标题： 河流地貌中的自相似性和扩散消失 显示英文标题

标题： Self-similarity and vanishing diffusion in fluvial landscapes

摘要： 当河流侵蚀在地貌演化中占主导地位时，复杂地形表现出普遍特性。 同样，我们表明，一个最简地貌演化模型的解在土壤扩散的影响相对于河流侵蚀在地貌尺度上减弱时，表现出不变行为，相对于无量纲的渠道化指数呈现出完全自相似性。 接近其零极限时，土壤扩散被限制在一个面积趋于零且具有大凹度或凸度的区域，对应于山脊和山谷网络的轨迹。 我们通过一维解析解和二维数值模拟来证明这些结果，并得到真实地形观测的支持。 我们在地貌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性耗散的作用。 在扩散消失极限下的地形奇异性暗示了非线性复杂系统中观察到的激波和奇异性。 显示英文摘要

摘要： 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 1D analytical solutions and 2D 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.