There has been an interest in quantitative modeling of early karstification with the objectives of estimating time-scales of conduit growth and understanding the nature of cave patterns. The influence of aperture variability on the growth of fissures by dissolution is investigated based on two-dimensional numerical simulations. The initial phase of karst development is studied from its nascent stage as a fissure into the early stages of turbulence.

In uniform fissures in rapidly dissolving minerals, the concentration reaches the solubility limit within a short distance along the flow path. However, the variability in the aperture field inherently provides instabilities to the system and growth is propagated along these perturbations. Flow is focused into preferential channels which are enlarged at a faster rate than surrounding regions of slow flow. As a result, a positive feedback mechanism takes place and creates growth in a highly selective manner. Only in large domains (> 25 correlation lengths), can the instabilities create competition for flow at the solution front as well and lead to significant branching. It is this branching which creates the non-monotonic behavior in breakthrough times (define as the point in which turbulent flow is first encountered). It has been observed that the non-monotonic behavior is scale dependent. Smaller domains do not exhibit this behavior because there are only a few correlation lengths between the fingertip and the lateral domain boundaries.

During the laminar stages, a dominant finger prevails and growth is highly selective, but when carried into turbulence, this is no longer true. Sub-dominate fingers regain strength and are eventually joined together with the dominant channel. Low-order surface reaction rates initiate the lateral growth and once coalescence takes place, the rapidly dissolving fingers are replaced by turbulent diffusion rates. The entire domain is smoothed out and becomes more uniform. Furthermore, unlike the development in the laminar phase, during turbulence, the heterogeneity does not appear to influence growth and in fact seems to even out the initial disparities.