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

摘要

Exactsolutionsofthesystemofnonlinearshallowwaterequationsonparaboloidareconstructedbythemethodofgroupanalysis.Thesesolutionsdescribefastwavemotionofthefluidlayerandslowevolutionofsymmetriclocalizedvortices.Explicitformulaeareobtainedforasymptoticsolutionrelatedtothelinearshallowwaterapproximation.Numericalmethodsareusedbythemodelingthetrajectoryofthevortexcenterinthecaseofasymmetricvortices...