Instability of the salinity profile during the evaporation of saline groundwater

We investigate salt transport during the evaporation and upflow of saline groundwater. We describe a model in which a sharp evaporation-precipitation front separates regions of soil saturated with an air-vapour mixture and with saline water. We then consider two idealised problems. We first investigate equilibrium configurations of the fresh-water system when the depth of the soil layer is finite, obtaining results for the location of the front and for the upflow of water induced by the evaporation. Motivated by these results, we develop a solution for a propagating front in a soil layer of infinite depth, and we investigate the gravitational stability of the salinity profile which develops below the front, obtaining marginal linear stability conditions in terms of a Rayleigh number and a dimensionless salt saturation parameter. Applying our findings to realistic parameter regimes, we predict that salt fingering is unlikely to occur in low-permeability soils, but is likely in high-permeability (sandy) soils under conditions of relatively low evaporative upflow.