A note on the propagation of water table waves: dual length scale considerations

Abstract

The problem of a coastal aquifers forced by oscillations in an adjacent sea and/or estuary across a sloping boundary has recently received considerable theoretical attention. Despite such a wealth of mathematical advancements, stringent testing of the limitations of these models has yet to be undertaken. In all of the currently available analytical solutions it has been assumed that a single length scale is sufficient to account for both the amplitude decay rate and the rate of increase in phase lag (the wave speed) as the water table wave propagates landward. All of the available field and laboratory data however indicate that this is not the case. That is, the real part of the water table wave number (the amplitude decay rate) is not equal to the imaginary part (the rate of increase in the phase lag). In this chapter, the detailed laboratory measurements of Cartwright et al. [2004] are used to highlight the limitation of assuming a single length scale in these mathematical models. In a step towards overcoming this limitation, a new approximate analytical solution is derived which allows for two different length scales as observed in the available data. In the absence of the ability to accurately predict the water table wave number using basic aquifer parameters, all of the solutions are applied to the data using water table wave numbers estimated from the data. Accurately predicting the water table wave number based on measurable aquifer parameters remains a challenge.