A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

作     者：陈益处 许弘莒 

作者机构：Department of Marine Environment and EngineeringNational Sun Yat-Sen University Tainan Hydraulics LaboratoryNational Cheng Kung University 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2009年第18卷第3期

页      面：861-871页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070201[理学-理论物理] 0704[理学-天文学] 0702[理学-物理学] 

主　　题：Lagrangian nonlinear standing waves particle trajectory Lagrangian wave frequency 

摘      要：Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor＇s series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level.