Localized vortices in a nonlinear shallow water model: examples and numerical experiments

All-Russian conference on Nonlinear Waves: Theory and New Applications

Beisel, S.A.^1 ; Tolchennikov, A.A.^2

Institute of Computational Technologies SB RAS, Novosibirsk, Russia^1

Institute for Problems in Mechanics RAS, Moscow, Russia^2

关键词: Asymmetric vortices;    Asymptotic solutions;    Explicit formula;    Localized vortices;    Non-linear shallow water equations;    Nonlinear shallow water;    Numerical experiments;    Shallow water approximation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012038/pdf
DOI  :  10.1088/1742-6596/722/1/012038

来源: IOP

【 摘 要 】

Exact solutions of the system of nonlinear shallow water equations on paraboloid are constructed by the method of group analysis. These solutions describe fast wave motion of the fluid layer and slow evolution of symmetric localized vortices. Explicit formulae are obtained for asymptotic solution related to the linear shallow water approximation. Numerical methods are used by the modeling the trajectory of the vortex center in the case of asymmetric vortices.