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The incompressible viscous flow along a right-angle corner, formed by the intersection of two semi-infinite flat plates, is considered. The effect of the three-dimensional geometry on the second-order ‘boundary layer’ flow away from the corner is determined and an interesting secondary flow is deduced. It is observed that this cross-flow prescribes the necessary asymptotic boundary conditions for the equations governing the flow inside the ‘corner layer’. A systematic matching scheme is specified and the corner flow problem is reformulated in terms of the ‘corner layer-boundary layer’ matching conditions.

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Abstract.The asymptotic behavior of the equations governing the viscous flow along a right-angle corner is considered. It is demonstrated that consistent asymptotic series exist for the inner corner layer region. These expansions satisfy the corner layer equations and associated boundary conditions. They exhibit algebraic decay of all the flow properties into the boundary layer away from the corner, and prescribe algebraic decay of the cross flow velocities into the outer potential flow. Of course the streamwise velocity and vorticity are constrained to decay exponentially into the potential flow. The form of this algebraic behavior is required in order to facilitate numerical solution of the corner layer equations. Of particular significance is the use of symmetry as a means of providing a boundary condition, predicting the appearance of logarithmic terms, and specifying the occurrence of arbitrary constants. These constants can only be determined from the complete corner layer solution.1. Introduction. The viscous flow along a corner that is formed by the intersection of two perpendicular flat plates has been studied by several authors and has recently been re-examined by Rubin [1] who discusses the past efforts on this problem in some detail. In Rubin's analysis three distinct regions were discernible ( Fig. 1): an irrotational potential flow where the coordinate gradients are in most generality, of equal order; boundary layers where surface normal derivatives are much larger than either of the derivatives in the plane of the surface, and the corner layer where the x-wise gradient alone is small. Solutions for the various sectors were obtained by the method of matched asymptotic expansions utilizing the small parameter (v/2UqX)1/2 = R~1/z. (U0 is the velocity at x -» -®). As is usually the case, the flow near the leading edge x = 0 cannot be obtained in this manner and only asymptotic similarity solutions were considered.Explicit results were presented for the first-order potential flow and first-and second-order boundary layer flows; the corner layer solution was deferred. The asymptotic behavior of the boundary-and corner-layer solutions for min (77, J")-*® is directly related to the nature of the potential flow at the corner point y2 + z2 = 0. 7) and f are the stretched corner layer coordinates; 77 = yRl/2/2x, f = zR1/2/2x. In this connection it was tacitly assumed that the potential flow is regular at y2 + z2 = 0. However, as will be shown, this assumption is unnecessary; with the inclusion of a singularity at the corner point (first appearing in the second-order potential flow) the *