Abstract:
Starting from the phenomenological model for sand ripple formation developed in [#!Bouchaud98!#], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [#!Csahok98!#]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength.
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Received 5 January 1999
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Valance, A., Rioual, F. A nonlinear model for aeolian sand ripples. Eur. Phys. J. B 10, 543–548 (1999). https://doi.org/10.1007/s100510050884
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DOI: https://doi.org/10.1007/s100510050884