We consider gravitational instability of a saline boundary layer formed by evaporation induced upward throughflow at a horizontal surface of a porous medium. Two paths are followed to analyse stability: the energy method and the method of linearised stability. The energy method requires constraints on saturation and velocity perturbations. The usual constraint is based on the integrated Darcy equation. We give a fairly complete analytical treatment of this case and show that the corresponding stability bound equals the square of the first root of the Bessel function J0. This explains previous numerical investigations by Homsy & Sherwood [1975, 1976]. We also present an alternative energy method using the pointwise Darcy equation as constraint, and we consider the time dependent case of a growing boundary layer. This alternative energy method yields a substantially higher stability bound which is in excellent agreement with the experimental work of Wooding et al. [1997a, b]. The method of linearised stability is discussed for completeness because it exhibits a different stability bound. The theoretical bounds are verified by two-dimensional numerical computations. We also discuss some cases of growing instabilities. The presented results have applications to the theory of stability of salt lakes and the salinization of groundwater.
|Title of host publication||Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere -- The Philip Volume|
|Editors||P.A.C. Raats, D. Smiles, A.W. Warrick|
|Place of Publication||Washington DC|
|Publisher||American Geophysical Union (AGU)|
|Number of pages||345|
|Publication status||Published - 2002|
|Name||Geophysical Monograph Series|
Duijn, van, C. J., Pieters, G. J. M., Wooding, R. A., & Ploeg, van der, A. (2002). Stability criteria for the vertical boundary layer formed by throughflow near the surface of a porous medium. In P. A. C. Raats, D. Smiles, & A. W. Warrick (Eds.), Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere -- The Philip Volume (pp. 155-169). (Geophysical Monograph Series; Vol. 129). American Geophysical Union (AGU).