Effect of transient solute loading on free convection in porous media

Abstract

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.