Passive scalar fluctuations with and without a mean gradient: A numerical study

We report a numerical study of a passive scalar advected by a random incompressible Gaussian velocity field. The calculations are carried out on a two-dimensional square lattice. Depending on the two dimensionless parameters in the problem, the scalar fluctuations at the center can be Gaussian, exponential, or stretched exponential. This is true not only when the passive scalar is subjected to a uniform mean gradient but also true when a new alternating boundary condition is used which results in a mean scalar profile that has a vanishing gradient in the central region.