### Abstract

A formal perturbation expansion is presented for the large-scale effective drift velocity and diffusion matrix of a medium with stationary random velocity, V(x), and constant nonrandom diffusion matrix, a, on a small scale. If mu denotes the mean of V(x), and V(x) is expressed as mu plus epsilon U(x), then the expansion is in powers of epsilon with mu , U and a fixed. Explicit expressions up to second order in epsilon are obtained which generalize the standard formulae to the case a does not equal 0 0.

Original language | English (US) |
---|---|

Pages (from-to) | 411-424 |

Number of pages | 14 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 44 |

Issue number | 2 |

State | Published - Apr 1984 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*44*(2), 411-424.

**PERTURBATION EXPANSION FOR DIFFUSION IN A RANDOM VELOCITY FIELD.** / Winter, C Larrabee; Newman, C. M.; Neuman, Shlomo P.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 44, no. 2, pp. 411-424.

}

TY - JOUR

T1 - PERTURBATION EXPANSION FOR DIFFUSION IN A RANDOM VELOCITY FIELD.

AU - Winter, C Larrabee

AU - Newman, C. M.

AU - Neuman, Shlomo P

PY - 1984/4

Y1 - 1984/4

N2 - A formal perturbation expansion is presented for the large-scale effective drift velocity and diffusion matrix of a medium with stationary random velocity, V(x), and constant nonrandom diffusion matrix, a, on a small scale. If mu denotes the mean of V(x), and V(x) is expressed as mu plus epsilon U(x), then the expansion is in powers of epsilon with mu , U and a fixed. Explicit expressions up to second order in epsilon are obtained which generalize the standard formulae to the case a does not equal 0 0.

AB - A formal perturbation expansion is presented for the large-scale effective drift velocity and diffusion matrix of a medium with stationary random velocity, V(x), and constant nonrandom diffusion matrix, a, on a small scale. If mu denotes the mean of V(x), and V(x) is expressed as mu plus epsilon U(x), then the expansion is in powers of epsilon with mu , U and a fixed. Explicit expressions up to second order in epsilon are obtained which generalize the standard formulae to the case a does not equal 0 0.

UR - http://www.scopus.com/inward/record.url?scp=0021408616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021408616&partnerID=8YFLogxK

M3 - Article

VL - 44

SP - 411

EP - 424

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -