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Global Interactive Boundary Layer (GIBL) for a channel

An asymptotic analysis of the structure of a two-dimensional steady, incompressible, laminar flow in a channel is presented. More precisely, for high Reynolds numbers, when the walls of the channel are slightly deformed, a new approach leads to a better understanding of possible flow separation. The starting point is to assume the structure of a Uniformly Valid Approximation (UVA) in the whole channel. The analysis is carried out with the Successive Complementary Expansion Method (SCEM). Thanks to the use of generalised asymptotic expansions, SCEM leads, with rational arguments, to a Global Interactive Boundary Layer (GIBL) theory valid in the whole channel.