an:06925220
Zbl 1415.76137
Shekar, Ashwin; Graham, Michael D.
Exact coherent states with hairpin-like vortex structure in channel flow
EN
J. Fluid Mech. 849, 76-89 (2018).
00412910
2018
j
76D05 37N10 76D17 76F06
boundary layer structure; nonlinear dynamical systems; turbulent flows
Summary: Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear travelling wave solutions to the Navier-Stokes equations in the channel flow geometry -- exact coherent states (ECS) -- that display hairpin-like vortex structure. This solution family comes into existence at a saddle-node bifurcation at Reynolds number \(\text{Re}=666\). At the bifurcation, the solution has a highly symmetric quasi-streamwise vortex structure similar to that reported for previously studied ECS. With increasing distance from the bifurcation, however, both the upper and lower branch solutions develop a vortical structure characteristic of hairpins: a spanwise-oriented `head' near the channel centreplane where the mean shear vanishes connected to counter-rotating quasi-streamwise `legs' that extend toward the channel wall. At \(\text{Re}=1800\), the upper branch solution has mean and Reynolds shear-stress profiles that closely resemble those of turbulent mean profiles in the same domain.