Homogeneous shear turbulence (HST) is the most canonical flow to investigate the interactions between mean flow and velocity fluctuations. There are so-called coherent structures, like velocity streaks and streamwise elongated vortices, which resembles to those in wall-bounded turbulence (Sekimoto, Dong & Jiménez, 2016 Phys. Fluids 28:035101; Dong, Lozano-Duran, Sekimoto & Jiménez, 2017, J. Fluid Mech. 816, 167-208). The coherent structures and their dynamics are considered as incomplete realisations of nonlinear invariant solutions in the incompressible Navier–Stokes equation, i.e. equilibrium solutions or periodic orbits, which have been reported in the plane Couette, Poiseuille, pipe flow, isotropic turbulence, and so on.

In this talk, we discussed on invariant solutions in DNS/LES of statistically stationary homogeneous shear flow.