研究人员表明，在景观尺度上，与河流侵蚀相比，土壤扩散的影响减小，最低限度景观演化模型的解表现出不变的行为，相对于无量纲渠化指数，产生完全的自相似性。当接近零极限时，土壤扩散被局限于消失区域和大的凹度或凸度的区域内，与山脊和山谷网络的位置相对应。
研究人员用一维解析解和二维数值模拟证明了这些结果，并得到了真实地形观测的支持。研究在景观自相似性和局部扩散方面的发现，类似于湍流的自相似性和粘滞耗散的作用。在消失扩散极限处的地形奇点，暗示了在非线性复杂系统中观测到的冲击波和奇点。
据悉，当河流侵蚀比其他地貌过程更能主导地貌演变时，复杂的地形表现出普遍的特性。
附：英文原文
Title: Self-similarity and vanishing diffusion in fluvial landscapes
Author: Anand, Shashank Kumar, Bertagni, Matteo B., Drivas, Theodore D., Porporato, Amilcare
Issue&Volume: 2023-12-14
Abstract: 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.
DOI: 10.1073/pnas.2302401120
Source: https://www.pnas.org/doi/abs/10.1073/pnas.2302401120