### Abstract

The parabolic differential equation that describes the isothermal isohaline transport of water through an unsaturated soil is shown to be the mathematically rigorous result of a fundamental stochastic hypothesis: that the trajectory of a water molecule is a nonhomogeneous Markov process characterized by space- and time-dependent coefficients of drift and diffusion. The demonstration is valid in general for heterogeneous anisotropic soils and provides for three principal results in the theory of water flow through unsaturated media. A dynamic argument at the molecular level is developed to show that the fundamental Markovian hypothesis is physically reasonable in the case of water movement through an unsaturated soil.

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

Pages (from-to) | 503-512 |

Number of pages | 10 |

Journal | Water Resources Research |

Volume | 12 |

Issue number | 3 |

State | Published - Jun 1976 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Aquatic Science
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology

### Cite this

*Water Resources Research*,

*12*(3), 503-512.

**ON THE STOCHASTIC FOUNDATIONS OF THE THEORY OF WATER FLOW THROUGH UNSATURATED SOIL.** / Bhattacharya, Rabindra N; Gupta, Vijay K.; Sposito, Garrison.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 12, no. 3, pp. 503-512.

}

TY - JOUR

T1 - ON THE STOCHASTIC FOUNDATIONS OF THE THEORY OF WATER FLOW THROUGH UNSATURATED SOIL.

AU - Bhattacharya, Rabindra N

AU - Gupta, Vijay K.

AU - Sposito, Garrison

PY - 1976/6

Y1 - 1976/6

N2 - The parabolic differential equation that describes the isothermal isohaline transport of water through an unsaturated soil is shown to be the mathematically rigorous result of a fundamental stochastic hypothesis: that the trajectory of a water molecule is a nonhomogeneous Markov process characterized by space- and time-dependent coefficients of drift and diffusion. The demonstration is valid in general for heterogeneous anisotropic soils and provides for three principal results in the theory of water flow through unsaturated media. A dynamic argument at the molecular level is developed to show that the fundamental Markovian hypothesis is physically reasonable in the case of water movement through an unsaturated soil.

AB - The parabolic differential equation that describes the isothermal isohaline transport of water through an unsaturated soil is shown to be the mathematically rigorous result of a fundamental stochastic hypothesis: that the trajectory of a water molecule is a nonhomogeneous Markov process characterized by space- and time-dependent coefficients of drift and diffusion. The demonstration is valid in general for heterogeneous anisotropic soils and provides for three principal results in the theory of water flow through unsaturated media. A dynamic argument at the molecular level is developed to show that the fundamental Markovian hypothesis is physically reasonable in the case of water movement through an unsaturated soil.

UR - http://www.scopus.com/inward/record.url?scp=0016963896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016963896&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0016963896

VL - 12

SP - 503

EP - 512

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 3

ER -