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A numerical retro-action model relates rocky coast erosion to percolation theory

机译:数值回归模型将岩石海岸侵蚀与岩石海岸侵蚀联系起来   渗流理论

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摘要

We discuss various situations where the formation of rocky coast morphologycan be attributed to the retro-action of the coast morphology itself on theerosive power of the sea. Destroying the weaker elements of the coast, erosioncan creates irregular seashores. In turn, the geometrical irregularityparticipates in the damping of sea-waves, decreasing their erosive power. Theremay then exist a mutual self-stabilization of the wave amplitude together withthe irregular morphology of the coast. A simple model of this type ofstabilization is discussed. The resulting coastline morphologies are diverse,depending mainly on the morphology/damping coupling. In the limit case of weakcoupling, the process spontaneously builds fractal morphologies with adimension close to 4/3. This provides a direct connection between the coastalerosion problem and the theory of percolation. For strong coupling, rugged butnon-fractal coasts may emerge during the erosion process, and we investigate ageometrical characterization in these cases. The model is minimal, but can beextended to take into account heterogeneity in the rock lithology and variousinitial conditions. This allows to mimic coastline complexity, well beyondsimple fractality. Our results suggest that the irregular morphology ofcoastlines as well as the stochastic nature of erosion are deeply connectedwith the critical aspects of percolation phenomena.
机译:我们讨论了各种情况,其中岩石海岸形态的形成可以归因于海岸形态本身对海洋侵蚀力的反作用。侵蚀能破坏海岸的薄弱环节,形成不规则的海滨。反过来,几何形状的不规则性参与了海浪的阻尼,从而降低了海浪的侵蚀能力。然后可能存在波幅的相互自稳定以及海岸的不规则形态。讨论了这种类型的稳定化的简单模型。产生的海岸线形态是多种多样的,主要取决于形态/阻尼耦合。在弱耦合的极限情况下,该过程自发地建立了分形形态,其维数接近4/3。这在海岸侵蚀问题和渗流理论之间提供了直接联系。对于强耦合,在侵蚀过程中可能会出现崎but的非分形海岸,我们在这些情况下调查了年龄特征。该模型是最小的,但可以扩展以考虑岩石岩性和各种初始条件中的非均质性。这可以模拟海岸线的复杂性,远远超出简单的分形性。我们的结果表明,海岸线的不规则形态以及侵蚀的随机性与渗流现象的关键方面密切相关。

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