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Strongly nonlinear vortices in the Stokes layer on an oscillating cylinder

Citation

Horseman, NJ and Bassom, A and Blennerhassett, PJ, Strongly nonlinear vortices in the Stokes layer on an oscillating cylinder, Proceedings of the Royal Society of London A, 452, (1948) pp. 1087-1111. ISSN 1364-5021 (1996) [Refereed Article]

Copyright Statement

Copyright 1996 The Royal Society

DOI: doi:10.1098/rspa.1996.0055

Abstract

The Stokes layer on a torsionally oscillating circular cylinder is susceptible to axially periodic vortices which are driven by a centrifugal mechanism which has some similarities to that which is responsible for Gortler vortices in boundary layers on concave surfaces. For small wavelength vortices an analytic description of linear, weakly nonlinear and fully nonlinear perturbations is possible and, as the growth rates of these modes are asymptotically greater than the timescale of the underlying Stokes layer, a quasi-steady stability analysis is attempted in preference to a Floquet-type approach. It is shown that highly nonlinear vortices can be expected to form on the surface of the cylinder; it is noted that these vortices alter the basic mean flow at leading order and occupy a zone which has depth comparable to the Stokes thickness. Depending on the Taylor number of the flow, three distinct types of vortex behaviour are found. In the first of these, corresponding to Taylor numbers just above that at which the Stokes layer becomes unstable over a part of its cycle, the vortices are relatively weak and remain attached to the cylinder throughout their lifetime. At larger Taylor numbers, the vortices initially grow whilst remaining on the cylinder but at some stage they break away and concentrate in a region within the Stokes layer. However, their strength reduces with time and they soon decay away. In the third regime identified, before this vortex activity region dies, the residual flow next to the cylinder becomes unstable once more. In this case a second vortex zone begins to grow so that for a certain time interval two active zones exist. The governing equations for the strongly nonlinear modes take the form of a free boundary value problem subject to ordinary differential constraints. Numerical solutions are presented and, although periodic solutions are by no means guaranteed by use of the quasi-steady approach, the computations show that remarkably periodic vortex configurations tend to result.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, A (Professor Andrew Bassom)
ID Code:108515
Year Published:1996
Web of Science® Times Cited:6
Deposited By:Mathematics and Physics
Deposited On:2016-04-21
Last Modified:2016-07-08
Downloads:0

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