On local inflexional instability in boundary-layer flows.

Development of a linearized theory of the two- and three-dimensional incompressible viscous flows ensuing from locally unstable velocity profiles. Indications of the theory with respect to the instability of the two-dimensional separation bubble and the mechanisms underlying formation of the turbulence wedge behind a fixed roughness element are pointed out. In connection with the aforementioned mechanisms, a theoretically based argument is advanced that, as a result of local inflectional instability of the velocity profile in a succession of skewed planes, a corresponding succession of stationary vortices is induced, the induction process terminating at the boundaries of the turbulence wedge when the velocity profiles along the boundaries themselves become unstable. It is suggested that a rational method of predicting the occurrence of roughness-induced turbulence wedges might be possible if a theory were available for the steady laminar flow caused by the roughness at a stage just prior to transition.