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The constant-V vortex
Published online by Cambridge University Press: 22 June 2001
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.
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- © 2001 Cambridge University Press
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