Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution.

Figure 1

Travertine formation at Angel Terrace, Mammoth Hot Springs, WY, USA. (a) A large pond, of order 1 m in diameter, and smaller features. (b) A portion of the flow system about 25 meters from the vent, on the scale of centimeters.

Figure 2

Travertine dome at Mammoth Hot Springs, WY, USA. (a) Dome whose central pond is 50.3 cm in diameter. (b) Dome height as a function of $\theta$. Horizontal axis: Analytical prediction from Eq. (4). Vertical axis: Simulated dome (CA) with no surface tension (squares), with surface tension (circles), and the profile of the dome in (a) (triangles, data digitized from photograph). The points all fall on a straight line with a unit slope above the fluting point, indicating agreement with Eq. (4) fitting only $r_0$. Below that, one extra parameter is required, as explained in the text. Inset: Comparison with dome from (a).

Figure 3

Results from simulation of the CA model. (a) Portion of a typical simulated landscape. The figure clearly shows distinct geomorphological regimes or facies, as observed in the field [6]. (b) Critical angle for the contact line formation on a travertine dome, plotted according to Eq. (5), showing data collapse, as predicted by theory. Inset: Raw data.