Application of Millionschikov's hypothesis to homogeneous and isotropic turbulence possessing helicity

Abstract

In this manuscript we construct a deductive theory for the stationary homogeneous turbulence, which is invariant under translations and rotations but lacks reflexional symmetry, considering the appropriate forms for the second- and third-order correlation functions. Appropriate invariant forms are considered for some second and third order correlation tensors, formed from the fluctuating components of velocity, acceleration, components of external force and pressures. In the light of the formulation of Millionschikov’s hypothesis we would point out further the treatment of first author [4] on the final period decay of isotropic turbulence using the points-merging technique employed here. We include also some enlightments of the process of future work that could be undertaken in this field of research.