Mathematics of Structure-Function Equations of All Orders

Exact equations are derived that relate velocity structure functions of arbitrary order with other statistics. "Exact" means that no approximations are used except that the Navier-Stokes equation and incompressibility condition are assumed to be accurate. The exact equations are used to determine the structure-function equations of all orders for locally homogeneous but anisotropic turbulence as well as for the locally isotropic case. There equations can be used for investigating the approach to local homogeneity and to local isotropy as well as the balance of the equations and identification of scaling ranges.