Abstract
The temporal evolution of a water-sand interface
driven by gravity is experimentally investigated. By means of a Fourier
analysis of the evolving interface the growth rates are determined for the
different modes appearing in the developing front. To model the observed
behaviour we apply the idea of the Rayleigh-Taylor instability for two
stratified fluids. Carrying out a linear stability analysis we calculate
the growth rates from the corresponding dispersion relations for finite
and infinite cell sizes and compose those results with the experimental
data. Alternatively, the situation of the sedimenting sand can be modeled
by a two-dimensional cellular automaton. A qualitative similarity between
that model and the experimental situation is obtained.
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