20
S. C. Lessoff and P. Indelman
(
B B )I/P
q = ql = K ; K = K, B, _ 0, '
(2)
where fJ is an empirical shape factor and ~ and Br are the saturated and residual
values of moisture content, respectively.
The solution of Eqs. (1) and (2) for an infiltration-redistribution cycle is
derived by Indelman et al. (1998) and is reviewed here for completeness. The soil
is assumed to be initially dry, i.e.,
(t=0, z~O).
(3)
The moisture content profile £X..z,t) and specific discharge are given by step
functions (see Fig. 1)
£X..z,t)= Br+[BJt)-Br]H[zJt)-z] ; q(z,t)=q,Az,t)H[zJt)-z]
(4)
where H(z) is the Heaviside step function. The front water saturation ~ and
discharge ql are determined separately for infiltration and redistribution stages.
Although the step function only roughly approximates the shape of real
infiltration fronts, subsequent averaging of the moisture content over a
heterogeneous collection of tubes produces realistic smooth wetting fronts.
) !
,......,.....---.,;-,
I
J
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
II
~ ~
~
a
-
b
Fig. 1 a,b. Definition sketch of approximate e profiles for infiltration for a few values of
' Y (a) and redistribution for y=1 (b)
Infiltration occurs for t infiltrate. It is convenient to introduce the parameter y by