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Unstable Wetting Fronts in Uniform and Nonuniform Soils¹

ABSTRACT

If the velocity of a plane wetting front increases with depth of penetration, then the front will be unstable, i.e., then a small perturbation of an initially plane front will tend to grow. On the basis of a simple hydraulic model due to Green and Ampt, criteria for instability are derived. It is found that decreases of depth of ponding and of capillary pressure head at the wetting front, increases with depth of the hydraulic conductivity and the initial water content, and compression of soil air ahead of the wetting front all have the effect of enhancing instability of the wetting front. The capillary pressure head at the wetting front is proportional to the surface tension and the cosine of the angle of contact of the water-air-soil interface and inversely proportional to the radius of curvature of the air-water interface, which in turn is proportional to the mean size of the soil particles. The analysis is at first restricted to uniform soils and later extended to nonuniform soils. Criteria for instability of flows in layered soils and soils with crusts are included as special cases.

¹ Contribution from the North Central Region, ARS, USDA, and the Dep. of Soil Science, Univ. of Wisconsin, Madison, Wis. 53706.

² Soil Scientist and Associate Professor.

Received for publication March 5, 1973. Accepted for publication May 9, 1973.

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