Invariant solutions in large eddy simulation of homogeneous shear turbulence

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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 solutions 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 at high-Reynolds numbers (K. Deguchi \& P. Hall, Phil. Trans. R. Soc A, 372:20130352 (2014)).