The anisotropy of scalar fluctuations induced by scalar flux and the return to isotropy of the anisotropic scalar field are investigated by using the modified zero-fourth-cumulant (MZFC) expansion. The spectral equations of axisymmetric scalar flux and variance in decaying isotropic turbulence are formulated by applying the MZFC expansion. Numerical calculation is made under the initial conditions for two different degrees of anisotropy: one is an isotropic state with a flux, and another is a two-dimensional state that is strongly anisotropic in the three dimensions. Results show that the scalar flux produces an anisotropy of the scalar distribution so that scalar concentration increases in the direction parallel to the symmetric axis and decreases in the direction transverse to it. The return to isotropy is rapid, except for large scale fluctuations, even in the strongly anisotropic case.
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Nakauchi et al. (1987) studied this question.
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