Mathematics of Structure-Function Equations of all Orders

摘要

Exact equations are derived that relate velocity structure functions of arbitraryorder with other statistics. 'Exact' mean that no approximations are used except that the Navier-Stokes equation and incompressibility conditions are assumed to be accurate. The exact equations are used to determine the structure-function equations of all orders for locally homogenous but anisotropic turbulence as well as for the locally isotropic case. These 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.