### 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 |

State | Published - 1991 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

**Enhanced diffusivity and intercell transition layers in 2-D models of passive advection.** / Avellaneda, Marco.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 32, no. 11, pp. 3209-3212.

}

TY - JOUR

T1 - Enhanced diffusivity and intercell transition layers in 2-D models of passive advection

AU - Avellaneda, Marco

PY - 1991

Y1 - 1991

N2 - 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 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* ∝ 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.

AB - 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 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* ∝ 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.

UR - http://www.scopus.com/inward/record.url?scp=0041740830&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041740830&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041740830

VL - 32

SP - 3209

EP - 3212

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

ER -