A resolution of Stewartson’s quarter-infinite plate problem

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 k...

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Bibliographic Details
Published in:Theoretical and computational fluid dynamics 2012, Vol.26 (1-4), p.117-140
Main Authors: Duck, P. W., Hewitt, R. E.
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary layer
Classical and Continuum Physics
Computation
Computational fluid dynamics
Computational Science and Engineering
Engineering
Engineering Fluid Dynamics
Flow velocity
Fluid dynamics
Incompressible flow
Mathematical analysis
Mathematical models
Numerical analysis
Original Artilcle
Similarity
Singularities
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Summary: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.
ISSN:0935-4964
1432-2250
DOI:10.1007/s00162-011-0229-7