FRACTAL CHARACTERISTICS OF THE HORIZONTAL MOVEMENT OF WATER IN SOILS
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Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to t(n), where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.