Refined similarity hypothesis using three-dimensional local averages

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kartik P IyerP K Yeung

Abstract

The refined similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermittent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number R_{λ}∼650, on a periodic box of 4096^{3} grid points to test the hypotheses using three-dimensional averages. In particular, we study the small-scale properties of the stochastic variable V=Δu(r)/(rε_{r})^{1/3}, where Δu(r) is the longitudinal velocity increment and ε_{r} is the dissipation rate averaged over a three-dimensional volume of linear size r. We show that V is universal in the inertial subrange. In the dissipation range, the statistics of V are shown to depend solely on a local Reynolds number.

References

Aug 24, 1992·Physical Review Letters·G StolovitzkyK R Sreenivasan
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V Yakhot

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Citations

Mar 17, 2017·Physical Review. E·Kartik P IyerP K Yeung
Jan 13, 2019·Physical Review Letters·Kartik P IyerP K Yeung

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