COARSENING OF VORTEX RIPPLES IN SAND

Author:

KRUG JOACHIM1

Affiliation:

1. Fachbereich Physik, Universität Essen, 45117 Essen, Germany

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. Andersen et 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 function f(λ). A potential formulation of the dynamics suggests that the final wavelength is determined by a Maxwell construction applied to f(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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Control and Systems Engineering

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Nonlinear Dynamics of Surface Steps;Nonlinear Dynamics of Nanosystems;2010-09-09

2. Separation vortices and pattern formation;Theoretical and Computational Fluid Dynamics;2009-05-29

3. Separation vortices and pattern formation;Iutam Bookseries;2009

4. Amplitude equation and long-range interactions in underwater sand ripples in one dimension;Physical Review E;2008-10-10

5. Universal non-equilibrium phenomena at submicrometric surfaces and interfaces;The European Physical Journal Special Topics;2007-07

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