基于曲线坐标系下缓坡方程模拟近岸波浪及波生流

Numerical simulation of nearshore waves and wave-induced currents based on mild-slope equation in curvilinear coordinates

为了更好地模拟曲线边界等不规则岸线附近,波浪传播及其破碎后形成的波生流问题,该文建立了正交曲线坐标下近岸波浪和波生流耦合数值模型;即采用可综合考虑近岸区波浪反射、折射和绕射等效应的双曲型缓坡方程计算波浪场,采用近岸深度平均的二维浅水方程计算波生流场,应用辐射应力的概念,使波浪模型为流场模型提供驱动力.波浪和波流模型基于相同的正交曲线网格,应用高效的ADI有限差分格式进行数值求解.将曲线坐标系下的耦合模型应用到半圆形水槽和凹型水槽两个物理模型中,数值模拟的结果分别和解析解、实验值及已发表的数值结果做了比较.模型实验验证表明,该文建立的数值模型比较准确、有效,可以应用到防波堤和河口等具有复杂边界和复杂地形的实际海域.

In order to correctly simulate water waves and wave-induced currents in areas with curved boundary and other irregular coastlines,this paper presented a combined numerical system in orthogonal curvilinear coordinates. The hyperbolic mild-slope equation,which is known as an efficient tool for nearshore wave field taking into account the wave reflection,refraction and diffraction effects,was employed as the wave model. The shallow water equations including radiation stresses were employed as the current model in curvilinear coordinates. The wave model was actually used as a driver-model to provide radiation stresses,the gradient of which generate the wave-induced current. The coupled models were numerically solved separately by ADI finite difference scheme in the same curvilinear grids. Two cases of numerical validation of a circular channel and a rip channel showed that the established numerical model was accurate and efficient,and had the potential to be applied to complicated domains with varied boundaries,such as estuaries and harbors in actual engineering.