“Complex” turbulent flows are those which cannot be predicted with acceptable accuracy by methods developed in classical thin shear layers. This is a subjective and time-dependent definition but even at its narrowest it includes a large class of engineering and environmental flows. Examples include shear layers which interact, in pairs or larger numbers, and shear layers which have been perturbed by body forces, such as buoyancy, or extra rates of strain such as longitudinal curvature or lateral divergence. This review assesses our current knowledge of complex turbulent flows and our ability to predict them. It also assesses the usefulness of the boundary layer approximation in engineering flows and suggests methods of extending it.

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