Vortex flows: the dynamics of shear layers and Hill's vortex
The dynamics of flows with concentrated vorticity are studied by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically, employing the contour dynamics formulation. It is shown 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 that 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. The investigate the dynamics of wake-type flows, the instability of two attached vortex layers with opposite vorticity are considered. For axisymmetric flows, the instability of Hill's vortex is analyzed, subject to axisymmetric perturbations. It is found 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.
- Research Organization:
- Illinois Univ., Urbana (USA)
- OSTI ID:
- 5247931
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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