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Instability, coalescence and fission of finite-area vortex structures

Published online by Cambridge University Press:  29 March 2006

J. P. Christiansen  and
N. J. Zabusky
J. P. Christiansen
Affiliation:
UKAEA Culham Laboratory, Abingdon, Berkshire
N. J. Zabusky
Affiliation:
Bell Laboratories, Whippany, N.J. 07981
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Abstract

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract and fuse (or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortex finite-area system corresponding to a von Kármán street of point vortices. Here the critical parameter is b/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At \[ b/a = 0.281 \] the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m = 2), triangular (m = 3), etc. surface modes owing to mutual interactions. At b/a = 0 the measured growth rate is smaller than that for the corresponding von Kármán system and at b/a = 0·6 the measured growth rate is larger. At b/a = 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 2 , 6 November 1973 , pp. 219 - 243
Copyright
© 1973 Cambridge University Press

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