Abstract
About 40 years ago Professor Zhou and Professor Tsai suggested a statistical theory of the axisymmetric vortex structures of homogeneous isotropic turbulence. Now we generalize it to the nonaxisymmetric vortices case. In this paper a spherical averaging method is used to study the statistical average rules. An exact general calculating formula of the orientation average is given. It can greatly simplify the calculations of high order correlation functions and moments.
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