7.1 Field Scale Detection of Free Convection
Free convection has been observed in laboratories and predicted by models for over a century. There are hundreds of papers on the theory, modeling and laboratory experiments of finger instabilities associated with free convection. Thus, finger instabilities are surmised to exist in field-based settings, but there is a lack of conclusive field-based evidence and data. A range of secondary inferences for the existence of free convection has been made in various studies. These include, but are not limited to:
- “Numerical experiments demonstrate the existence of a convection cell….” (Duffy and Al‐Hassan, 1988);
- “The observation that tritium exists throughout the profile is consistent with vertical circulation resulting from the density instability” (Wood et al., 2002);
- “The salt deficit may be accounted for by the slow downward convection of dense saline water beneath salt lake beds…” (Teller et al., 1982);
- “Abundant data indicate high fluid and solute fluxes in shaly sediments and account for the observed level of sediment diagenesis” (Sharp et al., 1988);
- “Assuming a critical Rayleigh number of 4π2 … both regions are predicted a priori to be unstable, and solute moves more rapidly by way of convective fingering” (Simmons et al., 2002); and,
- “Contamination from a waste dump at Noordwijk, Netherlands, resulted in a plume with downward velocity 45 times higher than the vertical velocity due to natural recharge” (Kooper, 1983).
None of these observations constitute primary evidence for the existence, or otherwise, of free convection. Numerical experiments do not demonstrate the existence of free convection in a field-based setting. Given the limitations in using the Rayleigh number in field settings as discussed in Section 5.2, compliance with Rayleigh stability criteria is also not a sufficient test. Rayleigh number calculations are supportive and suggestive of the existence of instabilities leading to convective cells in field settings, but they are not conclusive.
Some studies provide more direct indications for free convective phenomena in groundwater, for example, based on groundwater salinity measurements taken after the flooding of freshwater aquifers by seawater. During the preparation for a deliberate seawater intrusion experiment in Denmark, the field site of Andersen and others (2008) was flooded by brackish water from a fjord during a storm surge on 29 and 30 January 2000. The site was equipped with a network of approximately 100 observation wells that were installed along a 120 m transect across a beach. The brackish water flooded the beach up to 90 m from the coast and pooled for some days in the depressions. Before the storm surge, the electrical conductivity measurements indicated the presence of a saltwater wedge near the shoreline (Figure 29a). Twenty-eight days after the storm, high groundwater salinities were measured between 70 to 90 m from the coastline (Figure 29b). The shape of the high-salinity zone resembles that of a finger.
To support the interpretation of their data, Andersen and others (2008) conducted a numerical modeling study. They found that they had to consider the heterogeneity of the hydraulic conductivity field to obtain salt lobes with similar dimensions as in Figure 29b. While the homogeneous model predicted downward density-driven flow, its results did not match the field data. Andersen and others (2008) had hydraulic conductivity data from the slug tests at each of their piezometers so they could incorporate a heterogeneous hydraulic conductivity field in their model. While the heterogeneous model reproduced the observed salinity distribution in an overall sense, even with this information the modeled salinity profiles did not capture the small-scale variability of the observed salinity distribution. This finding is consistent with the discussion from the previous section, that is, while macroscopic features are amenable to prediction, microscopic features are not.
Somewhat similarly, Post and Houben (2017) investigated the salinization of a fresh groundwater lens on the northern German island of Baltrum following a storm flood that occurred in February 1962. They based their analysis on unpublished data that were collected by Otto Rülke, who had been doing geoelectrical measurements on the island before the flood (Rülke, 1969) and went over as soon as he could to install shallow observation wells. Chloride concentrations were measured in these wells at irregular intervals up to 8 years after the flood. The time series have an erratic shape with concentrations going up and down in the months after the flood. Based on numerical modeling, Post and Houben (2017) concluded that this must have been due to convective fingering. As the seawater inundated the lens, salt fingers moved down and as they grew vertically, they also migrated laterally (Figure 30). At a single point, this results in salt concentrations increasing or decreasing depending on the transient flow dynamics and finger geometry. Because of the difficulty in comparing model results to measured concentration versus time curves, they made comparisons between model-predicted concentration ranges for the depths of measurements. By comparison with density-invariant models, they could demonstrate that the free-convective model of salinization formed a much better explanation of the data than the density-invariant model.
While the studies by Andersen and others (2008) and Post and Houben (2017) provide strong indications for convective fingering, their data still do not provide direct evidence of the presence of salt fingers. Geophysical tomography techniques can provide snapshot images of the electrical resistivity of the subsurface and provide a way to visualize fingers in the field. These techniques have had success. Examples include the studies in the Okavango Delta in Botswana (Bauer Gottwein et al., 2007) and Padre Island, Texas (Stevens et al., 2009).
Around the same time, van Dam and others (2009) documented the existence of free convective fingering in the Sabkha Aquifer in the United Arab Emirates (Figure 31). This site was chosen because it is extensively characterized, homogeneous, density inversions exist and an unusual tritium distribution (Wood et al., 2002) was previously documented (van Dam et al., 2009). Large precipitation events helped to dissolve the halite crust at the surface and formed hypersaline brines seven weeks before data collection.
The electrical tomography results (Figure 32) show low resistivity ‘saline fingers’ (red) that protrude in higher resistivity background (green). The vadose zone and water table (~0.7 m below ground) show up as the layer with the highest resistivity (blue). Importantly, the near-perfectly homogeneous sedimentary sandy system means that geologic variation cannot be used to explain these lobe-shaped structures. Further work by van Dam and others (2014) has shown excellent agreement between field-based geophysical results and modeling. These results provide compelling field-based evidence for the existence of free convection in a groundwater field setting. Fascinatingly, the saline fingers have moved downwards about 15 meters in about seven weeks, a speed of approximately 0.3 m d−1 on average. Both diffusive migration and downward flow due to recharge are much slower processes than free convection and cannot explain this significant solute transport rate nor its finger shape.