A LowOrder Theory for Stability of NonParallel Boundary Layer Flows
Abstract
As a sequel to the earlier analysis of Govindarajan & Narasimha, we formulate here the lowestorder rational asymptotic theory capable of handling the linear stability of spatially developing twodimensional boundary layers. It is shown that a new ordinary differential equation, using similaritytransformed variables in FalknerSkan flows, provides such a theory correct upto (but not including) O(R ^{2/3}), where R is the local boundary layer thickness Reynolds number. The equation so derived differs from the OrrSommerfeld in two respects: the terms representing streamwise diffusion of vorticity are absent; but a new term for the advection of disturbance vorticity at the critical layer by the mean wallnormal velocity was found necessary. Results from the present lowestorder theory show reasonable agreement with the full O(R ^{1}) theory. Stability loops at different wallnormal distances, in either theory, show certain peculiar characteristics that have not been reported so far but are demonstrated here to be necessary consequences of flow nonparallelism.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 December 1997
 DOI:
 10.1098/rspa.1997.0135
 Bibcode:
 1997RSPSA.453.2537G