UNIFORM ASYMPTOTIC EXPANSIONS RELATED TO UNSTEADY-FLOW IN UNCONFINED AQUIFERS

A general uniform asymptotic expansion is constructed to remove certain anomalies which appeared in the ray method expansion developed previously for flow in unconfined aquifers. This makes the asymptotic method based upon the principles of geometrical optics even more useful than before. In particular, expansions uniform in a region containing a caustic, a line of zero depth, a combination of both, two caustics, and two lines of zero depth are explicitly constructed.