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The large-scale structure of unsteady self-similar rolled-up vortex sheets

Published online by Cambridge University Press:  19 April 2006

D. I. Pullin
D. I. Pullin
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

Two problems involving the unsteady motion of two-dimensional vortex sheets are considered. The first is the roll-up of an initially plane semi-infinite vortex sheet while the second is the power-law starting flow past an infinite wedge with separation at the wedge apex modelled by a growing vortex sheet. In both cases well-known similarity solutions are used to transform the time-dependent problem for the sheet motion into an integro-differential equation. Finite-difference numerical solutions to these equations are obtained which give details of the large-scale structure of the rolled-up portion of the sheet. For the semi-infinite sheet good agreement with Kaden's asymptotic spiral solution is obtained. However, for the starting-flow problem distortions in the sheet shape and strength not predicted by the leading-order asymptotic solutions were found to be significant.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 3 , 13 October 1978 , pp. 401 - 430
Copyright
© 1978 Cambridge University Press

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