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Large-scale structure of unsteady self-similar rolled-up vortex sheets

Pullin, D. I. (1978) Large-scale structure of unsteady self-similar rolled-up vortex sheets. Journal of Fluid Mechanics, 88 (3). pp. 401-430. ISSN 0022-1120. doi:10.1017/s0022112078002189.

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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.

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Additional Information:© 1978 Cambridge University Press. (Received 22 September 1977 and in revised form 17 February 1978) The author wishes to thank Dr A. E. Perry for several valuable discussions.
Issue or Number:3
Record Number:CaltechAUTHORS:20181120-153059718
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Official Citation:Pullin, D. (1978). The large-scale structure of unsteady self-similar rolled-up vortex sheets. Journal of Fluid Mechanics, 88(3), 401-430. doi:10.1017/S0022112078002189
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91095
Deposited By: George Porter
Deposited On:20 Nov 2018 23:36
Last Modified:16 Nov 2021 03:38

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