Flow separation

The calculation of laminar separation has always been one of the most relevant problems of boundary layer theory, even within Prandtl's classical assumption of vanishing transverse pressure gradients. However, the validity of this assumption is in question not only in certain problems of supersonic separation where the classical theory cannot provide an answer, but even in the simplest incompressible problem. Recent theories attempting to calculate separation after relaxing Prandtl's assumption are reviewed in this paper. The analytical procedure based on a multiple layer treatment developed independently by Neiland and by Stewartson and Williams is discussed in detail. A critical discussion follows, showing the insufficiency of the present asymptotic treatment of the return flow. A third procedure is discussed: the generalization of the von Karman momentum integral procedure taking into account the existence of transverse pressure gradients. The attempt to use this procedure by Holden and Moselle, containing some arbitrariness, is mentioned. It is shown how the arbitrary elements can be removed and a perfectly coherent set of equations in integral form obtained.