Tidal fluctuations in a leaky confined aquifer: Dynamic effects of an overlying phreatic aquifer

Tidal fluctuations in a leaky confined coastal aquifer are damped significantly due to leakage into an overlying phreatic aquifer. Jiao and Tang [1999] presented an analytical solution to a simple model describing this phenomenon. Their solution assumes that the tidal fluctuations in the overlying phreatic aquifer are negligible (i.e., a static phreatic aquifer). Here we examine dynamic effects of the overlying aquifer based on a new approximate analytical solution. The numerical results indicate that the dynamic effects can be significant for a relatively large leakage and a high transmissivity of the phreatic aquifer. 1. Problem Set Up As shown in Figure 1, we consider tidal fluctuations in both the confined and the phreatic aquifer. These two aquifers interact with each other through a thin leaky layer. The governing equations of the head fluctuations inboth aquifers are [e.g., Bear and Verruijt, 1987] Ohl O2hl sl •-= T1 • + L(h2hi), (la) Oh2 02h2 s2 -•-= T2 • + L(hlh2), (lb) where h • and h 2 are the heads in the confined and the phreatic aquifers, respectively; T• and T 2 are the transmissivities of these two aquifers, respectively; s • is the specific yield of the phreatic aquifer and s2 is the storativity of the confined aquifer; and L is the specific leakage of the semipermeable ayer. Note that linearization has been applied for the governing equation of the phreatic aquifer, (la), under the assumption that the tidal amplitude is small relative to the aquifer's thickness [Parlange et al., 1984]. Jiao and Tang [1999] assumed h• to be constant. Here we shall consider h • variable, reflecting tidal water table fluctuations in the phreatic aquifer. The boundary conditions for these semi-infinite aquifers are hi(0, t) = h2(0, t) = h•tsi• + A cos (tot), (2a) I øh2 I Ox = • = 0, (2b) where h MsL is the averaged mean sea level and.4 and to are the tidal amplitude and frequency, respectively. Physically, (2a) and (2b) describe a periodic boundary condition at the origin in an aquifer without a regional flow component. Only one tidal constituent is considered here. Since the problem is linCopyright 2001 by the American Geophysical Union. Paper number 2000WR900402. 0043-1397/01/2000WR 900402509.0