paper

Exact coherent states with hairpin-like vortex structure in channel flow

arXiv:1709.02484 · doi:10.1017/jfm.2018.409

Abstract

Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear traveling 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 Re=666. At the bifurcation, the solution has a highly symmetric quasistreamwise 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 centerplane where the mean shear vanishes connected to counter-rotating quasistreamwise "legs" that extend toward the channel wall. At 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.

14 pages, 11 figures; Accepted in Journal of Fluid Mechanics

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