Vortex Flows: The Dynamics of Shear Layers and Hill's Vortex
Pozrikidis, Constantine
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https://hdl.handle.net/2142/69777
Description
Title
Vortex Flows: The Dynamics of Shear Layers and Hill's Vortex
Author(s)
Pozrikidis, Constantine
Issue Date
1987
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Abstract
We study the dynamics of flows with concentrated vorticity by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically employing the contour dynamics formulation. We show that the growth of small, monochromatic perturbations on unstable vortex layers leads to the development of elliptical vortices whose asymptotic behavior is a function of the initial layer thickness and the form of the perturbation. Subharmonic disturbances initiate an interaction between vortices which may result in coalescence of large vortices and orbiting motion of small vortices. The calculations provide a criterion for the minimum vortex size required for coalescence. This phenomenon explains the transition to stochastic behavior characteristic of turbulent flows.
To investigate the dynamics of wake type flows, we consider the instability of two attached vortex layers with opposite vorticity. Depending on the layer thicknesses, the evolution may lead to diverse behavior including formation of a stable vortex street, dispersion of the circulation into small vortex blobs and development of vortex dipoles.
For axisymmetric flows, we analyze the instability of Hill's vortex subject to axisymmetric perturbations. We find that prolate perturbations cause the formation of a vortex tail behind the spherical core, while oblate perturbations lead to the development of a nearly steady vortex ring. The asymptotic state is a function of the amplitude of the initial perturbation. The asymptotic rings arising from oblate vortices are similar to steady rings described by previous authors (Norbury, 1973).
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