混沌动力学和湍流的统计理论

Chaotic Dynamics and Statistical Theory of Turbulence

湍流是一个非线性复杂大系统,精细地研究其奇异吸引子的几何结构和动力学行为是不可能和不必要的,必须进行统计研究。湍流具有结构这一发现并不否定统计研究的必要性和合理性。混沌动力学为在更高层次上发展湍流统计理论奠定了基础。

A turbulent fluid is a complex nonlinear large system and it is impossible as well as unnecessary to make detailed study of the geometrical structure and dynamical behavior of its strange attractors. Hence a statistical study is indispensable. The existence of structures in turbulence does not negate the necessity and legitimacy of the statistical study of turbulence. The statistical study of turbulence should be based upon the nonequilibrium statistical mechanics of chaotic trajectories along the strange attractors of turbulence.