# Shapes of ideal stalagmites

## TL;DR

This paper presents a theoretical model that explains the different shapes of stalagmites and how they can be used to study past climates.

## Contribution

The paper introduces an analytic theory that describes stalagmite shapes using a single parameter and connects them to paleoclimatic data.

## Key findings

- A closed-form expression for stalagmite shapes was derived, showing three distinct forms observed in nature.
- Transitions between shapes depend on a dimensionless parameter and specific cave conditions.
- Stalagmite shape affects 13C isotope shifts, which are crucial for paleoclimatic analysis.

## Abstract

Stalagmites come in a variety of shapes, with sizes ranging from centimeters to meters. Despite their intriguing regularity and their importance for paleoclimate studies, a theoretical description of their form has been lacking. We have developed an analytic theory that provides an explicit formula for the shapes of steadily growing stalagmites, and characterizes the variety of observed shapes in terms of a single parameter. Our results provide a unified perspective on different numerical approaches to stalagmite growth, and make connections to theories of stalactite growth as well. The results can also be used to help infer paleoclimatic information derived from isotope measurements.

Stalagmites are isolated columns of calcium carbonate growing on a cave floor; their growth is driven by the constant dripping of supersaturated solutions from the roof of the cave. In this paper, we derive a closed-form expression for the shape of a steadily growing stalagmite. Our analysis gives rise to three distinct shapes, all of them observable in nature, with the shape characterized by a single dimensionless parameter. Transitions between different shapes occur at a specific value of this parameter, with additional selection rules determining the shape and size of stalagmites evolving under specific cave conditions. Our theory shows that the stalagmite shape influences the 13C isotope shifts, which are an important source of paleoclimatic information.