Invariant solutions of the filtered Navier-{S}tokes equations representative of large-scale motions in the asymptotic suction boundary layer flow
Résumé
The outer region in turbulent boundary layer flows is dominated by large-scale streaky motions with the dimensions in the order of the boundary layer thickness (see [1] as an example). Large-scale motions are shown to be self-sustained numerically by filtering the small scales in the Navier-Stokes equations, [2]. Moreover, it has been shown that these streaky motions can be captured by exact invariant solutions of the filtered Navier-Stokes equations, [2, 3]. We investigate the exact invariant solutions of the filtered Navier-Stokes equations representative of the large-scale structures in the asymptotic suction boundary layer flow (ASBL), which is the flow over a flat plate with a constant and homogeneous suction into the plate. In the figure, energy spectra of ASBL with and without damping the small scales, and a large-scale travelling wave solution are shown. Our results are the first exact invariant solutions of the filtered equations in the asymptotic suction boundary layer flow. These solutions are a step towards extending the emerging dynamical systems view of turbulence to the dynamics of the large-scale motions in the turbulent boundary layer flows.