Advances in Non-Equilibrium Turbulence Research

The Richardson-Kolmogorov energy cascade theory is the most important fundamental theory in turbulence research. One of its consequences is that the transfer and the dissipation of energy should be in equilibrium state, which corresponding to that the dissipation coefficient C_\mathit\boldsymbol\epsilon is a constant. However, recent experiments and numerical results show a different dissipation scaling which is called non-equilibrium dissipation scaling. It is not coincident with Richardson-Kolmogorov cascade. Even though in this region the Reynolds number is high enough and the energy spectrum shows a Kolmogorov's -5/3 scaling, C_\mathit\boldsymbol\epsilon is not a constant and follows C_\mathit\boldsymbol\epsilon~Re_I^m/Re_Lⁿ, with m≈1≈n, Re_I the inlet Reynolds number and Re_L the local Reynolds number based on integral scale. In recent three years, researchers find that the skewness of longitudinal velocity derivative S_k and the time evolution of equation of Lagrangian velocity gradient correlation Φ'_ijij can also be used to measure the non-equilibrium turbulent phenomena, which opens a new path in the research of non-equilibrium turbulence.