Enhanced diffusivity and intercell transition layers in 2-D models of passive advection

Abstract

A class of two-dimensional, isotropic, divergence-free vector fields is introduced and the effective diffusivity of the corresponding advection–diffusion equations is studied. These examples are very idealized flows, but they can be solved exactly in the limit Pe≫1. Scaling laws D*∝D0(Pe)α are obtained, where D0=molecular diffusion, Pe=Peclet number, with exponents in the range 0<α<1, and examples of ‘‘stream functions’’ with logarithmic singularities for which D*∝D0Pe. The exponent α is related by a simple formula to the shape of the stream function along cell boundaries, suggesting that similar scaling laws should hold for more general 2-D closed-cell flows.