Steady states and linear stability analysis of precipitation pattern formation at geothermal hot springs

TL;DR

This paper develops a dynamical theory for geophysical precipitation patterns at hot springs, predicting steady shapes and stability, and explaining observed formations like travertine domes and terraces.

Contribution

It introduces a coupled model of flow and precipitation dynamics that predicts steady states and analyzes their stability, linking theory to observed geothermal formations.

Findings

Predicted shapes match observed travertine domes near vents.

Identified a linear instability responsible for terrace formation.

Linked capillary forces to pattern deviations from symmetry.

Abstract

A dynamical theory of geophysical precipitation pattern formation is presented and applied to irreversible calcium carbonate (travertine) deposition. Specific systems studied here are the terraces and domes observed at geothermal hot springs, such as those at Yellowstone National Park, and speleothems, particularly stalactites and stalagmites. The theory couples the precipitation front dynamics with shallow water flow, including corrections for turbulent drag and curvature effects. In the absence of capillarity and with a laminar flow profile, the theory predicts a one-parameter family of steady state solutions to the moving boundary problem describing the precipitation front. These shapes match well the measured shapes near the vent at the top of observed travertine domes. Closer to the base of the dome, the solutions deviate from observations, and circular symmetry is broken by a fluting pattern, which we show is associated with capillary forces causing thin film break-up. We relate our model to that recently proposed for stalactite growth, and calculate the linear stability spectrum of both travertine domes and stalactites. Lastly, we apply the theory to the problem of precipitation pattern formation arising from turbulent flow down an inclined plane, and identify a linear instability that underlies scale-invariant travertine terrace formation at geothermal hot springs.