Hydraulic transport, vertical flow

Hydraulic transport, vertical flow 1.96, 210 Hydrocyclones 55 Hygrometer 758... 

The external force applied may enhance the anomalous transport in fractal structures (Roman et al., 1989). Therefore, anomalous features can be even more pronounced in the gravity-affected vertical water transport than in the horizontal water transport. General considerations of Roman et al. (1989) imply that the scaling variable x/f1 in (Eq. [2]) should be in this case replaced by the scaling variable xFiogit). Presence of sharp changes in soil hydraulic and transport properties that can be encountered during vertical flow in soils may make the dispersion/distance relations considerably more complex than they are in the media where the FADE has been shown to be effective. The efficiency of the FADE in such situations remains to be seen. 

This quite arbitrary method of two-dimensional transport ignores the components of vertical flow and thus underestimates the transversal dispersion thereby induced. On the other hand we tested a simple non-reacting case with the same hydraulic conditions against an analytical solution and found that the longitudinal dispersion is not influenced by numerical dispersion, whereas the numerical solution overestimates the transversal dispersion by approximately 10 %. The influence of the boundary conditions for top and bottom of the aquifer (no gradient, no flux) is more important in terms of an increased transversal dispersion for these cells. All these effects are negligible compared to the influences of inhomogeneities of hydraulic conductivities onto the modelled transversal dispersion. 

This expression describes the fastest and most important mode of transport in groundwater. In fact, an important task of the hydrologist is to develop models to predict the effective velocity u (or the specific flow rate q). Like the Darcy-Weis-bach equation for rivers (Eq. 24-4), for this purpose there is an important equation for groundwater flow, Darcy s Law. In its original version, formulated by Darcy in 1856, the equation describes the one-dimensional flow through a vertical filter column. The characteristic properties of the column (i.e., of the aquifer) are described by the so-called hydraulic conductivity, Kq (units m s"1). Based on Darcy s Law, Dupuit derived an approximate equation for quasi-horizontal flow ... 

Flow occurs from the left to the right side due to a gradient of 2.5 %o, simulated by two constant head boundaries. The effective porosity of 20 % is assumed to be homogeneously distributed. The dispersivity for transport calculations is small, 0.5 m in longitudinal direction and 0.005 m in the vertical direction, since heterogeneities of hydraulic conductivity are already considered. 

In particular, horizontal advection and horizontal diffusion in the Chesapeake Bay are comparable while vertical difiiision is a fast process that acts over short distances, and a model must account for all three. In this environment, atrazine that is discharged to the surface waters could be horizontally distributed over a distance of 1 km over a period of one week, since the time scale of horizontal advection-difiusion processes is 10 -10 s (approximately 3 hours). As atrazine is distributed horizontally, it also mixes vertically down the water coluitm. With the estimates of verticd diffiisivity for the Bay that are available in the literature, for a depth of 10-20 m the time scale for vertical diffusion processes is on the order of 15 minutes, and can be as short as 3 minutes. The sidfidic vraters are in the sediment porewaters and atrazine needs to be transported to the water-sediment inter ce in order to encounter and react with reduced sulfiir species. The characteristic horizontal and vertical scales that describe the flow in the Bay indicate that it is possible for atrazine to reach the depth of the water-sediment interface before it is horizontally transported out of the system. The subsequent exchange at the water-sediment interface depends on many factors, including half-life of atrazine, the hydraulic residence time of the bottom layer, turbulent processes, and other characteristics of the water column above the sediment layer. Simple box models cannot capture the dynamics necessary to describe these exchanges that ultimately govern the te of atrazine in the Bay. 

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