Flow and solute transport through a levee separating fluids with different densities

Steady seepage through a levee or a dam separating reservoirs with different levels and densities is shown to result in five possible flow configurations. If densities are equal, the problem reduces to the classical problem of flow through a dam. If the lower reservoir is less dense, a stationary wedge may or may not form inside the levee near the downgradient reservoir level. If the lower reservoir is more dense, a wedge forms near the toe of the levee, as in the classical problem of saltwater intrusion. Another possibility is that the dense wedge can connect the two reservoirs, thus allowing bidirectional flow. Conditions are derived which define when these different flow configurations occur. For the case of a rectangular dam with vertical walls a closed form solution is obtained for the net mass flux between the reservoirs. Net volumetric flux is determined analytically for all flow configurations except the case of bidirectional flow. The expression for volumetric flux is a generalization of a result based on the Dupuit assumption for the case of constant density. A range of parameters is identified in which net volumetric flux is in one direction and net mass flux in the other. A numerical model based on the boundary integral equation method allows calculation of net volumetric flux for the case of bidirectional flow and also allows simulation of more complex levee geometries. The solution has direct application to levees separating ponds in solar salt production, to the causeway across the Great Salt Lake in Utah, and to the role of exchange flows in the genesis of evaporites in nearshore lagoons.