The role of velocity derivative skewness in understanding non-equilibrium turbulence**Project supported by the National Natural Science Foundation of China (Grant No. 11772032) and the Science Foundation of North University of China (Grant No. 11026829).

Abstract

The turbulence governed by the Navier–Stokes equation is paramount in many physical processes. However, it has been considered as a challenging problem due to its inherent nonlinearity, non-equilibrium, and complexity. Herein, we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence. Sk, a reasonable candidate for describing the non-equilibrium turbulence, which varies during the non-equilibrium procedure. A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum, which associated with the excitation of large scales, results in an obvious variation of Sk, and Sk is a negative value in this rapid energy decay process. The variation of positive Sk is closely related to the perturbation of transfer spectrum, and this corresponds to the backward energy transfer process. In addition, the skewness characterizes the production (or reduction) rate of enstrophy due to vortex stretching (or compression). Using the transport equation of turbulent energy dissipation rate and enstrophy, it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence. It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence, and also the improvement of turbulence models.