Vorticity distribution and circulation of a vortex ring

摘要

The structure of a vortex ring was investigated in detail by using flow visualization technique. The flow pattern in the cross section of a vortex ring shows spiral streak lines around the vortex center. The flow rate in the space between the neighboring two streak lines calculated with the velocities tangential to the streak lines keeps a constant value while the streak lines go around the vortex center. Therefore, the spiral streak lines can be regarded as the stream lines on the coordinate system moving with the vortex ring. The velocity t a point in a cross section of the vortex was calculated from the flow rate and the space between the neighboring spiral streak lines. The equi-vorticity lines are nearly concentric circles and they are different from the configuration of the spiral streak lines. The circulation of a vortex ring obtained from the vorticity distribution is in good agreement with that obtained by integrating the velocity along the vortex ring axis.