Mixing and stretching efficiency in steady and unsteady groundwater flows

Abstract

Mixing is the physical process through which solute is spread into a fluid by the stretching and folding of material lines and surfaces. Mixing, as compared to dilution, is important to solute spreading by groundwater because it operates on much shorter timescales than does dilution, and it provides the increased plume boundary area and high local concentration gradients that promote effective solute dilution. In this paper, the mixing process is investigated theoretically for subsurface tracer plume movement, using as heuristic examples both steady and unsteady groundwater flows in a perfectly stratified aquifer whose properties mimic those of the sand aquifer at the Borden site. It is shown that the stretching efficiency, a parameter that characterizes the effectiveness of mixing, is largest at transitions between regions of highly contrasting hydraulic conductivity and, more broadly, that pronounced spatial variability in the hydraulic conductivity is conducive to good mixing because of the periodic resurgences in material line stretching that it causes. Unsteady groundwater flow resulting from a decrease in vertical groundwater flux with time leads to greater rates of material line stretching than do steady flows, whereas little difference from the steady flow case occurs for unsteady groundwater flow under a time‐varying horizontal hydraulic head gradient. Overall, pronounced spatial variability in the hydraulic conductivity is the most important contributor to good mixing of a tracer solute plume, but highly effective mixing requires additional physical conditions that induce chaotic solute pathlines.