基于Boussinesq型方程的钱塘江涌潮数值模拟  

Numerical simulation of the tidal bore in the Qiantang River based on Boussinesq-type equations

作　　者：黄婷 张怀 石耀霖 HUANG Ting;ZHANG Huai;SHI YaoLin(Key Laboratory of Computational Geodynamics,College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai),Guangdong Zhuhai 519080,China)

机构地区：[1]中国科学院大学地球与行星科学学院,计算地球动力学重点实验室,北京100049 [2]南方海洋科学与工程广东省实验室(珠海),广东珠海519080

出　　处：《地球物理学报》2022年第1期79-95,共17页Chinese Journal of Geophysics

基　　金：国家杰出青年科学基金(41725017);国家重点研发计划“变革性技术关键科学问题”重点专项“非常规油气三维地震成像的数学方法与超分辨反演高效算法”(2020YFA0713400)联合资助.

摘　　要：钱塘江因其恢弘的涌潮现象而举世闻名,对钱塘江涌潮形成机理的探究具有理论与应用双重价值.本文建立了考虑非线性、频散以及耗散作用的二维高阶Boussinesq型方程,并结合有限体积数值方法来描述钱塘江涌潮这一物理过程,复演了最具代表性的“交叉潮”、“一线潮”和“回头潮”三大潮景,同时展现了涌潮的二次自由面起伏现象,重现了钱塘江涌潮的形成、发展和消亡三个完整阶段.从涌潮高度、涌潮速度等涌潮传播表征指标进行探究,分析了不同河段潮景的形成过程以及特征,模拟结果与实际观测结论相吻合.潮景的形成是涌潮进入不同发展阶段的重要标志,“交叉潮”出现在涌潮的形成初期,Froude数接近1,涌潮高度在0.5 m左右;涌潮进入盐官河段后,强度开始增强,形成“一线潮”,Froude保持在1.45以上,涌潮高度最大可达3 m以上;“回头潮”出现之后,涌潮强度开始减弱,于三工段区域再次形成小规模的“一线潮”,Froude数在1.3~1.4之间,涌潮高度约为2 m;七堡之后,上溯的涌潮进入消亡阶段,Froude数减小至1.3以下,涌潮高度约为1 m.此次研究有助于对钱塘江涌潮特性的进一步认识.The Qiantang River is well-known worldwide for its spectacular tidal bore.Numerical investigation of the mechanisms of the tidal bore in the Qiantang River has theoretical and practical values.In this work,the Boussinesq-type equations that include nonlinearity,frequency dispersion,and dissipation are used for the simulation.The dispersion term is introduced in the flow equations by considering the vertical acceleration′s effect on the pressure distribution.The finite volume method(FVM)based on these equations is used to simulate the formation,development,and extinction of tidal bore in the Qiantang River.The most typical phenomena cross-shape tidal bore,thread-shape tidal bore,and returned tidal bore are replicated,and the secondary free-surface undulations of the bore can be reproduced.The process and characteristics of these phenomena are systematically analyzed from several aspects,such as bore height and bore celerity,which are consistent with the observation results.Different bore phenomena suggest different development stages of tidal bore.The cross-shape tidal bore appears at the beginning of the Qiantang tidal bore,while its Froude number is close to 1,and its bore height is~0.5 m.When the tidal bore reaches the Yanguan outlet,its intensity increases,and the thread-shape tidal bore reforms,its Froude is above 1.45,and its maximum bore height is more than 3 m.After forming the returned tidal bore,the intensity begins to weaken,and a small-scale thread-shape tidal bore is formed in the section of the Sangongduan outlet,where its Froude number is between 1.3 and 1.4,the bore height is about 2 m.When the bore approaches its extinction stage following the Qibao outlet,its Froude number decreases to~1.3,and the bore height is~1 m.These studies lead to further understanding of the tidal bore in the Qiantang River.

关 键 词：钱塘江 涌潮 BOUSSINESQ型方程 频散 数值模型 

分 类 号：P541[天文地球—构造地质学]