Unsteady Seepage toward Sink beneath Free Surface

One of the mathematical techniques of linearized wave mechanics is applied to solve the problem of unsteady, axially symmetric seepage toward a sink of variable strength located beneath a free surface. Both finite and infinite aquifer depths are considered, and linearized solutions are given for two distinct types of problems. The first solution corresponds to the problem in which the flow rate to the sink is a specified function of time and the distribution of piezometric head is unknown. The second solution corresponds to the inverse problem in which the piezometric head near the sink is a specified function of time and the flow rate to the sink is unknown. Coordinates of the free surface are determined as part of the solution in each case. Finally, it is pointed out that the results can also be used to solve the analogous problem which occurs when an aquifer is recharged by a point source.