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Watching rocks grow

Nature Physics volume 4, pages 310–313 (2008)Cite this article

Abstract

Nature abounds with beautiful and striking landscapes, but a comprehensive understanding of their forms requires examples where detailed comparisons can be made between theory and experiment. Geothermal hot springs1 produce some of the most rapidly changing terrestrial landscapes, with reported travertine (calcium carbonate) growth rates as high as 5 mm per day2,3,4. Unlike most landscapes, the patterns of which are the result of erosion processes on timescales of millions of years, the hot-spring depositional landscapes exhibit a spectacular cascade of nested ponds and terraces5, for which the origins and quantitative characterization have remained elusive. Here, we take advantage of this millionfold difference in geological timescale to present a novel combination of data from time-lapse photography, computer simulation and mathematical modelling that explains the emergence of the large-scale pond and terrace patterns, predicts and verifies the dynamics of their growth and shows that these patterns are scale invariant.

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Figure 1: Dynamics of synthetic hot-spring landscapes.
Figure 2: Watching rocks grow.
Figure 3: Tracing out the data.
Figure 4: Static statistical properties of travertine landscapes.
Figure 5: Schematic diagram of one time step in the cellular model.

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References

  1. Ford, T. & Pedley, H. A review of tufa and travertine deposits of the world. Earth Sci. Rev. 41, 117–175 (1996).

    Article  ADS  Google Scholar 

  2. Friedman, I. Some investigations of the deposition of travertine from hot springs: I. The isotope chemistry of a travertine-depositing spring. Geochim. Cosmochim. Acta 34, 1303–1315 (1970).

    Article  ADS  Google Scholar 

  3. Pentecost, A. & Viles, H. A. A review and reassessment of travertine classification. Geogr. Phys. Quaternaire 48, 305–314 (1994).

    Article  Google Scholar 

  4. Fouke, B. W. et al. Depositional facies and aqueous-solid geochemistry of travertine-depositing hot springs (Angel Terrace, Mammoth Hot Springs, Yellowstone National Park, USA). J. Sed. Res. 70, 265–285 (2000).

    Article  Google Scholar 

  5. Allen, E. T. & Day, A. L. Hot springs of the Yellowstone National Park. Tech. Rep. publication 466, Carnegie Institute of Washington (1935).

  6. Murray, A. B. & Paola, C. A cellular model of braided rivers. Nature 371, 54–57 (1994).

    Article  ADS  Google Scholar 

  7. Goldenfeld, N., Chan, P. & Veysey, J. Dynamics of precipitation pattern formation at geothermal hot springs. Phys. Rev. Lett. 96, 254501 (2006).

    Article  ADS  Google Scholar 

  8. Short, M. B., Baygents, J. C. & Goldstein, R. E. Stalactite growth as a free-boundary problem. Phys. Fluids 17, 083101–083112 (2005).

    Article  ADS  Google Scholar 

  9. Short, M. B. et al. Stalactite growth as a free-boundary problem: A geometric law and its platonic ideal. Phys. Rev. Lett. 94, 018501–018504 (2005).

    Article  ADS  Google Scholar 

  10. Hammer, Ø., Dysthea, D. & Jamtveit, B. The dynamics of travertine dams. Earth Planet. Sci. Lett. 256, 258–263 (2007).

    Article  ADS  Google Scholar 

  11. Jeong, H.-C. & Williams, E. D. Steps on surfaces: Experiment and theory. Surf. Sci. Rep. 34, 171–294 (1999).

    Article  ADS  Google Scholar 

  12. Grotzinger, J. P. & Rothman, D. H. An abiotic model for stromatolite morphogenesis. Nature 383, 423–425 (1996).

    Article  ADS  Google Scholar 

  13. Joós, B., Einstein, T. L. & Bartelt, N. C. Distribution of terrace widths on a vicinal surface within the one-dimensional free-fermion model. Phys. Rev. B 43, 8153–8162 (1991).

    Article  ADS  Google Scholar 

  14. Stone, D. & Goldstein, R. Tubular precipitation and redox gradients on a bubbling template. Proc. Natl Acad. Sci. 101, 11537–11541 (2004).

    Article  ADS  Google Scholar 

  15. Efron, B. & Tibshirani, R. An Introduction to the Bootstrap (Chapman & Hall/CRC, New York, 1994).

    MATH  Google Scholar 

  16. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in C 2nd edn (Cambridge Univ. Press, New York, 1992).

    MATH  Google Scholar 

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Acknowledgements

This work was carried out as part of a comprehensive geochemical and microbial ecology study of Yellowstone’s carbonate hot springs. We thank our colleagues B. Fouke, M. Kandianis and T. Schickel for valuable discussions. A special debt is due to ranger B. Suderman of the US Park Service for photography, N. Guttenberg for assistance rendering simulations and P. Y. Chan for discussions and penmanship. This work was funded by the US National Science Foundation.

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Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green St., Urbana, Illinois 61801, USA

    John Veysey II & Nigel Goldenfeld

Authors
  1. John Veysey II
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  2. Nigel Goldenfeld
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Contributions

J.V. and N.G. contributed equally to all aspects of this research.

Corresponding author

Correspondence to Nigel Goldenfeld.

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Veysey II, J., Goldenfeld, N. Watching rocks grow. Nature Phys 4, 310–313 (2008). https://doi.org/10.1038/nphys911

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