On Rayleigh expansion for nonlinear long water waves  

作　　者：Wooyoung Choi 

机构地区：[1]Department of Mathematical Sciences,New Jersey Institute of Technology,Newark,NJ 07102-1982,USA

出　　处：《Journal of Hydrodynamics》2019年第6期1115-1126,共12页水动力学研究与进展B辑（英文版）

基　　金：This work was supported by the US National Science Foundation(Grant Nos.DMS-1517456,OCE-1634939);I am grateful to Prof.Theodore Y.Wu who has provided continuous encouragement and advice since I joined his research group in 1988 as a Ph.D.student.

摘　　要：We consider strongly nonlinear long waves on the surface of a homogeneous fluid layer.By modifying the formulation for the high-order spectral(HOS)method for waves in water of finite depth,we present a higher-order nonlinear system for the surface elevation and the velocity potential on the free surface to describe the two-dimensional evolution of large amplitude long waves.It is shown that the resulting system preserves the Hamiltonian structure of the Euler equations and can be transformed to the strongly nonlinear long-wave model for the depth-averaged velocity.Due to truncation of the linear dispersion relation for water waves,both the system for the surface velocity potential and that for the depth-averaged velocity are ill-posed when the order of approximation is odd and even,respectively.To avoid this ill-posedness,fully dispersive models are also proposed.Under the same order approximation,the long-wave model is found more effective for numeral studies of large amplitude long waves than the finite-depth model.

关 键 词：Long surface gravity waves strongly nonlinear waves Hamiltonian system regularized model 

分 类 号：O17[理学—数学]