Could Mammoth Cave be reduced to a single equation?

Since the evolution of any cave system is largely deterministic, in theory the processes responsible for this development could be described mathematically. In a practical sense, we will never have such a model to realistically describe the evolution of the Mammoth Cave System in detail. However, the search itself can provide a framework within which to understand what processes are important. This can guide the design of rate process studies that would eventually be coupled to provide a comprehensive understanding of the cave's evolution. Data gaps, as well, are identified during this process. The geometry of a cave system depends on the individual growth rates of sequential sets of passage cross-sections. The growth of each of these cross-sections is determined by a set of coupled processes, the rates of which are related to well-defined variables. Major processes include limestone dissolution and precipitation (dependent on water and rock chemistry, flow characteristics, wetted passage perimeter, and temperature), sediment entrainment, deposition, and abrasion (dependent on flow velocity distributions and properties of the sediment supply), and breakdown processes (dependent on fracture characteristics). Our ability to model the complete picture depends on our grasp of these individual behaviors, as well as their interactions. A long-term study of the behaviors of two single active passage cross-sections is underway in the Right and Left forks of Hawkins River of Mammoth Cave, where continuous water quality data are being obtained through two 145 m deep wells. Experiments are currently underway to determine storm- and seasonal-scale changes in limestone dissolution rates. Planned studies will explore sediment dynamics and the impact of sediment masking on dissolution rates, as well as potential impacts of sediment abrasion on passage growth. Complete understanding of a single cave slice is an important step to understanding cave evolution in general.