The enhancement of mixing by chaotic advection

The stirring and mixing of passive scalars by laminar flows that generate chaotic particle trajectories is studied by numerical experiment and scale analysis. There are two principal results. The first result is that the time scale of the maximum mixing rate of diffusive particles across a material contour diverges like the logarithm of the Péclet number as Pe→∞ (Pe=UL/D where U, L, and D are a typical velocity scale, length scale, and the molecular diffusivity, respectively). This logarithmic divergence is explained on the basis of a simple scaling argument that equates the striation thickness of the advected tracer with a characteristic diffusion length. A similar analysis, performed for a linear shear flow, suggests that in this limit the divergence is more rapid for integrable advection, for the shear flow it is like Pe1/3. The second result is that the time scale for the homogenization of tracer within a bounded domain is also proportional to the logarithm of Pe. This result can also be explained by equating length scales, in this case the separation distance between adjacent filaments of the tracer distribution and a diffusion length. In contrast, the time scale of homogenization when particle trajectories are regular is linear in Pe.