障碍物后边界的处理方法,建立了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎、障碍物影响的近岸多向不规则波传播变形数学模型。该模型以组成波的谱值及波向为变量,在实数域内求解,适合大面积海区波场计算。

A mathematical model for irregular multi-directional wave propagation incorporating multi-factors of transformation in the coastal waters-I. setup of the model

On the basis of regular wave transformation equation in a reference1] incorporating comprehensively environmental current(current factor),nonlinear dispersion effect(nonlinear factor),rapidly varying topography effect(topography factor),energy loss due to bottom friction(friction factor),refraction and diffraction, the governing equations are derived for irregular multi-directional wave transformation incorporating multi factors according to the principle of superposition of linear wave and the wave directional spectrum theory.And then,by means of the finite difference method and by giving the treatment methods of wave breaking and the back boundaries of obstacles,mathematical model based on the above equations is set up incorporating current factor,nonlinear factor,topography factor,friction factor,refraction,diffraction,wave breaking and obstacle effect.The mathematical model takes spectrum value and wave direction as variables and is solved in real domain,it is suited for wave computation of large sea area.