1. Finite Reynolds Number Effect on Small-Scale Statistics in Decaying Grid Turbulence.
- Author
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Tang, Shunlin, Danaila, Luminita, and Antonia, Robert Anthony
- Subjects
REYNOLDS number ,TURBULENCE ,TRANSPORT equation ,STATISTICS ,ADVECTION - Abstract
Since about 1997, the realisation that the finite Reynolds number (FRN) effect needs to be carefully taken into account when assessing the behaviour of small-scale statistics came to the fore. The FRN effect can be analysed either in the real domain or in the spectral domain via the scale-by-scale energy budget equation or the transport equation for the energy spectrum. This analysis indicates that the inertial range (IR) is established only when the Taylor microscale Reynolds number R e λ is infinitely large, thus raising doubts about published power-law exponents at finite values of R e λ , for either the second-order velocity structure function (δ u) 2 ¯ or the energy spectrum. Here, we focus on the transport equation of (δ u) 2 ¯ in decaying grid turbulence, which represents a close approximation to homogeneous isotropic turbulence. The effect on the small-scales of the large-scale forcing term associated with the streamwise advection decreases as R e λ increases and finally disappears when R e λ is sufficiently large. An approach based on the dual scaling of (δ u) 2 ¯ , i.e., a scaling based on the Kolmogorov scales (when the separation r is small) and another based on the integral scales (when r is large), yields (δ u) 2 ¯ ∼ r 2 / 3 when R e λ is infinitely large. This approach also yields (δ u) n ¯ ∼ r n / 3 when R e λ is infinitely large. These results seem to be supported by the trend, as R e λ increases, of available experimental data. Overall, the results for decaying grid turbulence strongly suggest that a tendency towards the predictions of K41 cannot be dismissed at least at Reynolds numbers which are currently beyond the reach of experiments and direct numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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