The flow along an external corner revisited

We revisit the problem of the flow of an almost inviscid fluid along an external corner made from the junction of two quarter infinite plates joined at an angle $0 < \alpha < \pi/2$. The structure of the boundary layer which develops along the corner is explored using a computational approach based upon a spectral element discretisation of the steady two-dimensional boundary-layer equations. We pay particular attention to the case when the angle $\alpha$ is small, thus approximating the semi-infinte quarter plate problem considered by Stewartson (1961) and recently revisited by Duck \& Hewitt (2012). Our results, which demonstrate a thickening of the boundary-layer near the sharp corner, will be discussed in the context of the asymptotic theory developed in the aforementioned papers.