The effect of water saturation on macrodispersion in bimodal, heterogeneous, variably saturated formations under steady state, gravity-dominated flow conditions was analyzed here. The present study was motivated by the inconsistency between the results of the first-order analysis of Russo <2002> and those of the simulations of Russo et al. <2001>. The latter results suggested that near saturation, increasing mean pressure head H (i.e., decreasing water saturation) may decrease log conductivity variance, σy2, and concurrently, may decrease macrodispersion, while the former results suggested the opposite. Results of the present first-order analysis suggest that this inconsistency stems from the fact that σy2 derived by Russo <2002> is valid only for H = 0. The σy2 derived in the present study, valid for H ≥ 0, is a concave function of H, which exhibits a minimum at H = Hm, (Hm > 0), and may exceed its counterpart in saturated flow when H > Hc (Hc > Hm). The latter σy2 leads to a time-dependent macrodispersion tensor whose principal components decrease with increasing H when 0 Hm' and may exceed their counterparts in saturated flow when H > Hc', (Hc' Hc'. When P* is relatively large, however, the reverse situation occurs. |