Structure of turbulent line vortices

A theory is given to explain the observed dependence on Reynolds number of the decay of turbulent line vortices. It is argued that the turbulent vortex has a triple structure. There is an outer region for r > r1 (r1 is the radius of maximum tangential velocity) with a logarithmic distribution of circulation, and for r < r1 an inner region and viscous core in both of which the motion is close to solid body rotation. It is predicted that r1 ~ (vT1 t2)1/4, where 1 is the circulation at r1. Further, T1/T0 is predicted to be a slowly decreasing function of T0/v, where T0 is the strength of the vortex. The development of an overshoot of circulation in the outer region is discussed, and the axial velocities produced by growth of a trailing vortex are calculated.