Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling

•A spectral non-equilibrium process in isotropic turbulence is defined theoretically.•A decomposition method is proposed to divide a non-equilibrium turbulence field.•An improved Smagorinsky model is proposed to correct the non-equilibrium behavior.

The non-equilibrium property in turbulence is a non-negligible problem in large-eddy simulation but has not yet been systematically considered. The generalization from equilibrium turbulence to non-equilibrium turbulence requires a clear recognition of the non-equilibrium property. As a preliminary step of this recognition, the present letter defines a typical non-equilibrium process, that is, the spectral non-equilibrium process, in homogeneous isotropic turbulence. It is then theoretically investigated by employing the skewness of grid-scale velocity gradient, which permits the decomposition of resolved velocity field into an equilibrium one and a time-reversed one. Based on this decomposition, an improved Smagorinsky model is proposed to correct the non-equilibrium behavior of the traditional Smagorinsky model. The present study is expected to shed light on the future studies of more generalized non-equilibrium turbulent flows.