A linear model of conduit waves in karstic aquifers

Abstract

A conduit within an otherwise homogeneous aquifer changes the aquifer properties fundamentally, permitting the transmission of “conduit waves”, involving variations of head and exchanges of water between conduit and matrix, for many kilometers. A linear theory of conduit waves is developed in case the hydraulic gradient associated with the waves is small compared with the regional gradient. This theory yields a decay rate λ and phase speed ν of harmonic waves in terms of the physical parameters of the aquifer and the wave frequency, ω. These theoretical results are combined with values of λ and ν, extracted from observations of water level in the Woodville Karst Plain (WKP) of North Florida, to obtain estimates of the conduit radius and aquifer permeability. Using the nearly semi-diurnal tidal mode, the comparison yields a mean conduit radius of 10 m and an effective permeability of 0.017 m s−1. This theory, which models an aquifer with a rigid, impermeable bottom, is incompatible with the observational data from the nearly diurnal tidal mode, suggesting that a model employing a floating bottom might be more appropriate for the WKP.