Physics of
Fluids **6** (1994) pp. 1036-1051

### Similarity states of passive scalar transport in isotropic turbulence

- J. R.
Chasnov
*Center for Turbulence Research, NASA Ames Research Center*

We determine the time-evolution of the kinetic energy and scalar-variance in
decaying isotropic turbulence transporting passive scalars using simple analytical
arguments and large-eddy simulations. The evolution of a passive scalar
field with and without a uniform mean gradient is considered.
Firstly, we consider similarity states of the flow during the final period of
decay. Exact analytical solutions may be
obtained and these depend only on the form of the energy and scalar-variance
spectra at low wavenumbers, and the molecular transport coefficients. The
solutions for a passive scalar field with mean-scalar gradient are
of special interest and we find that the scalar-variance may grow or decay
asymptotically in the final period depending on the initial velocity distribution.
Secondly, we consider similarity states of the flow at high Reynolds and Peclet
numbers. Here we assume that the solutions
also depend on the low wavenumber spectral coefficients, but not on the
molecular transport coefficients. This results in a non-linear dependence of
the kinetic energy and scalar-variance on the spectral coefficients, in
contrast to the final period results. The analytical results obtained may be
exact when the similarity solutions depend only on spectral coefficients which
are time-invariant. Our analysis also leads directly to a similarity state
for a passive scalar field with uniform mean scalar gradient.
Lastly, we perform large-eddy simulations of the flow field to test the
theoretical results. Asymptotic similarity states at large times in the
simulations are obtained and found to be in good agreement with predictions of
the analysis. We also determine several dimensionless quantities which compare
favorably to earlier experimental results. An argument
for the inertial subrange scaling of the scalar-flux spectrum is presented which yields a
spectrum proportional to the scalar gradient and decaying as k^{-7/3}. This result is
partially supported by the small scale statistics of the large-eddy simulations.

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