The constant-V vortex

Abstract

It has been found that the generation of swirl by a continuous rotary oscillation of a right-circular cylinder partially filled with water can leave a vortex with a radially constant tangential velocity, V, i.e. ∂V/∂r = 0, excepting a small central core and the sidewall boundary layer. This vortex maintains ∂V/∂r = 0 during viscous decay by the turbulent bottom boundary layer, a fact that suggests that ∂V/∂r = 0 is a stable condition for a decaying vortex.Theory shows that such a profile of V and its steady decay is possible only if the radial transport per unit length in the turbulent Bödewadt boundary layer is TB,t = AVr/2 where A ≈ 0.072 is a dimensionless constant found from the experiment. This model of turbulent transport is extended to a case with ∂V/∂r ≠ 0 by an analysis of vortex decay in an experiment started from solid rotation. For this case an additional term proportional to ∂V/∂r is added to the transport equation.