Time-reversibility of Navier-Stokes turbulence and its implication for subgrid scale models

Among existing subgrid scale models for large-eddy simulation (LES) some are time-reversible in the sense that the dynamics evolve backwards in time after a transformation $\bm u \rightarrow -\bm u$ at every point in space. In practice, reversible subgrid models reduce the numerical stability of the simulations since the effect of the subgrid scales is no longer strictly dissipative. This lack of stability constitutes often a criterion to reject this kind of models. The aim of this paper is to examine whether time-reversibility can constitute a criterion that a subgrid model has to fulfill, or has not to. Thereto we investigate by direct numerical simulation the time-dependence of the kinetic energy of the resolved scales when the velocity is reversed in all or part of the lengthscales of the turbulent flow. These results are compared with results from existing LES subgrid models. It is argued that the criterion of time-reversibility to assess subgrid models is incompatible with the main underlying assumption of LES.