Coherent Structures, Self-Sustaining Process and Bifurcations in Shear Flows

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9803685WaleffeBuilding on an understanding of a fundamental self-sustaining process in shear-flows, an approach is developed to calculate hidden ordered states in shear flows such as plane Couette, plane Poiseuille and pipe flows. Knowledge of these states provides new starting points for the analysis of the onset of turbulence in shear flows. A complete characterization of the sequence of bifurcations leading to turbulence will be attempted based on the calculation of hidden steady states, analyses of their local stability properties and controlled numerical simulations. The striking similarity between those hidden ordered states and the coherent structures observed experimentally near boundaries will be investigated. It is also proposed to develop simplified models of the self-sustaining process, such as a low-order model developed in earlier work.This work illustrates the unique capabilities of high-performance Scientific Computing. The flow features that are revealed by this approach are not accessible by any other means, including analytical or experimental techniques or even numerical simulations. These features are the order hidden beneath the turbulence and their elucidation is of deep theoretical and practical interest. Turbulence is the defining characteristic of fluid flows in engineering and geophysical settings as well as of many biological flows. Therefore, progress in the fundamental understanding of turbulence is of wide-ranging practical relevance. A direct application of this research is to the development of robust models for prediction and control of turbulent flows in pipes and channels and over wings and surfaces, with an aim at drag and noise reduction.