Abstract
The anisotropy of a passive scalar field at the level of second-order moments of the scalar derivatives is studied starting from the exact equations for the components of the second-rank tensor E defined by Eij=2D(∂θ′/∂xi)(∂θ′/∂xj)¯ (D is the molecular diffusivity of scalar θ). Analysis requires also the equations for the components of a mixed tensor defined by the correlations between scalar and velocity gradients. After the examination of this set of equations, it is conjectured that, in the case of forcing by a mean scalar gradient in isotropic turbulence, the anisotropy of tensor E is produced by cliffs of temperature occurring in the direction of the mean gradient. A model for this mechanism is proposed including possible indirect influence of shear through the large-scale anisotropy of the scalar field. Predictions in the situation where a mean scalar gradient is combined with homogeneous shear agree tolerably well with experimental data. This suggests that the proposed picture describing production of small-scale anisotropy implied by mean gradient forcing has to be completed.
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