Reynolds number effect on the velocity derivative flatness factor. (10th December 2018) - Meldi, M.; Djenidi, L.; Antonia, R.
Abstract : This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ( F ) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for F (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017 b, 051702). These terms and hence F become constant when the Taylor microscale Reynolds number, Re_[STIX]x1D706 exceeds approximately 10^4 . For smaller values of Re_[STIX]x1D706, F, like the skewness -S, increases with Re_[STIX]x1D706 ; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that Re_[STIX]x1D706 is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov ( Dokl. Akad. Nauk SSSR, vol. 30, 1941 a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941 b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which Re_[STIX]x1D706 is well below 10^4 may not be immune from the FRN effect. Another implication is that a power-law increase of F with respect to Re_[STIX]x1D706, as suggested by the Kolmogorov 1962 theory, is not tenable when Re_[STIX]x1D706 is large enough.