Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

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Proper orthogonal decomposition (POD) is applied to the direct numerical simulation (DNS) of a turbulent boundary layer performed by Wu & Moin (2010), and the resulting POD modes of various scales are examined. The modes include structures resembling those observed in instantaneous flow fields, such as large-scale motions of streamwise velocity with ramp-like wall-normal growth. Other modes correspond closely to nearwall streaks. In addition, POD modes that are constant across the spanwise domain width are observed to grow from the wall with the mean boundary layer thickness. The results support the existence of boundary layer coherent motions described by the hairpin packet model (Adrian 2007).

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