INTERNAL RESONANT INTERACTIONS OF THREE FREE SURFACE-WAVES IN A CIRCULAR CYLINDRICAL BASIN

作     者：马晨明 

作者机构：Institute of Mathematics Fudan University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2003年第24卷第12期

页      面：1411-1420页

核心收录：

学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：theNationalNaturalScienceFoundationofChina (1 0 1 71 0 2 0 ) 

主　　题：free surface-wave internal resonant interaction stationary solution 

摘      要：The basic equations of free capillary_gravity surface_waves in a circular cylindrical basin were derived from Luke s principle. Taking Galerkin s expansion of the velocity potential and the free surface elevation, the second_order perturbation equations were derived by use of expansion of multiple scale. The nonlinear interactions with the second order internal resonance of three free surface_waves were discussed based on the above. The results include:derivation of the couple equations of resonant interactions among three waves and the conservation laws; analysis of the positions of equilibrium points in phase plane; study of the resonant parameters and the non_resonant parameters respectively in all kinds of circumstances; derivation of the stationary solutions of the second_order interaction equations corresponding to different parameters and analysis of the stability property of the solutions; discussion of the effective solutions only in the limited time range. The analysis makes it clear that the energy transformation mode among three waves differs because of the different initial conditions under nontrivial circumstance. The energy may either exchange among three waves periodically or damp or increase in single waves.