Characterization of near-wall turbulence in terms of equilibrium and periodic solutions

Near-wall turbulence in the buffer region is qualitatively characterized in terms of recentlyfound nonlinear three-dimensional solutions to the incompressible Navier–Stokes equation for wall-bounded shear flows. Jiménez & Simens’ (2001) traveling-wave solution for an autonomous wall flow, Nagata’s (1990) steady and Kawahara & Kida’s (2001) periodic solutions for a plane Couette flow are considered for characterization. These equilibrium and periodic solutions are classified into two families, of which one is dominated by streamwise vortices, and the other by streaks. The former family, which is composed of autonomous solutions, Nagata’s upper-branch solutions and time-periodic solutions, is similar to fully-turbulent simulationss in the near-wall region.