Turbulence is a chaotic phenomenon for which control efforts have often failed because the number of degrees of freedom involved is large. However, kinetic energy and drag are controlled by relatively few slowly evolving large structures that sit on top of a multiscale cascade of smaller eddies. They are essentially single-scale phenomena whose evolution can be described using less information than for the full flow. In evolutionary terms they are ‘punctuated equilibria’ for which chaotic evolution is only intermittent. The rest of the time, they can be considered coherent and predictable for relatively long periods. Coherent structures studied in the 1970s in free-shear flows (e.g. jets) eventually led to increased understanding and to industrial applications. In wall-bounded flows (e.g. boundary layers or pipes), proposed structures range from exact permanent waves to qualitative hairpins or ejections. Although most of them have been described at low Reynolds numbers, there are reasons to believe that they persist at higher ones in the ‘LES’ sense in which small eddies are only treated statistically. Recent computational and experimental advances provide enough temporally and spatially resolved data to quantify the relevance of such models to fully developed flows. The idea of the project has been to use mostly existing numerical data bases to test the various models of wall-bounded coherent structures, to quantify how often and how closely the flow approaches them, and to develop moderate-time predictions. Existing solutions were to be extended to the LES equations, methods sought to identify them in fully turbulent flows, and reduced-order models developed and tested. In practical situations, the idea was to be able to detect large eddies and to predict them ‘most of the time’, and, if simple enough models could be found, implement the process in the laboratory and use it to suggest control strategies.
