Starting vortex dipoles in a viscous fluid: Asymptotic theory, numerical simulations, and laboratory experiments

Translational velocity of the starting vortex dipoles generated by the continuous or impulsive action of a localized force is obtained theoretically on simple physical grounds. Solutions of the diffusion equation for vorticity which take into account the translational motion of fluid particles are then obtained and compared with the results of direct numerical simulations of vortex dipoles as well as with the laboratory experiments. The comparison shows good quantitative agreement in both cases. Theoretical results for the translational velocity of the three-dimensional (axisymmetric) flows such as starting jets or vortex rings are discussed as well.