Andrea Baldassarri, Bernard Sapoval, Simon Félix
We discuss various situations where the formation of rocky coast morphology
can be attributed to the retro-action of the coast morphology itself on the
erosive power of the sea. Destroying the weaker elements of the coast, erosion
can creates irregular seashores. In turn, the geometrical irregularity
participates in the damping of sea-waves, decreasing their erosive power. There
may then exist a mutual self-stabilization of the wave amplitude together with
the irregular morphology of the coast. A simple model of this type of
stabilization is discussed. The resulting coastline morphologies are diverse,
depending mainly on the morphology/damping coupling. In the limit case of weak
coupling, the process spontaneously builds fractal morphologies with a
dimension close to 4/3. This provides a direct connection between the coastal
erosion problem and the theory of percolation. For strong coupling, rugged but
non-fractal coasts may emerge during the erosion process, and we investigate a
geometrical characterization in these cases. The model is minimal, but can be
extended to take into account heterogeneity in the rock lithology and various
initial conditions. This allows to mimic coastline complexity, well beyond
simple fractality. Our results suggest that the irregular morphology of
coastlines as well as the stochastic nature of erosion are deeply connected
with the critical aspects of percolation phenomena.
View original:
http://arxiv.org/abs/1202.4286
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