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

Abstract

Among existing subgrid scale (SGS) models for large-eddy simulation (LES), some are time reversible in the sense that the dynamics evolve backward in time after a transformation 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 (DNS) the time dependence of the kinetic energy of the resolved scales when the velocity is reversed in all or part of the length scales 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.

Keywords:

• large-eddy simulation
• subgrid models
• time reversibility

Acknowledgments

The authors acknowledge interaction with Grégoire Winckelmans and Robert Rubinstein and the valuable comments of the reviewers. The authors also acknowledge an anonymous reviewer of a previous manuscript, who, by asking a question about the time reversibility of subgrid models, triggered the current investigation. L. Shao acknowledges support from BUAA SJP 111 program (grant no. B08009).