基于精确色散Boussinesq方程的珊瑚礁波浪传播模拟  

Numerical simulation of wave propagation over coral reef bathymetries based on fully⁃dispersive Boussinesq equations

作　　者：刘维杰[1] 宁越 LIU Weijie;NING Yue(Ocean College,Zhejiang University,Zhoushan 316021,China;College of History,Geography and Tourism,Shangrao Normal University,Shangrao 334001,China)

机构地区：[1]浙江大学海洋学院,浙江舟山316021 [2]上饶师范学院历史地理与旅游学院,江西上饶334001

出　　处：《长沙理工大学学报（自然科学版）》2023年第4期47-54,共8页Journal of Changsha University of Science and Technology:Natural Science

基　　金：浙江省自然科学基金项目(LY21E090007);国家自然科学基金项目(51809234)。

摘　　要：【目的】提高激波捕捉类Boussinesq模型预测珊瑚礁地形上次重力波空间分布的准确性。【方法】基于具有精确色散性能的Boussinesq方程构建混合数值格式的数值模型,并对二维以及三维珊瑚礁地形上的波浪传播进行了数值模拟。【结果】相比目前较为流行的弱色散激波捕捉类模型,本文模型可更为准确地模拟二维珊瑚礁地形上的波能转换特征以及相应的次重力波空间分布,同时,本文模型对于三维珊瑚礁-裂口-潟湖地形上的波浪传播问题也具有较好的适应性。但由于控制方程的弱非线性,本文模型对于礁前陡坡上波浪浅化和潟湖上波高的预测仍有一定差异,且方程中的卷积项也会降低模型的计算效率。【结论】控制方程的色散性能应是限制激波捕捉类Boussinesq模型模拟珊瑚礁次重力波准确性的主要因素,如何在保持方程色散性的情况下兼顾模型的非线性性能和计算效率应是后续激波捕捉类Boussinesq模型在珊瑚礁地形上改进的主要方向。[Purposes]The aim of this study is to improve the accuracy of shock-capturing Boussinesq model in predicting the spatial distribution of infragravity wave over coral reef bathyemetries.[Methods]This study proposed a hybrid numerical scheme model based on a set of fully-dispersive Boussinesq equations and applied the model to simulate wave propagation over two-dimensional and three-dimensional coral reef bathymetries.[Findings]The results show that compared with currently popular weak dispersive shock-capturing model,the present model can simulate the wave energy transfer and the corresponding spatial distribution of infragravity waves over two-dimensional coral reef topography more accurately.Morever,the present model is also suitable for wave propagation over the three-dimensional reef-chanel-lagoon bathymetry.However,due to the weak nonlinearity of the governing equations,there are still some differences in the prediction of shallow water effect of waves on the fore-reef steep slope and wave height in the lagoon,and the computational efficiency of the convolution terms of in the governing equations also reduce the computational efficiency of the model.[Conclusions]Therefore,the dispersion performance of the governing equations should be the main factor limiting the accuracy of shock-capturing Boussinesq model in predicting infragravity waves over coral reefs.Future improvement of the shock-capturing Boussinesq model for coral reef topography should consider nonlinear performance and computational efficiency of the model while maintaining the dispersion property of the equations.

关 键 词：精确色散 BOUSSINESQ方程 珊瑚礁地形 次重力波 激波捕捉 波浪传播 

分 类 号：TV148[水利工程—水力学及河流动力学]