基于层析水波理论的浅化破碎时域模拟研究

Time Domain Simulation on Wave Shoaling and Breaking Based on HLGN Equations

由于近岛礁海域的水深变浅,海浪的非线性增强,容易发生波浪破碎。层析水波理论发展之初就被用来模拟非线性浅水波传播演化,经过近十年的发展,其适用范围已经得到大幅拓展,然而目前研究尚未考虑因地形变化而发生的波浪破碎。该文基于高级别层析水波理论,开展规则波在斜坡地形下的浅化破碎时域模拟研究。高级别层析水波理论采用多项式函数描述流体速度垂向结构,非线性自由面条件在瞬时波面精确满足。为了考虑波浪浅化破碎,还引入了与当地水深相关的涡黏模型。将时域模拟结果与物理水池实验进行了比较,研究表明,引入涡黏破碎模型的高级别层析水波理论,能够准确高效地模拟波浪在斜坡地形上浅化变形,并能够考虑因水深变浅导致的波浪破碎问题。此外,该文还对涡黏破碎模型的特征参数进行了敏感性分析。

Due to the decreasing of water depth near the islands and reefs,the nonlinearity of ocean waves is growing and the wave breaking occurs easily.The Green-Naghdi equations was initially developed for the simulation of evolution of nonlinear shallow water waves.After the development in this decade,the scope of the Green-Naghdi equations has been greatly expanded,despite the wave breaking resulting from the variation of topography has not yet been considered.Based on the high-level Green-Naghdi(HLGN)equations,the time domain simulation is performed on the wave shoaling and breaking of regular water waves propagating on an underwater slope in this work.Polynomial series are used in HLGN equations to describe the vertical structure of fluid velocity and the nonlinear free surface condition is accurately satisfied at the instantaneous water surface.In order to consider wave breaking,an eddy viscosity model related to local water depth is introduced.The numerical results are compared with available laboratory data.It is shown that the HLGN equations combined with the wave-breaking model not only accurately and efficiently simulate the propagation and evolution of water waves approaching the underwater slope,but also consider the wave breaking caused by wave shoaling.In this work,the sensitivity analysis is additionally performed on the characteristic parameters of the eddy viscosity breaking model.