The stably-stratified filling of an open enclosure produces an interfacial gradient layer which is transported through the enclosure with the bulk flow. The evolution of this interfacial layer is strongly time-dependent and is driven by the nature of the interaction between the internal gravity waves and the inlet-driven interfacial shear. Measurements of density profile evolution have been completed for a rectangular enclosure with a single corner inlet and density variation produced by saline concentration. This system serves as a mass transfer analog to large-scale, thermally-stratified energy storage devices, preserving dynamic similitude in a laboratory-scale system. The experiments covered jet Reynolds numbers of 200-2200 and Froude numbers of 0.06-0.6 in an enclosure with a width 23 times the jet inlet height. The density profiles are seen to be strongly asymmetric and exhibit growth rates significantly different than due to simple one-dimensional molecular diffusion. In addition, shadowgraph and hydrogen bubble visualizations of the density and velocity fields in the gradient layer show the persistence of complex multi-dimensional flow structure even at relatively late stages of the filling process when the gradient layer has been transported well away from the enclosure inlet. The evolution of the vertical density profile has been compared quantitatively to a quasi one-dimensional model based upon empirical diffusivity coefficients.