分层流体中的二维代数孤立波及其垂向结构  

Two-Dimensional Algebraic Solitary Wave and Its Vertical Structure in Stratified Fluid

作　　者：苏晓冰[1] 魏岗[1] 戴世强[2] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院 [2]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《应用数学和力学》2005年第10期1143-1151,共9页Applied Mathematics and Mechanics

基　　金：国防预研基金资助项目(51443030103QT0601);中国博士后基金资助项目(2004036099);海洋工程国家重点实验室基金资助项目(0502)

摘　　要：研究具有自由面的,上部为浅层的大深度分层流体中代数孤立波,考察其垂向结构所对应的本征值问题,给出了二维Benjamin_Ono方程的一个解析解,并根据色散关系作了物理解释.作为数值例子,研究了具有Holmboe型密度分布的密跃层结构的特殊情形,并用射线理论探讨了这种内波的传播机制.The algebraic solitary wave and its associated eigenvalue problem in a deep stratified fluid with a free surface and a shallow upper layer were studied. And its vertical structure was examined. An exact solution for the derived 2D Benjamin-Ono equation was obtained, and physical explanation was given with the corresponding dispersion relation. As a special case, the vertical structure of the weakly nonlinear internal wave for the Holmboe density distribution was numerically investigated, and the propagating mechanism of the internal wave was studied by using the my theory.

关 键 词：二维Benjamin-Ono方程 分层流体 本征值问题 内波垂向结构 

分 类 号：O353.2[理学—流体力学]