Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

On the seasonal variations of salinity of the tropical Atlantic mixed layer

The physical processes controlling the mixed layer salinity (MLS) seasonal budget in the tropical Atlantic Ocean are investigated using a regional configuration of an ocean general circulation model. The analysis reveals that the MLS cycle is generally weak in comparison of individual physical processes entering in the budget because of strong compensation. In evaporative regions, around the surface salinity maxima, the ocean acts to freshen the mixed layer against the action of evaporation. Poleward of the southern SSS maxima, the freshening is ensured by geostrophic advection, the vertical salinity diffusion and, during winter, a dominant contribution of the convective entrainment. On the equatorward flanks of the SSS maxima, Ekman transport mainly contributes to supply freshwater from ITCZ regions while vertical salinity diffusion adds on the effect of evaporation. All these terms are phase locked through the effect of the wind. Under the seasonal march of the ITCZ and in coastal areas affected by river (7°S:15°N), the upper ocean freshening by precipitations and/or runoff is attenuated by vertical salinity diffusion. In the eastern equatorial regions, seasonal cycle of wind forced surface currents advect freshwaters, which are mixed with subsurface saline water because of the strong vertical turbulent diffusion. In all these regions, the vertical diffusion presents an important contribution to the MLS budget by providing, in general, an upwelling flux of salinity. It is generally due to vertical salinity gradient and mixing due to winds. Furthermore, in the equator where the vertical shear, associated to surface horizontal currents, is developed, the diffusion depends also on the sheared flow stability.