Forms of hydrothermal and hydraulic flow in a homogeneous unconfined aquifer

Abstract

SUMMARY Groundwater flow in an unconfined aquifer (a porous layer with an open top) can be driven either by hydraulic forces, i.e. the gradient of the water table, or by differences in the density of porewater due to thermal expansion and changes in salinity. In this study we assume that the salinity is constant, and we investigate the spatial forms of the hydraulic and hydrothermal flows, with emphasis on the case where both components are present. Since basic flow patterns are under consideration, the simple case of a homogeneous (but anisotropic) layer is studied by numerical solution of the governing equations. When the surface hydraulic gradient is zero, free thermal convection can occur in strictly cellular forms. Just above the critical Rayleigh number the first form of convection is 2-D rolls; later square cells become stable. These flows exhibit asymmetrical patterns due to the different conditions prevailing at the top and bottom boundaries. In natural circumstances no strict cellularity can be expected: instead of regular squares, irregular polygonal cells develop and remain time-dependent. When the hydraulic governing force is added to the thermal forces, i.e. the gradient of the water table is no longer zero, first we have polygonal cells. When the hydraulic gradient increases gradually, the polygons are replaced by longitudinal rolls (i.e. rolls parallel to the gradient direction). This occurs in a regime where the hydrothermal and hydraulic governing forces are equally important. Later, when the hydraulic gradient is even higher, the flow pattern changes abruptly to transverse rolls. At low anisotropies, these transverse rolls drift with the main hydraulic flow in the direction of the slope of the water table. Finally, at strong hydraulic gradients, the cells of convection are completely suppressed by the fast hydraulic flow, which is now organized in a ‘unicell’ form. Domain boundaries are established for all these circulation patterns as functions of the Rayleigh number, surface hydraulic gradient and anisotropy. Characteristics of the heat transfer are also analysed.