Finite‐time break‐up can occur in any unsteady interacting boundary layer

This theoretical work shows formally that unsteady interactive boundary layers can break up within a finite time by encountering a nonlinear localized singularity. The theory is an extension of, and is guided to a large extent by, Brotherton-Ratcliffe and Smith's (1987) work on a special case. Two major types of singularity are proposed, a “moderate” type yielding a singular pressure gradient and a “severe” type associated with a pressure discontinuity. Each type produces a singular response in the skin friction in the case of wall-bounded flows. The present finite-time singularity applies to any unsteady interactive flow, e.g., incompressible or compressible boundary layers, internal flows, wakes, in two or three dimensions; and the singularity and its associated change in flow structure have numerous repercussions, which are discussed, physically and theoretically, concerning boundary-layer transition in particular.