Simulating Drainage from a Flooded Sinkhole

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.