Mixing and dispersion in coastal aquifers are strongly influenced by periodic temporal flow fluctuations on multiple time scales ranging from days (tides), seasons (pumping and recharge) to glacial cycles (regression and transgressions). Transient forcing effects lead to a complex space and time-dependent flow response which induces enhanced spreading and mixing of dissolved substances. We study effective mixing and solute transport in temporally fluctuating one-dimensional flow for a stable stratification of two fluids of different density using detailed numerical simulation as well as accurate column experiments. We quantify the observed transport behaviors and interface evolution by a time-averaged model that is obtained from a two-scale expansion of the full transport problem, and derive explicit expressions for the center of mass and width of the mixing zone between the two fluids. We find that the magnitude of transient-driven mixing is mainly controlled by the hydraulic diffusivity, the period, and the initial interface location. At an initial time regime, mixing can be characterized by an effective dispersion coefficient and both the interface position and width evolve linearly in time. At larger times, the spatial variability of the flow velocity leads to a deceleration of the interface and a compression of its width, which is manifested by a subdiffusive evolution of its width as t1/2.
- periodic fluctuations
- transient forcing