Normal mode analysis of the linear equation of groundwater flow

Abstract

The study of groundwater flow, given equations of motion and boundary conditions which are mathematically linear, can be analyzed by using a normal mode approach. For the fully continuous case the simplest example is the familiar double Fourier analysis. Analogous results exist for the semidiscrete case, in which only time is treated as a continuous variable, and a method can be given for computing normal modes whose corresponding recession factors lie within prescribed ranges. One application of this approach suggests an empirical form for the base flow component of a stream hydrograph. The fully discrete case can also be treated and provides a convenient basis for the comparison of the more common approximations to the solution of the transient groundwater flow equation. In particular, it can be shown why the study of model problems does not provide a useful guide to the accuracy of the alternating direction implicit method applied to more general situations.