Reynolds number effect on the velocity derivative flatness factor. (10th December 2018)

• Record Type: Journal Article
• Authors: Meldi, M.; Djenidi, L.; Antonia, R.
• Is Part Of: Journal of fluid mechanics. Volume 856(2018)
• Page Start: 426
• Page End: 443
• Publication Date: 2018-12-10
• Subjects: isotropic turbulence, -- turbulence modelling, -- turbulent flows; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.717
• Languages: English
• ISSNs: 0022-1120

Abstract

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, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$ . For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$ ; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ 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 $Re_{\unicode[STIX]{x1D706}}$ 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 $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.