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Transient forcing effects on mixing of two fluids for a stable stratification
Author(s) -
Pool María,
Dentz Marco,
Post Vincent E. A.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr019181
Subject(s) - mechanics , stratification (seeds) , mixing (physics) , stratified flow , stratified flows , advection , flow (mathematics) , transient (computer programming) , thermal diffusivity , dispersion (optics) , magnitude (astronomy) , geology , turbulence , physics , thermodynamics , seed dormancy , botany , germination , optics , quantum mechanics , astronomy , dormancy , computer science , biology , operating system
Abstract 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 ast 1 / 2.