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Instability of the salinity profile during the evaporation of saline groundwater. (English) Zbl 1155.76026
Summary: 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 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.

76E20 Stability and instability of geophysical and astrophysical flows
76E17 Interfacial stability and instability in hydrodynamic stability
86A05 Hydrology, hydrography, oceanography
Full Text: DOI
[1] DOI: 10.1017/S0022112060001031 · Zbl 0096.21801
[2] DOI: 10.1029/96WR03533
[3] Vukalovitch, Thermodynamic Properties of Water and Water Vapour (1955)
[4] van Duijn, Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere (2002)
[5] DOI: 10.1016/S0309-1708(98)00008-6
[6] DOI: 10.1071/SR04051
[7] DOI: 10.1023/A:1006656730543
[8] DOI: 10.1016/j.euromechflu.2005.04.008 · Zbl 1101.76023
[9] DOI: 10.1134/1.1574380
[10] Phillips, Flow and Reactions in Permeable Rocks (1991)
[11] DOI: 10.1023/B:FLUI.0000015231.85569.2a · Zbl 1154.76382
[12] Lide, CRC Handbook of Chemistry and Physics (2001)
[13] Straughan, The Energy Method, Stability, and Nonlinear Convection (1992) · Zbl 0743.76006
[14] DOI: 10.1029/WR024i010p01781
[15] DOI: 10.1029/2002GB001935
[16] Helmig, Multiphase Flow and Transport Processes in the Subsurface (1997)
[17] DOI: 10.1029/WR024i003p00321
[18] DOI: 10.1016/0309-1708(95)00012-8
[19] DOI: 10.1016/j.jhydrol.2005.07.035
[20] DOI: 10.1016/S0304-4238(98)00193-9
[21] DOI: 10.1029/96WR03684
[22] DOI: 10.1063/1.1461829
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