On a Singularity Initiating a Boundary-Layer Collision

Consider the flow near the entrance to a loosely coiled pipe when the inlet velocity is taken to be uniform over the cross-section of the pipe and the Dean number is large. It has previously been shown that the boundary layer on the pipe wall separates on the inner generator. In this paper we show that a singularity develops in the boundary-layer solution as separation is approached. Its structure is novel, consisting of an inner region where the forward motion is brought to rest, and an outer region whither the oncoming flow is displaced. The boundary-layer thickness increases without limit as the axial distance from separation tends to zero.