Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field

Abstract

Using direct numerical simulations (DNS) and large-eddy simulations (LES) of velocity and passive scalar in isotropic turbulence (up to 512³ grid points), we examine directly and quantitatively the refined similarity hypotheses as applied to passive scalar fields (RSHP) with Prandtl number of order one. Unlike previous experimental investigations, exact energy and scalar dissipation rates were used and scaling exponents were quantified as a function of local Reynolds number. We first demonstrate that the forced DNS and LES scalar fields exhibit realistic inertial-range dynamics and that the statistical characteristics compare well with other numerical, theoretical and experimental studies. The Obukhov–Corrsin constant for the k^−5/3 scalar variance spectrum obtained from the 512³ mesh is 0.87±0.10. Various statistics indicated that the scalar field is more intermittent than the velocity field. The joint probability distribution of locally-averaged energy dissipation ε_r and scalar dissipation χ_r is close to log-normal with a correlation coefficient of 0.25±0.01 between the logarithmic dissipations in the inertial subrange. The intermittency parameter for scalar dissipation is estimated to be in the range 0.43≈0.77, based on direct calculations of the variance of lnχ_r. The scaling exponents of the conditional scalar increment δ_rθ[mid ] _χr,_εr suggest a tendency to follow RSHP. Most significantly, the scaling exponent of δ_rθ[mid ] _χr,_εr over ε_r was shown to be approximately −⅙ in the inertial subrange, confirming a dynamical aspect of RSHP. In agreement with recent experimental results (Zhu et al. 1995; Stolovitzky et al. 1995), the probability distributions of the random variable β_s = δ_rθ[mid ] _χr,_εr/ (χ^1/2_r ε^−⅙_rr^1/3) were found to be nearly Gaussian. However, contrary to the experimental results, we find that the moments of β_s are almost identical to those for the velocity field found in Part 1 of this study (Wang et al. 1996) and are insensitive to Reynolds number, large-scale forcing, and subgrid modelling.