Regular Stalagmites: The Theory Behind Their Shape

Author

Wolfgang Dreybrodt
Douchko Romanov

Files

Publication Date

6-2008

Publication Title

Acta Carsologica

Volume Number

37

Issue Number

2-3

Abstract

Under growth conditions constant in time stalagmites grow into an equilibrium shape, which is established, when all points of its surface are shifting by the same vertical distance during a time interval . Thereby is the precipitation rate in , is the calcium concentration of the supersaturated solution dripping to the apex of the stalagmite, and its equilibrium concentration with respect to calcite and the in the cave atmosphere. From these ingredients a numerical model of stalagmite growth into an equilibrium shape is presented. In this model one assumes idealistically that the water dripping to the apex flows continuously down the stalagmite, spreading out radially. By simple mass balance one finds that the equilibrium radius is , where is the volume of a drop and the drip interval. Furthermore numerical modeling repro- duces the vertical shifting of the stalagmite’s equilibrium shape. Finally an interesting similarity rule is found. If one scales two stalagmites of differing to the same size and chooses their growth axes as common axis and their apexes as common origin, both show identical shapes. In other words regular stalagmites are similar geometrically. This similarity rule is verified by digitizing the shapes of various natural stalagmites with diameters between 5 cm and 20 m. Within small natural variations, the rescaled shapes are identical and close to the shape of the numerical model.

Keywords

Stalagmites, Morphology, Growth rates, Scaling law

Document Type

Article

Language

English and Slovenian

Identifier

K26-00160

Recommended Citation

Dreybrodt, Wolfgang and Romanov, Douchko, "Regular Stalagmites: The Theory Behind Their Shape" (2008). KIP Articles. 50.
https://digitalcommons.usf.edu/kip_articles/50