EMERGENCE OF SELF-SIMILARITY IN EROSION-DOMINATED LANDSCAPES

Natural topographies exhibit universal properties due to the dominance of fluvial erosion over other geomorphological processes. Here we analyze the solutions of a minimalist landscape evolution model that describes surface dynamics based on linear soil diffusion, detachment-limited fluvial erosion, and uplift. As the governing dimensionless index approaches very large values, signifying very high fluvial erosion intensity over the landscape compared to soil diffusion, a regime of complete self-similarity emerges. Within this self-similar regime, spatially averaged quantities (e.g., normalized relief) become invariant. The impact of soil diffusion becomes localized to a region of vanishing area and large concavity or convexity, corresponding to 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 bears resemblance to the self-similarity of turbulent flows and the role of viscous dissipation at very large Reynolds numbers.