简介：ToillustratethegeneralpropertiesoftheBeltramiflows,anewsufficientandnecessarycondi-tionofthegeneralsolutionoftheBeltramiflowshasbeengiven,onwhosebasissomesufficientandnecessaryconditionsandsufficientconditionsinliteratureareunified.TheadvantagesofthenewexpressionsarethatonemaygetsolutionsofBeltramiflowswithconstantproportionalfactorswhichsatisfysomegivenasymptoticdecayingconditionsatinfinity.Finally,wefindaclassofsphericalvorticesofBeltramiflows,wherethemo-tiontrajectoriesofthefluidparticlesareconfinedwithinasphereortwoadjacentconcentricsphericalshells.Wefindthatthesuperpositionsofthesphericalvorticesofthesameorderwithdifferentpolaraxesmayproducechaotictrajectories.

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