New Model for Intense Self-Similar Vortices

Abstract

A new model that is capable of generating singleor double-celled steady, incompressible, intense vortices is proposed. As was evident in earlier experiments, depending on the values of scaling constants, it is shown that the axial-velocity component may attain proŽ les ranging from jet-like to wake-like. In general, the radial-velocity proŽ le has a similar shape as the tangential velocity, developing a direction reversal near the axis of rotation when the two-celled vortex appears. For the case of a one-celled vortex, the tangential velocity behaves like that of Rankine’s vortex with viscous smoothing near the core. However, as the reverse  ow inside the core matures the tangential velocity reduces gradually from the forcedvortex proŽ le while its maximum value is augmented. The evolution from a one-celled to a two-celled vortex is also characterized by a migration of the vorticity peak from the central axis toward the core. The present theory suggests that the implementation of the experimental data for the tangential velocity near the core depends on the quality of the secondary  ow.