About forty years ago Prof. Chou and Tsai had suggested a statistical theory of the Axisymmetric vortices structure of homogeneous isotropic turbulence. Now we generalize it to nonaxisymmetric vortices case. in this paper a Chou-Saffman average method is used to study the statistical average rules. An exact general calculating formula of the orientation average is given. It can simplify the calculations of high order correlation functions and moments greatly.
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