On similarity solutions occurring in the theory of interactive laminar boundary layers

Abstract

A theoretical investigation of similarity solutions for interactive laminar boundary layers is presented. The questions of uniqueness and of the appearance of homogeneous eigensolutions are discussed. The similarity solutions yielding the asymptotic behaviour of the nonlinear triple-deck equations in the far field can be used either to improve the development of computational schemes or to check the accuracy of numerical results. A special similarity solution governed by a modified Falkner-Skan boundary-value problem determines the shape of a wall generating the largest possible deflection of a laminar boundary layer in supersonic flow if separation is to be avoided. Increasing the controlling parameter of this special pressure distribution (for both supersonic and subsonic flows) beyond a cutoff value leads to a global breakdown of the interacting laminar-boundary-layer approach which cannot be removed or avoided.