Abstract
Understanding sinkhole-drainage capacity and functioning is critical to realizing the effects that may be created when directing stormwater drainage into sinkholes. In this paper, the basics of sinkhole drainage are reviewed in terms of point vortex flow created by drainage down a sinkhole swallet. Then, several different, relatively simple sinkhole shapes are presented and mathematical models developed to simulate drainage from inflowing water. The models emphasize the significance of drainage rate as a function of sinkhole shape and sinkhole wetted cross-sectional area relative to changes in water level and time. Model simulations provide insights into the sensitivity of sinkholes to inflow rates and water-level changes withtime. Major findings include insights into the rapidity by whichinflows may increase the water level in a sinkhole and the significance of sinkhole shape and cross-sectional area as it relates to sinkhole drainage rate. The numerical solution is completely general so it allows for varying inflow rates in any manner desired. Application of the model to real sinkholes should assist in the management of sinkhole-flooding problems.
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