  This work considers the gravitational instability of a saline boundary layer
formed by an evaporation-induced flow through a fully-saturated porous slab.
Evaporation of saline waters can eventually result in the formation of salt
lakes as salt accumulates. As natural convection can impede the accumulation of
salt, establishing a relation between its occurrence and the value of physical
parameters such as evaporation rate, height of the slab or porosity is crucial.
One step towards determining when gravitational instabilities can arise is to
compute the ground-state salinity, that evolves due to the uniform upwards flow
caused by evaporation. The resulting salt concentration profile exhibits a
sharply increasing salt concentration near the surface, which can lead to a
gravitationally unstable setting. In this work, this ground state is
analytically derived within the framework of Sturm-Liouville theory. Then, the
method of linear stability in conjunction with the quasi-steady state approach
is employed to investigate the occurrence of instabilities. These instabilities
can develop and grow over time depending on the Rayleigh number and the
dimensionless height of the porous medium. To calculate the critical Rayleigh
number, which can determine the stability of a particular system, the
eigenvalues of the linear perturbation equations have to be computed. Here, a
novel fundamental matrix method is proposed to solve this eigenvalue problem
and shown to coincide with an established Chebyshev-Galerkin method in their
shared range of applicability. Finally, a 2-dimensional direct numerical
simulation of the full equation system via the finite volume method is employed
to validate the time of onset of convective instabilities predicted by the
linear theory. Moreover, the fully nonlinear convection patterns are analyzed.
