On the beltram I flows

Abstract

To illustrate the general properties of the Beltrami flows, a new sufficient and necessary condition of the general solution of the Beltrami flows has been given, on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified. The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity. Finally, we find a class of spherical vortices of Beltrami flows, where the motion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells. We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories.