Reynolds number effect on the velocity derivative flatness factor

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), 2017b, 051702). These terms and hence F become constant when the Taylor microscale Reynolds number, Re A exceeds approximately 10(4). For smaller values of Re-lambda, F, like the skewness -S, increases with ReA; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that Re-lambda A is large enough for the FRN effect to he negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301-305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16-18; J. Fluid Mech. vol. 13, 1962, pp. 82-85) can he assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which Re-lambda is well below 10(4) may not he immune from the FRN effect. Another implication is that a power-law increase of with respect to Re-lambda, as suggested by the Kolmogorov 1962 theory, is not tenable when Re-lambda is large enough.

Marcello Meldi, L. Djenidi, R. Antonia. Reynolds number effect on the velocity derivative flatness factor. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 856, pp.426-443. ⟨hal-01947035⟩

Journal: Journal of Fluid Mechanics

Date de publication: 10-12-2018

  • Marcello Meldi
  • L. Djenidi
  • R. Antonia

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