We introduce a shell model for the small-scale statistics of a scalar field passively carried by a three-dimensional turbulent fluid. The model mimics a cascade process for the spectral transfer of both velocity and a passive scalar. It is found to exhibit an intermittency correction to the 5/3 Obukhov-Corrsin power law for the power spectrum of a passive scalar, at wave numbers k where molecular diffusion and viscosity play a negligible role (inertial convective subrange). The structure functions and the probability distribution functions of the increments of the passive scalar are also computed. The results of our model are in excellent agreement with the experimental data.
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Jensen et al. (1992) studied this question.
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