非均衡湍流研究进展

Richardson-Kolmogorov能量级串理论是湍流研究中最重要的基础理论，其中一个推论是能量的传输和耗散应当是均衡的，对应于耗散系数${C_\mathit{\boldsymbol{\epsilon}}}$为常数.然而近些年的实验及数值模拟都发现了不符合Richardson-Kolmogorov能量级串理论的非均衡耗散律，即使在此区域内Reynolds数足够高，能谱满足Kolmogorov的-5/3标度律，${C_\mathit{\boldsymbol{\epsilon}}}$也不为常数，而满足${C_\mathit{\boldsymbol{\epsilon}}}$~Re_Im/Re_Ln，其中m≈1≈n，Re_I为入口Reynolds数，Re_L为以积分尺度为特征长度的当地Reynolds数.近三年来又发现流向速度梯度扭率S_k和Lagrange速度梯度自相关的时间演化Φ'_ijij也可以用来度量非均衡湍流现象，为非均衡湍流的研究开辟了新路. 

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_Im/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.