Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs

Abstract

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.

Sculpting of Rocks by Reactive Fluids

“…At the time, we did not know that physics professor Nigel Goldenfeld and his colleagues at the University of Illinois at Urbana-Champaign were also starting to work on this phenomenon using similar methods. We were both somewhat surprised and delighted when we saw each other's first publications (Goldenfeld et al, 2006;Hammer et al, 2007).…”

“…The model reproduces several peculiarities of travertine terrace growth observed in nature, such as downslope migration of steps, coarsening by merging and drowning of upstream steps and stretching of dams in the downslope direction. Goldenfeld et al (2006) and Veysey and Goldenfeld (2008) developed a somewhat similar model, with further simplification of the flow (using a discrete model for Stokes flow) but including several other processes such as surface tension and simplified chemistry and heat transport. These simulations also assumed a relationship between flow velocity and precipitation rate, producing very realistic terrace patterns.…”

“…The emergence of patterns in such systems is not trivial and intuition often fails us. Our group and the group of Nigel Goldenfeld at the University of Illinois at Urbana-Champaign have studied travertine terracing in detail using a fruitful combination of field observation, laboratory experiments and computer modelling (Jettestuen et al, 2006;Goldenfeld et al, 2006;Veysey and Goldenfeld 2008;Hammer et al, 2007;2008;2010). A particularly interesting aspect of this work was the way in which we attacked the problem at many different levels of abstraction, in order to answer several types of questions.…”

Watching rocks grow

“…Our cell dynamical system (CDS) is a set of rules, described in detail in the Methods section, that updates the lattice variables representing the heights of the landscape and fluid above each cell. The rules mimic fluid depositional dynamics and the influence of landscape features on the flow pattern 6,7 , enabling efficient computations of complex landscapes. Such a formalism complements analytic descriptions of carbonate precipitation patterns, such as our work on travertine domes 7 and recent studies of needle-like speleothem growth 8,9 .…”

“…The rules mimic fluid depositional dynamics and the influence of landscape features on the flow pattern 6,7 , enabling efficient computations of complex landscapes. Such a formalism complements analytic descriptions of carbonate precipitation patterns, such as our work on travertine domes 7 and recent studies of needle-like speleothem growth 8,9 . We were able to verify that our CDS model is quantitatively equivalent to the more conventional approach using differential equations, by using it to analyse the growth of single travertine domes 7 .…”