Self-similarity and vanishing diffusion in fluvial landscapes
Self-similarity and vanishing diffusion in fluvial landscapes
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DOI：
10.1073/pnas.2302401120
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发表时间：
2023-12-19
影响因子：
11.1
通讯作者：
Porporato，Amilcare
中科院分区：
文献类型：
--
作者：
Anand，Shashank Kumar;Bertagni，Matteo B.;Porporato，Amilcare
当河流侵蚀主导景观演化而非其他地貌过程时，复杂地形表现出普遍的性质。同样，我们表明，随着土壤扩散的影响与景观尺度上的河流侵蚀相比逐渐减弱，极简景观演变模型的解显示出不变的行为，从而在无量纲渠化指数方面产生了完全的自相似性。当土壤扩散接近零极限时，土壤扩散被限制在一个消失区和大凸度的区域内，对应于山脊和山谷网络的轨迹。我们使用一维解析解和二维数值模拟，支持现实世界的地形观测，证明了这些结果。我们的景观自相似性和本地化扩散的研究结果类似于湍流的自相似性和粘性耗散的作用。在消失的扩散极限的地形奇异性暗示的冲击波和奇异性观察到的非线性复杂系统。
Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network. We demonstrate these results using one dimensional analytical solutions and two dimensional numerical simulations, supported by real-world topographic observations. Our findings on the landscape self-similarity and the localized diffusion resemble the self-similarity of turbulent flows and the role of viscous dissipation. Topographic singularities in the vanishing diffusion limit are suggestive of shock waves and singularities observed in nonlinear complex systems.