Technical Report No. 51
THE RESPONSE TO TIDAL FLUCTUATIONS OF TWO NON-HOMOGENEOUS COASTAL AQUIFER MODELS
John A. Williams, and Ta-Chiang Liu
September 1971
ABSTRACT
Mathematical and electric analog (R-C circuit) models for two one-dimensional non-homogeneous coastal aquifers have been developed. The first is a semi-infinite aquifer having a discontinuous change in permeability at a distance L from the coastline and the second is an aquifer of length L whose permeability changes linearly with distance from the coastline and whose interior boundary represents either a constant head or a no-flow condition. Both models were subjected to a sinusoidal tidal input. Results, in the form of graphs of amplitude and phase angle vs position, show excellent agreement between the outputs of the mathematical and electric analog models. In the case of a discontinuous permeability, these graphs indicate a positive or negative reflection from the discontinuity for a decrease or increase, respectively, in the permeability. In the case of the linearly varying permeability model, the graphs of amplitude indicate that energy is attenuated at a greater rate near the coastline-when KL/KO, <1 for both types of boundary condition. Graphs of the phase angle are concave downwards for the constant-head boundary condition but for the no flow condition they exhibit a point of inflection whose position depends on tO and KL/KO. Electric analog model results show that for the semi-infinite aquifer no significant error will result from the circuit configuration if a < A/50 and the circuit length is equivalent to 2A, furthermore, “lumped” components, i.e., a = A/5, may be used to extend the circuit beyond x = -.4A if measurements are restricted to x > -.2/A.