Characterization of near-wall turbulence in terms of equilibrium and “bursting” solutions

Abstract

Near-wall turbulence in the buffer region of Couette and Poiseuille flows is characterized in terms of recently-found nonlinear three-dimensional solutions to the incompressible Navier–Stokes equations for wall-bounded shear flows. The data suggest that those solutions can be classified into two families, of which one is dominated by streamwise vortices, and the other one by streaks. They can be associated with the upper and lower branches of the equilibrium solutions for Couette flow found by Nagata [“Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity,” J. Fluid Mech. 217, 519 (1990)]. The quiescent structures of near-wall turbulence are shown to correspond to the vortex-dominated family, but evidence is presented that they burst intermittently both in minimal and in fully turbulent flows. The intensity and period of the bursts are Reynolds-number dependent, but they saturate at high enough Reynolds numbers. The time-periodic exact solution found for Couette flow by Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001)] can be used as a simplified model for the bursting process.