## Abstract

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.

Original language | English |
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Pages (from-to) | 45-54 |

Number of pages | 10 |

Journal | Stochastic Hydrology and Hydraulics |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1991 |

## Keywords

- Lagrangian description
- Solute transport
- nonlinear effects
- random velocity
- travel time