Invariant solutions in large eddy simulation of homogeneous shear turbulence

The unstable invariant solutions in the large eddy simulation of homogeneous shear turbulence with vanishing kinematic viscosity are obtained by Newton-Krylov-hookstep method. The small scale is represented by the standard Smagorinsky model with a constant Cs. It is shown that these solutions appear by a saddle-node bifurcation as decreasing Cs and have the same symmetry with Nagata’s equilibrium solution in Couette flow (JFM 217, 519-527 (1990)). Both lower- and upper- branch solutions are characterized by staggered streamwise-inclined vortex pairs. Also, lower-branch solutions are localized in the vertical direction, while upper-branch solutions are characterized by taller flow structures, which is consistent with the asymptotic theory of any shear flow at high-Reynolds numbers (K. Deguchi & P. Hall, Phil. Trans. R. Soc A, 372:20130352 (2014)).