THE RESPONSE OF AQUIFERS TO PERIODIC FORCING

In the analysis of aquifer behavior, it is common to distinguish betwe en steady-state and dynamic or unsteady behavior. A special case of th e latter is periodic behavior, in which an aquifer responds to forcing that varies sinusoidally in time. This paper presents an efficient me thod for obtaining analytical solutions far periodic aquifer bow, base d on the use of complex algebra. It also provides a number of solution s which are simpler in form than those that are currently available. T he solutions provide valuable insights into the spatial variations of amplitudes of head fluctuations and of the phase lags between periodic forcing and aquifer response. The classical problem of the response o f a one-dimensional aquifer to tidally fluctuating boundary levels is re-examined. A solution is presented for the response of a one-dimensi onal aquifer to seasonal or diurnal variations in net recharge; intere sting results include the amplification of head fluctuations beyond th e expected maximum, and an explanation for the 3-month and 6-h lags ob served in annual and daily time series, respectively. Other examples i nclude the effects of mixed boundary conditions, and the behavior of r adially symmetric flow systems, either with flow inwards towards a pum ping well, or flow outwards, as on a circular island. The amplitude an d phase of fluxes through boundaries are also examined.