Mathematics of Structure-Function Equations of All Orders
Abstract
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. 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.
Cite
@article{arxiv.physics/0102055,
title = {Mathematics of Structure-Function Equations of All Orders},
author = {Reginald J. Hill},
journal= {arXiv preprint arXiv:physics/0102055},
year = {2016}
}
Comments
17 pages, no figures As of Nov. 17, 2016 A factor of 2 missing from equations 14, 19, 43 has been corrected. An improved table of divergences and Laplacians for orders 4 to 8 is included