一个将岩石海岸侵蚀与渗流理论联系起来的数值反演action模型
A numerical retro-action model relates rocky coast erosion to percolation theory
摘要：
我们讨论了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的各种情况。侵蚀破坏了海岸的脆弱部分，造成了不规则的海岸。反过来，几何不规则性参与了海浪的阻尼，降低了它们的侵蚀力。然后，可能存在一个相互的自稳定的波幅与海岸的不规则形态。这种类型的稳定的一个简单的模型进行了讨论。由此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，该过程自发地构建具有接近4/3的维度的分形形态。这提供了海岸侵蚀问题和渗流理论之间的直接联系。对于强耦合，崎岖的，但非分形海岸可能会出现在侵蚀过程中，我们调查在这些情况下的几何特征。该模型是最小的，但可以扩展到考虑岩石岩性和各种初始条件的异质性。这允许模仿海岸线的复杂性，远远超出简单的分形。我们的研究结果表明，海岸线的不规则形态以及侵蚀的随机性与渗透现象的关键方面有着深刻的联系。
英文摘要：
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.
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