Transient forcing effects on mixing in stable variable-density systems

Abstract:

Mixing and dispersion in coastal aquifers are controlled by concentration gradients, which are influenced by temporal fluctuations on multiple time-scales caused by waves and tides, as well as seasonal pumping, recharge and droughts. We study effective mixing and solute transport in temporally fluctuating one-dimensional flow for a stable stratification of two fluids of different density. Previous studies have demonstrated that temporal flow fluctuations parallel to the main flow directions have an impact on mixing and solute dispersion (see, e.g., Kinzelbach and Ackerer, 1986; Goode and Konikow, 1990). Most of these findings were obtained under the pseudo steady state assumption, that is, a storativity of zero, which implies an instantaneous flow response to hydraulic perturbations and spatially-uniform flow. However, a finite storativity induces a spatially non-uniform flow distribution in response to temporal head fluctuations, which in turn perturbs concentration gradients, leading to enhanced spreading and mixing of solutes. In this study, we derive explicit expressions for the concentration distribution and variance to identify the controls of the coupling between mixing and oscillatory density-dependent flow. We find a sizeable increase of the effective dispersion coefficients as a function of the hydraulic diffusivity and the initial interface location. We identify an effective boundary condition which is given by the attenuation distance of the head signal. This boundary explains the sublinear growth of the width of the mixing zone determined at intermediate times. At long times the concentration profile assumes a non-symmetric shape that is controlled by the spatial dependence of the effective dispersion coefficient. Sand column experiments under well-controlled laboratory conditions are presented to validate the theoretical effective model defined.

References

-Goode, D. J., and L. Konikow (1990). Apparent dispersion in transient groundwater flow, Water Resour. Res., 26(10), 2339–2351.

-Kinzelbach, W., and P. Ackerer (1986), Mode’lisation de la propagation d’un contaminant dans un champ d’e’coulement transitoire, Hydrogeologie, 2, 197–206.