An Analytical Solution for Contaminant Transport in Nonuniform Flow

We obtain an analytical solution for two-dimensional steady state mass transport in a trapezoidal embankment in a spatially varying velocity field through its replacement with a hydrologically equivalent rectangular embankment. Application of the Dupuit approximation and conform transformation allow for computation of the concentration field in the resulting rectangle in the complex potential plane. The latter allows deriving expression for the mass flow rate of contaminants, which is analogous to the Dupuit-Forchheimer discharge formula for volumetric water flow rate. Numerical simulation of advection-dispersion in the actual domain compares favorably with these analytical results, and provides limits of the ratio between transverse and longitudinal dispersivities within which the Dupuit approximation is applicable to mass transport problems.