A numerical study of passive scalar evolution in peripheral regions

We study the effect of slip and no-slip wall boundaries on the decay rate of a passive scalar in a spatially smooth and random in time velocity field. Numerical simulations are carried out to verify the effect of the peripheral (near-wall) regions on the decay of the scalar variance. Using two kinematic flow models with simple velocity fields, we show that, in the case of slip boundaries, the passive scalar is characterized by an initial rapid stirring followed by an exponential decay of the scalar variance. In stark contrast, results for the case with no-slip boundaries show that, following an initial rapid stirring of the scalar within the bulk, there is an intermediate-time regime where the variance follows a power-law decay. This intermediate regime is established as a result of the trapping of the scalar in the peripheral regions near the no-slip walls. Finally, the behavior of the scalar variance switches to a final regime that is characterized by an exponential decay rate. The results presented here indicate that the recent ensemble-based theories regarding the evolution of a passive scalar in the peripheral regions correctly predict the main stages of the scalar evolution that arise in a single flow realization. (c) 2007 American Institute of Physics.