Growth rates and morphology of stalagmites are determined by the precipitation kinetics of calcite and the supply rates of water to their apex. Current modeling attempts are based on the assumption that precipitation rates decrease exponentially with distance along the surface. This, however, is an arbitrary assumption, because other functions for decrease could be used as well. Here we give a process-oriented model based on the hydrodynamics of a water sheet in laminar radial flow spreading outwards from the apex, and the well known precipitation rates F = α(c − ceq); c is the actual calcium concentration at distance R from the growth axis, ceq the equilibrium concentration of calcium with respect to calcite, and α is a kinetic constant. This enables us to calculate the concentration profile c(R) for any point of an actual surface of a stalagmite and consequently the deposition rates of calcite there. The numerical results show that under conditions constant in time the stalagmite grows into an equilibrium shape, which is established, when all points of its surface are shifting vertically by the same distance during a time interval. We also show this by strict mathematical proof. This new model is based entirely on first principles of physics and chemistry. The results show that the modeled precipitation rates can be approximated by a Gaussian decrease along the equilibrium surface. In general from the mathematical proof one finds a relation between the equilibrium radius of the stalagmite, Q the supply rate of water, and α the kinetic constant. This is also verified by numerical calculations. An interesting scaling law is found. Scaling all stalagmites by 1/Req and presenting them with the origin at their apex yields identical shapes of all. The shapes of the modeled stalagmites are compared to natural ones and show satisfactory agreement. Finally we explore the effect of varying water supply Q and kinetic constant α on the shape of a growing stalagmite, and estimate the minimum period of change that can be imprinted into the morphology of the stalagmite.

Pumping tests conducted on wells intersecting karst heterogeneities such as the conduit network are difficult to interpret. Nevertheless, this case can be solved by assimilating the horizontal karst conduit to a finite conductivity vertical fracture. In this case, several flow patterns corresponding to the respective contributions of karst subsystems (fractured matrix, small conduits, and main karst drainage network) can be identified on the diagnostic plot of the drawdown derivative. This is illustrated on two examples from Mediterranean karst systems in southern France. A pumping test on a well intersecting the main karst drainage network of the Cent-Fonts karst system shows (i) a preliminary contribution of the karst conduit storage capacity followed by (ii) linear flows into the fractured matrix. A pumping test on a well intersecting a small karst conduit of the Corbières karst system shows the existence of (i) bi-linear flow within both the karst conduit and the fractured matrix at early times, followed by (ii) radial flows within the fractured matrix and (iii) finally the contribution of a major karst cavity. The use of diagnostic plots allows identifying the various flow regimes during pumping tests, corresponding to the response of the individual karst aquifer subsystems. This is helpful for improving the understanding of the structure of the karst aquifer and flow exchanges between subsystems.