On the third moments in helical turbulence

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Abstract
The evolution of the correlation characteristics in homogeneous helical turbulence is studied. Additional Kármán-Howarth-type equations describing the evolution of the mixed correlation tensor of the velocity and vorticity are obtained. In the helical scaling region, the solution of the obtained equation gives the exact relation between the antisymmetric component of a rank-three correlation tensor and the average dissipation of helicity; this relation is a kind of analog of Kolmogorov’s well-known 4/5 law [A. N. Kolmogrov, Dokl. Akad. Nauk SSSR 32(1), 19 (1941)].