Abstract
It is shown that the well-known conservation laws for magnetic helicity and passive-scalar fluctuation intensity in the case of negligible molecular diffusion require that the hierarchy of nonlinear equations for the averaged Green function and the hierarchy of Bethe-Salpeter-type equations for fluctuation intensity be treated in a mutually consistent manner. These hierarchies are obtained to the sixth order in turbulent velocity correlators. Asymptotic formulas describing the evolution of scalar fluctuations and magnetic field are presented. A number of new effects are revealed that strongly affect diffusion, but are beyond the scope of the frequently used model of a delta-correlated turbulent field.
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