A comprehensible low-order model for wall turbulence dynamics

Abstract

Streamwise vortices play an important role in the sustainment of wall turbulence. They are associated with regions with strong Reynolds shear stress production. In turbulent plane Couette flow at low Reynolds numbers, these streamwise vortices fill the whole gap between the plates. Using a low-order model obtained from the Navier-Stokes equations through a two-step Galerkin projection, the dynamics of these streamwise vortices is shown to be similar to the dynamics observed in the near-wall region of turbulent boundary layers [M. Lagha, J. Kim, J. D. Eldredge, and X. Zhong, “Near-wall dynamics of compressible boundary layer,” Phys. Fluids 23, 065109 (2011)]. A spanwise vortex filling the whole gap between the plates and with vorticity opposite in sign to that of the base flow, is tilted in the streamwise direction by the spanwise shear of the streaks. The resultant vortex has a crescent shape and its legs are two streamwise vortices. They regenerate the streaks by the lift-up effect. Through its ability to generate periodic spatio-temporal flow patterns, this model is shown to provide an ideal tool for studying the different mechanisms at work.