Sensitivity analysis of the second and third-order velocity structure functions to the Reynolds number in decaying and forced isotropic turbulence using the EDQNM model

Abstract

Numerical calculations based on a recent version of the eddy-damped quasi-normal model (EDQNM-LMFA) are carried out for homogeneous isotropic turbulence (HIT) with the aim of investigating the dependency on the Reynolds number of second and third order velocity structure functions. The quantities investigated include the energy spectrum E, the non-linear energy transfer T as well as the second (S2) and third (S3) order moments of the longitudinal velocity increment. Both free decaying HIT and (steady state) forced HIT are considered. The analysis of the structure functions for Reλ∈[50,106] indicates that, regardless of whether one considers decaying or forced HIT, the large scales affect S2 and S3 in the scaling range. In that range, forcing affects S2 and S3 differently. For forced HIT, S2∕(ϵ¯r)2∕3 exhibits a distinct “bump” near the upper end of the scaling range while no such bump is seen for S3∕(ϵ¯r). The latter quantity remains approximately constant for values of r which extend to the scale corresponding to the forcing. For decaying HIT, there is no discernible bump in either S2∕(ϵ¯r)2∕3 or S3∕(ϵ¯r). The slope of S3 in the scaling range approaches the theoretical value of 1, when Reλ is sufficiently large. However, at similar Reλ, the slope of S2 has not yet reached a constant for either decaying or forced HIT.