## 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* ∝ D_{0}(Pe)^{α} are obtained, where D _{0} = molecular diffusion, Pe = Peclet number, with exponents in the range 0 < α < 1, and examples of "stream functions" with logarithmic singularities for which D* ∝ D_{0}Pe. 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.

Original language | English (US) |
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Pages (from-to) | 3209-3212 |

Number of pages | 4 |

Journal | Journal of Mathematical Physics |

Volume | 32 |

Issue number | 11 |

DOIs | |

State | Published - 1991 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics