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The shape of patterns to come: From initial formation to long-term evolution

Publication ,  Journal Article
Murray, AB; Goldstein, EB; Coco, G
Published in: Earth Surface Processes and Landforms
January 1, 2014

Many studies focus on the emergence and development of rhythmic landscape patterns. In this contribution we explore the different behaviors found as patterns evolve; the trajectories that patterns exhibit as they transit from infinitesimal-amplitude perturbation to a statistically steady state (or in some cases to continued statistical evolution). The variety of behaviors observed, either through field and laboratory experiments or numerical modeling, can be reduced to four classes: (a) simple stabilization where predictions based on the initial growth of small perturbations corresponds with the characteristics of patterns observed in nature; (b) significant pattern coarsening en route to saturated wavelength, where non-linear interactions between finite-amplitude pattern elements change the geometric properties of a pattern as it approaches steady-state; (c) perpetual coarsening where the wavelength associated with the emerging pattern continues to grow over time and is only limited by physical boundaries or external constrains; (d) slow evolution toward a different attractor, a novel behavior observed in numerical modeling that involves profound temporal changes in pattern characteristics. Within these classes we also observe generalizable non-linear behaviors: dependence on initial conditions, the emergence of pattern-scale variables such as pattern defects, and the presence of multiple stable states. Predicting the shape of patterns to come remains a challenge - one that we suggest requires a range of modeling approaches to address both initial instabilities and the emergent properties of evolving patterns, which involve disparate forms of non-linear interactions. Consideration of generic system behaviors at the pattern scale could enhance future pattern formation studies, facilitating appropriate pairings of analysis approaches and pattern-evolution modes. © 2013 John Wiley & Sons, Ltd.

Duke Scholars

Published In

Earth Surface Processes and Landforms

DOI

EISSN

1096-9837

ISSN

0197-9337

Publication Date

January 1, 2014

Volume

39

Issue

1

Start / End Page

62 / 70

Related Subject Headings

  • Geography
  • 3709 Physical geography and environmental geoscience
  • 3707 Hydrology
  • 3705 Geology
  • 0406 Physical Geography and Environmental Geoscience
  • 0403 Geology
 

Citation

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Murray, A. B., Goldstein, E. B., & Coco, G. (2014). The shape of patterns to come: From initial formation to long-term evolution. Earth Surface Processes and Landforms, 39(1), 62–70. https://doi.org/10.1002/esp.3487
Murray, A. B., E. B. Goldstein, and G. Coco. “The shape of patterns to come: From initial formation to long-term evolution.” Earth Surface Processes and Landforms 39, no. 1 (January 1, 2014): 62–70. https://doi.org/10.1002/esp.3487.
Murray AB, Goldstein EB, Coco G. The shape of patterns to come: From initial formation to long-term evolution. Earth Surface Processes and Landforms. 2014 Jan 1;39(1):62–70.
Murray, A. B., et al. “The shape of patterns to come: From initial formation to long-term evolution.” Earth Surface Processes and Landforms, vol. 39, no. 1, Jan. 2014, pp. 62–70. Scopus, doi:10.1002/esp.3487.
Murray AB, Goldstein EB, Coco G. The shape of patterns to come: From initial formation to long-term evolution. Earth Surface Processes and Landforms. 2014 Jan 1;39(1):62–70.
Journal cover image

Published In

Earth Surface Processes and Landforms

DOI

EISSN

1096-9837

ISSN

0197-9337

Publication Date

January 1, 2014

Volume

39

Issue

1

Start / End Page

62 / 70

Related Subject Headings

  • Geography
  • 3709 Physical geography and environmental geoscience
  • 3707 Hydrology
  • 3705 Geology
  • 0406 Physical Geography and Environmental Geoscience
  • 0403 Geology