A model for universal time scale of vortex ring formation
An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nondimensional stroke length L/D (referred to as "formation number," following Gharib et al. [J. Fluid Mech. 360, 121 (1998)]) predicted by the model satisfactorily matches the experimental observation of Gharib et al. The model introduces two nondimensional parameters that govern the limiting formation number: nondimensional energy End and circulation Gammand. The predicted value of End matches very well with the experimental data. It is also predicted that there is a limiting value for the nondimensional circulation in the range 1.77 <~ Gammand <~ 2.07.
©1998 American Institute of Physics. (Received 23 April 1998; accepted 16 June 1998) We would like to thank K. Shariff of NASA Ames Research Center for his interest in this work. M.G. would like to acknowledge the support by ONR Grant No. URI N00014-91-J-1610.