Linear stability analysis of a novel experimental simulation of convection driven by an unstable density gradient in soil

Abstract

When the upper part of a soil solution has a larger density than the lower part, an unstable layer devel-ops, and convection may occur. However, our theoretical understanding of this convective flow pattern is limited, given the complexity of its governing equations. In this study, we conducted a simple experiment to generate con-vection, and used linear stability theory to explain its flow pattern. Glass beads with 0.2-mm diameter were placed in a 6×14×1 cm rectangular container. The lower half of this container was saturated with water, while the upper half was saturated with a concentrated and regulated NaCl so-lution. The resulting solution density interface undulated, and finger convection emerged. We found that the average speed of the fingers could be expressed using the equa-tion: hydraulic conductivity×solution density difference / solution density of the lower part. This is consistent with predictions from linear stability theory. We also found that the number of fingers had a non-linear relationship with the solution density difference. The number of fingers corre-sponded to the wave number for the larger steady solution, when the length of the density gradient area was twice the distance from the density interface to the front of the fin-ger.