Inverse solution for one-dimensional infiltration, and the ratio A/K1
1990
Philip, J.R.
The inverse method of solving the nonlinear diffusion equation is extended to give exactly the two leading terms of the infiltration series solution of the nonlinear Fokker-Planck equation of unsaturated flow. We use the method, together with a new integral result for the ratio A/K1, to investigate the, hitherto imperfectly understood, physical determinants of A/K1. K1 is the saturated conductivity, and A the second coefficient of the two-term infiltration equation i = St1/2 + At. We separate out the relatively superficial direct effect of the initial moisture content (important only when initial soil moisture content is very large) from the more complicated effect, dependent both on soil texture and on initial soil moisture content, of the shapes of the diffusivity D and the conductivity derivative dK/d(initial soil moisture content). Normalized first moments of these functions measure the steepness of their variation. We explore the full range of combinations of shapes of D and dK/d(initial soil moisture content) from essentially flat to essentially infinitely steep. For soils with K0/K1 negligibly small (K0 = K(initial soil moisture content)), A/K1, lies in the range 0 to 2/3. The dominant physical effect is that A/K1 decreases monotonically as dK/d(initial soil moisture content) increases in steepness. On the other hand, A/K1 increases (relatively slowly) with the steepness of D.
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