Relations between third-order and second-order structure functions for axisymmetric turbulence

An equation relating third-order and second-order velocity increments at tw o points separated by a distance r is derived using the assumption of axisy mmetric turbulence, when the direction <(<lambda>)over right arrow> of the axis of symmetry and the separation vector (r) over right arrow are both pa rallel to the mean flow direction x(1). This assumption is more constrainin g than homogeneity, but less restrictive than isotropy. The resulting equat ion represents the axisymmetric version of Monin's equation, which is valid for isotropic turbulence. Axisymmetric expressions for the energy dissipat ion rate and the one-point vorticity budget are also derived.