In this paper, it will be shown that the concentration distribution in a plume is multifractal-like if we choose the measure as the integral of concentration over a finite time interval in the recorded concentration data. This kind of multifractality is most possibly due to that of the kinematic energy dissipation field. Some phenomenological explanation is given to this multifractality through the use of the binomial multiplicative process model and the so-called random dilution coefficient model. It will also be shown that both models give lognormality of the pdf of concentration, which is an empirical result of experimental studies. Moreover, by processing the experimental data, the f(α) spectra are obtained for the concentration field of the plume, and it is found that the distortion of flow due to the sphere appears to reduce the maximum singularity exponents α_max.