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

An equation relating third-order and second-order velocity increments at two points separated by a distance r is derived using the assumption of axisymmetric turbulence, when the direction of the axis of symmetry and the separation vector are both parallel to the mean flow direction x 1. This assumption is more constraining than homogeneity, but less restrictive than isotropy. The resulting equation represents the axisymmetric version of Monin's equation, which is valid for isotropic turbulence. Axisymmetric expressions for the energy dissipation rate and the one-point vorticity budget are also derived.