Unsteady Fully-Developed Flow in a Curved Pipe

It is shown that the boundary layer which develops from rest in a loosely coiled pipe of circular cross-section, following the imposition of a constant pressure gradient, terminates in singular behaviour at the inside bend after a finite time. This singularity of the boundary-layer equations is interpreted as an eruption of boundary-layer fluid into the interior or core flow. This result complements earlier work by Stewartson et al. [1] who consider the steady inlet flow to a curved pipe at high Dean number. In that case a singularity also develops, now at a finite distance from the entrance at the inside bend, which is again interpreted in terms of a boundary-layer collision or eruption.