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A resolution of Stewartson’s quarter-infinite plate problem

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Abstract

We revisit a problem originally considered by Stewartson in 1961: the incompressible, high-Reynolds-number flow past a quarter-infinite plate, with a leading edge that is perpendicular to, and a side edge that is parallel to, an undisturbed oncoming freestream. Particular emphasis is placed on the key region close to the side edge, where the flow is (superficially) three-dimensional, although the use of similarity variables reduces the dimensionality of the problem down to two. As noted by Stewartson, this problem has several intriguing features; it includes singularities and is also of a mixed parabolic type, with edge conditions influencing the solution in both directions across the flow domain. These features serve to greatly complicate the (numerical) solution process (the problem is of course also highly non-linear), and computation was clearly infeasible in 1961. In the present paper, a detailed computational study is presented, answering many of the questions that arose from the 1961 study. We present detailed numerical results together with asymptotic analyses of the key locations in the flow.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    P. W. Duck & R. E. Hewitt

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  1. P. W. Duck
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  2. R. E. Hewitt
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Correspondence to P. W. Duck.

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Communicated by: M. Y. Hussaini.

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Duck, P.W., Hewitt, R.E. A resolution of Stewartson’s quarter-infinite plate problem. Theor. Comput. Fluid Dyn. 26, 117–140 (2012). https://doi.org/10.1007/s00162-011-0229-7

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  • DOI: https://doi.org/10.1007/s00162-011-0229-7

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