Exact invariant solutions in the near-wall region of boundary layer turbulence at high Reynolds numbers
Résumé
In boundary layer flows, small-scale streaky structures with typical spacing of roughly one hundred wall units 1 dominate the dynamics close the wall, where they control dissipation and wall drag. We investigate near-wall exact invariant solutions of the Navier-Stokes equations which may underly the characteristic near-wall streaks at high Reynolds numbers (Re τ = 1900-5800). Invariant solutions for asymptotic suction boundary layer flow (ASBL) are constructed in a minimal flow unit 2 using small-scale filtering approaches 3. These solutions are a step towards extending the emerging dynamical systems view of turbulence to the near-wall region of boundary layer flows at Reynolds numbers high enough for scale-separation to set in. Figure 1: Upper pannels: Cross-flow versus along-flow energy for a long periodic orbit found in ASBL in different values of the filtering cutoff , Cs. Lower panels: Evolution of the low-speed (blue) and high-speed (red) streaks near the wall in only half of the period for Cs = 0.15.