Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation

Andersen, Ken Haste; Abel, Markus; Krug, Joachim; Ellegaard, C.; Søndergaard, Leif; Udesen, Jesper

doi:10.1103/physrevlett.88.234302

Cited by 29 publications

(35 citation statements)

References 17 publications

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“…The model (1) thus predicts an entire band of stable homogeneous states with wavelengths λ c <λ < λ max , in qualitative accordance with experiments [3,4,6]. The existence of a multitude of linearly stable, stationary states is a property that the model shares with many other systems in granular physics.…”

Section: The Mass Transfer Modelsupporting

confidence: 56%

“…λ c < λ * < λ max . Third, it is invariant under multiplication of f by an arbitrary factor 6 . Nevertheless it is wrong: Comparison with simulations shows that λ * > λ eq always.…”

Section: Wavelength Selection From Generic Unstable Statesmentioning

confidence: 99%

“…Preliminary simulations show that this does indeed increase the final wavelength, but not sufficiently to reach λ * . A noisy version of the model has been described in [6]. Noise also increases the final wavelength, however in addition it introduces a new coarsening mechanism involving rare fluctuations [9], which in principle drives the wavelength towards λ max , as long as ripple creation is not included.…”

Section: Wavelength Selection From Generic Unstable Statesmentioning

confidence: 99%

“…We consider a fully developed ripple pattern of the kind obtained in a quasi one-dimensional annular geometry [3,6,7] (see Figure 1, which is taken from [6]). Each of the N ripples is described by a single size parameter λ n (t), which can be thought to represent its length, or the amount of sand it contains.…”

Section: The Mass Transfer Modelmentioning

confidence: 99%

“…We focus here on the mathematical aspects of the problem, and refer the reader to the literature for further motivation and a detailed comparison to experiments [5,6]. The model of interest is introduced in the next section.…”

Section: Introductionmentioning

confidence: 99%

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Coarsening of Vortex Ripples in Sand

Krug

2003

Challenges in Granular Physics

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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. [Phys. Rev. E 63, 066308 (2001)]. 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 factors of 2 and rational ratios such as 4/3.Unsüberfüllts. Wir ordnens. Es zerfällt. Wir ordnens wieder und zerfallen selbst.

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Section: The Mass Transfer Modelsupporting

confidence: 56%

“…λ c < λ * < λ max . Third, it is invariant under multiplication of f by an arbitrary factor 6 . Nevertheless it is wrong: Comparison with simulations shows that λ * > λ eq always.…”

Section: Wavelength Selection From Generic Unstable Statesmentioning

confidence: 99%