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

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 (S-2) and third (S-3) 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 Re-lambda is an element of [50, 10(6)] indicates that, regardless of whether one considers decaying or forced HIT, the large scales affect S-2 and S-3 in the scaling range. In that range, forcing affects S-2 and S-3 differently. For forced HIT, S-2/((epsilon) over barr)(2/3) exhibits a distinct "bump'' near the upper end of the scaling range while no such bump is seen for S-3/((epsilon) over barr). 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 S-2/((epsilon) over barr)(2/3) or S-3/((epsilon) over barr). The slope of S-3 in the scaling range approaches the theoretical value of 1, when Re-lambda is sufficiently large. However, at similar Re-lambda, the slope of S-2 has not yet reached a constant for either decaying or forced HIT. (C) 2021 Elsevier Masson SAS. All rights reserved.