Journal of Fluid Mechanics

Papers

Instability of the salinity profile during the evaporation of saline groundwater

ANDREJ T. IL'ICHEVa1, GEORGE G. TSYPKINa2, DAVID PRITCHARDa3 and CHRIS N. RICHARDSONa4

a1 Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, 119991 Moscow, Russia ilichev@mi.ras.ru

a2 Institute for Problems in Mechanics, Russian Academy of Sciences, Av. Vernadskogo 101, 119420 Moscow, Russia tsypkin@ipmnet.ru

a3 Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland dtp@maths.strath.ac.uk

a4 BP Institute for Multiphase Flow, University of Cambridge, Madingley Rise, Cambridge CB3 0EZ, UK chris@bpi.cam.ac.uk

Abstract

In this paper 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 idealized problems. We first investigate equilibrium configurations of the freshwater system when the depth of the soil layer is finite, obtaining results for the location of the front and the upflow of water induced by the evaporation. We then develop a solution for a propagating front in a soil layer of infinite depth and 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.

(Received June 19 2007)

(Revised July 04 2008)

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