Exact invariant solutions capturing large-scale motions in the turbulent asymptotic suction boundary layer

A dynamical systems description of high-Reynolds-number turbulence requires capturing large-scale motions (LSMs), coherent structures that span the entire domain and control global energy and momentum transport. As LSMs emerge as correlated collective structures within a background of small-scale fluctuations, they are unlikely represented by invariant solutions of the full Navier-Stokes equations. Using spatial filtering approaches, we thus associate large-scale motions in the asymptotic suction boundary layer flow with exact invariant solutions of model equations that govern large-scale motions without the background fluctuations in the open boundary layer. We specifically construct several steady and time-periodic invariant self-sustained solutions of the filtered Navier-Stokes equations at the friction Reynolds number of 1168. Interactions of the large-scale streaks and vortices within these solutions are reminiscent of known processes including the streak-vortex quasi-periodic regeneration cycle and large-scale hairpin-like vortices. 

These results are a step towards transferring the dynamical systems picture from transitional flows to fully-developed turbulent boundary layer flows.