The application of the matched-asymptotic-expansion method to two-dimensional laminar flows with finite separated regions

Theoretical investigations of stationary incompressible two-dimensional laminar flows with finite regions of catastrophic separation, applying the method of matched asymptotic expansions, are presented. The difficulties associated with the Goldstein singularity are attacked in two ways, corresponding to the limiting values of a complex parameter kappa. Each case is applied to a unified model geometry using triple-deck equations. The flow model of Batchelor (1955) is shown not to fulfill the asymptotic-expansion assumptions; the model of Kirchhoff (1869), actually a degenerate version of the Batchelor model for the case omega-0 = 0, is found to be the uniquely valid one under these conditions.