Periodic orbits in large eddy simulation of box turbulence

We describe and compare two time-periodic flows embedded in large eddy simulation (LES) of turbulence in a three-dimensional, periodic domain subject to constant external forcing. One of these flows models the regeneration of large-scale structures that was observed in this geometry by Yasuda et al (2014 Fluid Dyn. Res. 46 061413), who used a smaller LES filter length and thus obtained a greater separation of scales of coherent motion. We speculate on the feasibility of modelling the regenerative dynamics with time-periodic solutions in such a flow, which may require novel techniques to deal with the extreme ill-conditioning of the associated boundary value problems.