COARSENING OF VORTEX RIPPLES IN SAND

Joachim Krug
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Joachim Krug: Fachbereich Physik, Universität Essen, 45117 Essen, Germany

Advances in Complex Systems (ACS), 2001, vol. 04, issue 04, 353-362

Abstract: The coarsening of an array of vortex ripples prepared in an unstable state is discussed within the framework of a simple mass transfer model first introduced by K. H. Andersenet al.(see Ref. 1). Two scenarios for the selection of the final pattern are identified. When the initial state is homogeneous with uniform random perturbations, a unique final state is reached which depends only on the shape of the interaction functionf(λ). A potential formulation of the dynamics suggests that the final wavelength is determined by a Maxwell construction applied tof(λ), but comparison with numerical simulations shows that this yields only an upper bound. In contrast, the evolution from a perfectly homogeneous state with a localized perturbation proceeds through the propagation of wavelength doubling fronts. The front speed can be predicted by standard marginal stability theory. In this case the final wavelength depends on the initial wavelength in a complicated manner which involves multiplication by powers of two and rational ratios such as 4/3.

Keywords: Sand ripples; pattern formation; wavelength selection; coarsening; front propagation; marginal stability; metastable states (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219525901000280

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