Large-Eddy Exact Coherent Structures for Wall-Bounded Turbulent Shear Flows
Résumé
The dynamical systems approach recently applied to understand subcritical transitions in wall-bounded shear flows is combined with the use of large-eddy simulations to investigate the nature of large-scale coherent motions in turbulent Couette and Poiseuille flows. Exact invariant solutions of the filtered Navier-Stokes (LES) equations have been computed by using the Smagorinsky model to parametrize small-scale motions and are therefore labeled `large-eddy' exact coherent structures (LECS). These solutions have been continued into exact solutions of the Navier-Stokes equations therefore providing a bridge between coherent large-scale motions in wall-bounded fully developed turbulent flows and invariant solutions appearing in transitional flows. We show that the reverse is also possible by continuing exact coherent solutions (ECS) of the Navier-Stokes equations into LECS solutions for finite values of the Smagorinsky constant.