Bank-Storage Problem and the Dupuit Approximation

Two-dimensional solutions, which include both vertical velocity components and compressibility effects, are compared with one-dimensional Dupuit solutions, which neglect vertical velocity components and compressibility effects, for flow into a riverbank when a flood wave passes downstream. The flood wave is modeled with an instantaneous rise in river level that remains constant for an infinite time thereafter; and the two-dimensional solutions also include aquifer anisotropy, which cannot be included in the Dupuit solutions. The comparisons show that the Dupuit solutions closely approximate the more accurate two-dimensional solutions only for sufficiently small values of a dimensionless parameter that contains the relative depth and the horizontal-to-vertical permeability ratio. Aquifer and fluid compressibility effects, which are also neglected in the Dupuit solutions, are shown to be significant only for very small values of time and can probably be neglected in most applications, although this effect can be important in a few problems.