# 7.3 Future Research Directions

Understanding, conceptualizing, measuring, predicting, and modeling variable-density processes in groundwater remains a challenge and an opportunity. This book shows that there are important differences in the implicit and explicit assumptions and approaches made between the earliest free convection studies in classical fluid mechanics and those in hydrogeology. Geologic heterogeneity especially presents a challenge, as it controls the onset, growth and/or decay of plumes. This means that there are problems with application of Rayleigh numbers to evaluate the potential for unstable flow conditions because the Rayleigh number is based on mean quantities, and it is difficult to quantify relevant average properties in heterogeneous media. Furthermore, the Rayleigh number is based on a steady-state analysis to determine the onset of convection. It is difficult to identify relevant length scales and the appropriate critical Rayleigh numbers are unknown in most practical settings. It is unlikely that critical Rayleigh numbers based on highly idealized conditions such as the famous value of 4*π*^{2} are likely to be appropriate.

Rayleigh numbers computed in many groundwater settings with a potentially unstable density stratification are well above the range of critical Rayleigh numbers identified by Nield (1968). This suggests that highly transient oscillatory regimes, which are the most difficult to characterize, are commonplace in nature. Heterogeneity can suppress convection in potentially unstable systems but its role in field settings is still unclear. All these results suggest that, despite the scientific progress that has been made to date, there are challenges to conceptual understanding and prediction of convective flow and transport processes. Some other topics that are likely to be important in the future include:

- better understanding quantification and controls of dispersion;
- better links with geological constraints (e.g., sedimentary facies data/structural geology);
- thermohaline (double-diffusive) and multi-species transport problems; and,
- complex geochemical reactions, fluid-matrix interactions and multiphase flow in carbon sequestration processes.

As a final word, we note that there are hundreds of modeling and theory papers and far fewer field-based papers that attempt to measure free convection directly. The “measurement to theory” ratio needs to be increased. Rigorous field-based studies and detailed measurements, coupled with state-of-the-art modeling approaches, will help to further enhance both conceptual understanding and predictive capabilities. More studies should focus on direct, explicit evidence, such as field observations of fingering patterns, or upwelling and downwelling circulation associated with free convection cells. Secondary inference for the existence of convection is a good indirect starting point but there is a continuing need to develop field techniques to gather better data that can constrain and validate numerical models. Important discoveries still need to be made, so the prognosis for better understanding variable-density flow is good.