Finite Reynolds number corrections of the 4/5 law for decaying turbulence

Abstract

We examine finite Reynolds number contributions to the inertial range solution of the third order structure functions D 3,0 and D 1,2 stemming from the unsteady and viscous terms. Under the assumption that the second order correlations f and g are self-similar under a coordinate change, we are able to rewrite the exact second order equations as a function of a normalized scale r only. We close the resulting system of equations using a power law and an eddy-viscosity ansatz. If we further assume K41 scaling, we find the same Reynolds number dependence as previously in the literature. We proceed to extrapolate towards higher Reynolds numbers to examine the unsteady and viscous terms in more detail. We find that the intersection between the two terms, where their contribution to the solution of the structure function equations is relatively small, scales with the Taylor scale λ.