Blown by wind: Nonlinear dynamics of aeolian sand ripples

Hezi Yizhaq, Neil J. Balmforth, Antonello Provenzale

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


A nonlinear continuum model is considered that describes the dynamics of two-dimensional aeolian sand ripples. This integro-differential model is based on a phenomenological approach due to Anderson. Linear stability analysis using this model shows that a flat sand bed exposed to the action of wind is linearly unstable to long-wavelength perturbations. As the ripples grow, nonlinear effects become important, ripples become asymmetric and the wavelength increases due to merging events. A long-wavelength approximation to the full integral model is then derived. The ripple field produced by the long-wave theory undergoes coarsening, drifts downwind and displays bifurcations and defects which move from one ripple to another, similar to what is observed for sand ripples in the desert.

Original languageEnglish
Pages (from-to)207-228
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - 15 Aug 2004


  • Aeolian sand ripples
  • Geomorphology
  • Pattern formation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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