Groundwater waves in aquifers of intermediate depths

In order to model recent observations of groundwater dynamics in beaches, a system of equations is derived for the propagation of periodic watertable waves in unconfined aquifers of intermediate depths, i.e. for finite values of the dimensionless aquifer depth n omega d/K which is assumed small under the Dupuit-Forchheimer approach that leads to the Boussinesq equation. Detailed consideration is given to equations of second- and infinite-order in this parameter. In each case, small amplitude (eta/d much less than 1) as well as finite amplitude versions are discussed. The small amplitude equations have solutions of the form eta(x, t) = eta(0)e(-kx)e(i omega t) in analogy with the linearized Boussinesq equation but the complex wave numbers k are different. These new wave numbers compare well with observations from a Hele-Shaw cell which were previously unexplained. The ''exact'' velocity potential for small amplitude watertable waves, the equivalent of Airy waves, is presented. These waves show a number of remarkable features. They become non-dispersive in the short-wave limit with a finite and quite slow decay rate affording an explanation for observed behaviour of wave-induced porewater pressure fluctuations in beaches. They also show an increasing amplitude of pressure fluctuations towards the base, in analogy with the evanescent modes of linear surface gravity waves. Copyright (C) 1996 Elsevier Science Ltd