Townley, L.R. (1995), The response of aquifers to periodic forcing, Advances in Water Resources, 18(3), 125-146.

In the analysis of aquifer behavior, it is common to distinguish between steady state and dynamic or unsteady behavior. A special case of the latter is periodic behavior, in which an aquifer responds to forcing that varies sinusoidally in time. This paper presents an efficient method for obtaining analytical solutions for periodic aquifer flow, based on the use of complex algebra. It also provides a number of solutions which are simpler in form than those that are currently available. The 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 of a one-dimensional aquifer to tidally fluctuating boundary levels is re-examined. A solution is presented for the response of a one-dimensional aquifer to seasonal or diurnal variations in net recharge; interesting results include the amplification of head fluctuations beyond the expected maximum, and an explanation for the three-month and six-hour lags often observed in annual and daily time series, respectively. Other examples include the effects of mixed boundary conditions, and the behavior of radially symmetric flow systems, either with flow inwards towards a pumping well, or flow outwards, as on a circular island. The amplitude and phase of fluxes through boundaries are also examined.