The structure and the small-scale intermittency of passive scalars in homogeneous turbulence

Results generated by direct numerical simulations (DNS) are used to study the structure and the small-scale intermittency of a passive scalar contaminant in a homogeneous turbulent shear flow. Simulations are conducted of flows with and without a constant mean scalar gradient. In all cases, the probability density functions (PDFs) of the scalars adopt an approximate gaussian distribution at the final stages of mixing. In the presence of the mean gradient, the scalar fields yield a nearly identical asymptotic state independent of initial conditions. In these cases, the gradient of the fluctuating scalar field shows preferred directions of orientation with respect to the strain eigenvectors; and the mean transverse velocity conditioned on the scalar is linear. These fields also portray increased flatness and skewness of the scalar-difference field as the separation distance becomes small. Larger than gaussian tails are observed in the PDF of both the velocity- and the scalar-derivatives, and the intermittency of the scalar derivative is shown to be more pronounced in the presence of the mean scalar gradient. Conditional averages of the angle between the scalar gradient and the strain eigenvectors suggest that the scalar field may be viewed as a random gaussian background field superimposed with sporadic scalar structures which are responsible for intermittency. With this view, a Langevin transport equation is proposed for the mapping of the scalar derivative PDF from a gaussian reference field. This is done in the context of the "two-fluid" model of She (1990). With this model, the PDF of the scalar dissipation is produced and the results are compared with DNS data.