Dissipation of Energy in Isotropic Turbulence

In my paper [1] the definition of the notion of local isotropy was stated and the functions were introduced, where r denotes the distance between the pointsM and M´, ud(M´) and ud(M) are the velocity components at the points M and M’ in the direction of, and un(M) and un(M´) are the velocity components at M and M’ respectively, in a direction perpendicular to.