Exact equations for structure functions and equations for source terms up to the sixth order

TL;DR

This paper derives exact equations for the source terms in fourth and sixth order structure function equations, distinguishing viscous and pressure contributions, under assumptions of homogeneity and isotropy.

Contribution

It provides explicit equations for unclosed source terms in high-order structure function equations, enhancing understanding of turbulence modeling.

Findings

Derived explicit equations for source terms in fourth and sixth order structure functions.

Identified viscous and pressure contributions as separate classes of source terms.

Clarified the unclosed nature of these source terms in turbulence equations.

Abstract

We derive equations for the source terms appearing in structure function equations for the fourth and sixth order under the assumption of homogeneity and isotropy. The source terms can be divided into two classes, namely those stemming from the viscous term and those from the pressure term in the structure function equations. Both kinds are unclosed.