Abstract: The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regions and ordered islands on the Poincare sections. Interpretations of these phenomena are also given.

Key words: nonlinear dynamic system, bifurcation, stability, Beltrami flow, spherical vortex, general properties, Poincare sec-tion, chaotic trajectory, ordered island, numerical calculation