Exact Invariant Solutions for Coherent Turbulent Motions in Couette and Poiseuille Flows

Abstract

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 are computed by using the Smagorinsky model to parametrize small-scale motions. These solutions can be 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.