  We study gravitationally unstable, transient, diffusive boundary layers in
porous media using modal and nonmodal stability methods. Using nonmodal
stability theory, we demonstrate that both the onset of linear instabilities
and the shape of optimal perturbations are highly sensitive to perturbation
amplification measures and also the time at which the boundary layer is
perturbed. This behavior is in contrast to traditional studies of steady or
non-transient diffusive boundary layers where perturbation dynamics are
independent of perturbation measure or time. We demonstrate that any analysis
of transient layers produced through classical methods can result in physically
unrealizable perturbation structures. To resolve the issue, we propose a
nonmodal stability procedure which additionally constrains the perturbation
dynamics to physically admissible fields. The proposed procedure predicts that
instabilities grow primarily due to unstable perturbations featuring much
larger spanwise wavenumbers (modes) and smaller amplifications compared to
perturbations predicted using classical methods. We validate our predictions
using direct numerical simulations that emulate the onset of convection in
physical systems.
