[1] Previous studies have examined free convection and the development of fingers in variable-density groundwater environments, but the penetration rates of fingering processes (i.e., fingering speeds) have not been systematically investigated. Unlike common groundwater processes driven by advection and whose flow rates may be computed using Darcy's law, fingering speeds are far less intuitive. In this study, fingering speeds are analyzed in a natural convection system using two measurable diagnostics: deepest plume front (DPF, providing upper bounds on plume speeds) and vertical center of solute mass (COM, providing global speeds). The permeability, porosity, and dispersion (longitudinal and transverse dispersivities) were varied using a perturbation-based stochastic approach to investigate their effects on fingering speeds. Modeling results show that the characteristic convective velocity, commonly used to represent theoretical fingering speeds, needs to incorporate effective porosity in a similar fashion to hydraulically driven average linear velocity and needs to be further adjusted by multiplying by a corrective factor f for predicting various fingering behaviors (approximately f ¼ 0.115 for DPF and f ¼ 0.034 for COM) in this study. A stochastic analysis demonstrates small variability in the time-varying speed of both DPF and COM between model realizations. This indicates that reproducing fingering speeds is likely to be achieved and that one single realization can adequately produce f for the characteristic convective velocity. This study also identifies that f for speeds of DPF is most likely to be constrained by (0.115, 1.000), which is extremely useful in the design of laboratory and field experimentation.
[1] Previous studies of free convection in porous media almost exclusively consider time-invariant solute boundary conditions and neglect the transient fluctuations that are inherent in natural systems. We study the effect of transient solute loading on the migration of dense salt plumes in an unstable setting using numerical simulations of a modified form of the classic solute analogue Elder problem. The numerical results show that for the periodic solute loading case, (1) a free convection slipstream (i.e., the downward movement of groundwater associated with a convection cell behind a descending salt blob) is observed such that newly developed successor fingers may be drawn toward the tails of convection cells associated with predecessor fingers; (2) the free convection slipstream intersects the top boundary layer, creating a boundary layer convective memory during solute loading-off periods in cases with periodicity less than some critical transitional convective periodicity (approximately 5 to 10 years for the current setting); and (3) the boundary layer convective memory causes newly developed successor fingers to form in the same locations and to migrate along the same pathways as their predecessor fingers (mutual dependence between successor and predecessor finger sets) and subsequently reinforce old fingers and enhance solute transport. Results from both quantitative diagnostics (e.g., Sherwood number, total mass of solute, vertical center of mass) and qualitative inspection clearly demonstrate that the periodicity of the solute-loading function controls the fingering process and the total solute transport behavior. Transient solute loading is more important in unstable free convection processes than has previously been recognized.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.