NONLINEAR INTERFACIAL CAPILLARY-GRAVITY WAVES IN SHEAR FLOW  

作　　者：Zhu Yong Laboratory for Nonlinear Mechanics of Continuous Media,Inst.of Mech.CAS,Beijing 100080,P.R.China 

出　　处：《Journal of Hydrodynamics》1992年第1期106-116,共11页水动力学研究与进展B辑（英文版）

基　　金：On leave from Shanghai Institute of Applied Mathematics and Mechanics;Shanghai University of Technology,Shanghai 200072,P.R.China.

摘　　要：In this paper,the capillary-gravity solitary waves in a two-fluid system with shear flow are theoretically investigated.Three cases are considered.For the first case(the nor- mal case),the KdV equation,with the effect of shear flow being taken into account,is derived and it is found that there may exist single mode travelling solitary waves,slowly travelling soli- tary waves and even more slowly travelling solitary waves at some shear flow conditions.The second case considered is that the fluid system is at the first kind critical condition.The modified KdV equation in which the cubic nonlinearity balances the dispersion is obtained and the solution of mKdV solitary wave in shear flow is put forward.The third case is that the fluid system is at the second kind critical condition.The generalized KdV equation with the effect of shear flow considered is given.It is shown that there exist normal and oscillatory solitary waves and the condition of existence of oscillatory solitary waves are also presented.In this paper,the capillary-gravity solitary waves in a two-fluid system with shear flow are theoretically investigated.Three cases are considered.For the first case(the nor- mal case),the KdV equation,with the effect of shear flow being taken into account,is derived and it is found that there may exist single mode travelling solitary waves,slowly travelling soli- tary waves and even more slowly travelling solitary waves at some shear flow conditions.The second case considered is that the fluid system is at the first kind critical condition.The modified KdV equation in which the cubic nonlinearity balances the dispersion is obtained and the solution of mKdV solitary wave in shear flow is put forward.The third case is that the fluid system is at the second kind critical condition.The generalized KdV equation with the effect of shear flow considered is given.It is shown that there exist normal and oscillatory solitary waves and the condition of existence of oscillatory solitary waves are also presented.

关 键 词：nonlinear wave perturbation method shear flow 

分 类 号：TV131.2[水利工程—水力学及河流动力学]