Hamburg 2001 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 17: Granulare Materie / Kontaktdynamik

DY 17.8: Vortrag

Montag, 26. März 2001, 17:30–17:45, S 7

Wavelength selection for a mass transfer model of vortex ripples in sand — •Krug Joachim — Fachbereich Physik, Universität Essen, 45117 Essen

We study a simple model for the dynamics of sand ripples formed under oscillatory flow, which was proposed by K.H. Andersen (PhD thesis, Copenhagen University 1999). The key ingredient in the model is a nonmonotonic mass transfer function, which measures the amount of sand transferred to a ripple due to the separation vortex which forms on its lee side. The stability of a pattern is determined by the sign of the derivative of the mass transfer function. We consider the evolution of the mean wavelength starting from an unstable state with random fluctuations. Based on the existence of a Lyapunov function for the time evolution, a selection criterion for the final stable wavelength is suggested, which is shown to become exact in the limit of steep transfer functions. Wavelength selection through front propagation from localized perturbations is also discussed, and is shown to lead to a complicated dependence of the final wavelength on the initial wavelength.