Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer.

We consider two sources of geology-related uncertainty in making predictions of the steady-state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow.

The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31, 469-485 (doi:10.1063/1.866828)) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

A partially open porous media flow with chaotic advection: towards a model of coupled fields.

In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.