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 εr and scalar dissipation χr 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 lnχr. The scaling exponents of the conditional scalar increment
δrθ[mid ]
χr,εr
suggest a tendency to follow RSHP. Most significantly, the scaling exponent of
δrθ[mid ]
χr,εr
over εr 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
βs = δrθ[mid ]
χr,εr/
(χ1/2r
ε−⅙rr1/3) were found to be nearly Gaussian. However, contrary to the
experimental results, we find that the moments of βs 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.
The Scaling Exponents of Intermittent Fully Developed Turbulence Based on a New Model
