On a test case for density-dependent groundwater flow and solute transport models: The salt lake problem

Abstract

Like any other computer model, density-dependent mathematical groundwater models must be 'verified' to ascertain that they accurately represent the physics implied by a governing set of equations. Very few test cases for density-dependent groundwater numerical models exist. As such, there is still a need for new and more robust tests of these modeling codes. In this paper a numerical model of an idealized evaporating salt lake is produced using the two-dimensional density-dependent saturated-unsaturated transport (SUTRA) model, the results of which are compared with an equivalent laboratory Hele-Shaw cell system developed by Wooding et al. [1997a, b]. Evaporation results in dense brine overlying less dense fluid, which is hydrodynamically unstable and leads to downward convection of salt fingers or plumes. A comparison of experimental and numerical plume growth shows good spatial and temporal agreement. The numerically generated plume pattern is sensitive to changes in random noise level applied just below the evaporation surface that serves as a trigger for the growth of instabilities. Experimental plume patterns were best matched with a noise level corresponding to 1% of the total salinity difference between boundary layer and background fluid concentrations at saturation. In a second comparison the stream-function-based finite difference model described by Wooding et al., [1997a, b] which differs significantly in principle from SUTRA is shown, after revision, to give good spatial and temporal agreement with experimental results. This test for density-dependent groundwater models appears to be the most comprehensive and detailed available to date.