Laminar Boundary-layer Theory: A 20th Century Paradox?

TLDR: In this paper, an interactive boundary-layer theory is introduced in the context of unsteady separation, leading onto a consideration of large-Reynolds number asymptotic instability theory.

Abstract: Boundary-layer theory is crucial in understanding why certain phenomena occur. We start by reviewing steady and unsteady separation from the viewpoint of classical non-interactive boundary-layer theory. Next, interactive boundary-layer theory is introduced in the context of unsteady separation. This discussion leads onto a consideration of large-Reynolds-number asymptotic instability theory. We emphasize that a key aspect of boundary-layer theory is the development of singularities in solutions of the governing equations. This feature, when combined with the pervasiveness of instabilities, often forces smaller and smaller scales to be considered. Such a cascade of scales can limit the quantitative usefulness of solutions. We also note that classical boundary-layer theory may not always be the large-Reynolds-number limit of the Navier-Stokes equations, because of the possible amplification of short-scale modes, which are initially exponentially small, by a Rayleigh instability mechanism.