The effects of strong suction on laminar boundary layers

Abstract

The title problem is investigated with the view of clarifying the nature of the separation in an adverse pressure gradient when the suction υ₀ is very strong. A linear model is investigated, but it is argued that this must contain many of the essential features of the exact (non-linear) problem. With a free-stream U = 1 − x the similarity solution u = (1 − x)f(y) is appropriate when (υ₀x − y) ≫ 1, x = O(1), 1−x = O(1). There is an O(1) layer centred on y = υ₀x in which more complex x-dependence first appears and then, when (y − υ₀x) ≫ 1, the solution assumes its final asymptotic behaviour. The y = υ₀x layer is non-uniform in x and exhibits a marked change in behaviour when (1 − x;) = O(l/υ₀). The solution in this narrow rectangle is singular like (1 − x)⁻² at the trailing edge. It is these singular terms that induce separation and reversed flow in an exponentially small neighbourhood of the trailing-edge.