A free-boundary model of diffusive valley growth: theory and observation

Yi, R.; Cohen, Yehuda; Seybold, Hansjörg; Stansifer, Eric; McDonald, N. Robb; Mineev-Weinstein, Mark; Rothman, Daniel H.

doi:10.1098/rspa.2017.0159

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…The formation of networks of ridges and valleys, brought about by the regular boundary conditions, also reveals the tendency of the system to develop configurations suggestive of optimization principles (11) typical of nonequilibrium thermodynamics and complex systems (16,(25)(26)(27)(28)(29)(30)(31)(32). Our analysis is different from recent interesting contributions on groundwater-dominated landscapes (33,34), where branching and valley evolution is initiated at seepage points in the landscape.…”

mentioning

confidence: 57%

Channelization cascade in landscape evolution

Bonetti

Hooshyar

Camporeale

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

110

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The hierarchy of channel networks in landscapes displays features that are characteristic of nonequilibrium complex systems. Here we show that a sequence of increasingly complex ridge and valley networks is produced by a system of partial differential equations coupling landscape evolution dynamics with a specific catchment area equation. By means of a linear stability analysis we identify the critical conditions triggering channel formation and the emergence of characteristic valley spacing. The ensuing channelization cascade, described by a dimensionless number accounting for diffusive soil creep, runoff erosion, and tectonic uplift, is reminiscent of the subsequent instabilities in fluid turbulence, while the structure of the simulated patterns is indicative of a tendency to evolve toward optimal configurations, with anomalies similar to dislocation defects observed in pattern-forming systems. The choice of specific geomorphic transport laws and boundary conditions strongly influences the channelization cascade, underlying the nonlocal and nonlinear character of its dynamics.

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mentioning

confidence: 57%

Channelization cascade in landscape evolution

Bonetti

Hooshyar

Camporeale

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

110

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“…In our study of the EDM, the first step is to determine the two-dimensional topographic surface at the initial state with the mathematical formula, 𝑧 = 𝑓(𝑥, 𝑦), where z is the land elevation at the Cartesian coordinate (𝑥, 𝑦) [13,40]. First, the initial curved surface should mimic the natural landscape with a gentle concave ditch and a convex hill.…”

Section: Mathematical Representation Of Initial Topographic Surfacementioning

confidence: 99%

Transient emergence of ramified river channels: simulations of geographical cycle by Erosion-Diffusion Model (EDM)

Serizawa,

Amemiya,

Itoh

2023

JASSE

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We present a minimal version of Landscape Evolution Models (LEMs) to capture the essence of tree-shaped channel network formation on the assumption of two mechanisms, soil erosion and diffusion. The continuous tectonic uplift is not required, which affects landscape evolution only at the starting point. We refer to the mathematical model as the Erosion-Diffusion Model (EDM). No steady state exists in the EDM except for the perfectly flat plane, which is realized at the ultimate final stage of the landform transition. It is suggested that generated channel patterns are temporal and transient creatures during long-term gravitational and erosional processes on the earth.

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“…There are a wide range of complex geophysical problems for which the extraction of statistical features is a driving interest. Examples abound from climate science [40,23,39], atmospheric science [32,33,48,8,41], morphology formation [20,9,36,49,13], and thermal convection studies [17,29,25]. The rigorous statistical analysis presented in this paper may ultimately prove valuable for applications such as these.…”

Section: Introductionmentioning

confidence: 99%

Rigorous criteria for anomalous waves induced by abrupt depth change using truncated KdV statistical mechanics

Sun¹,

Moore²

2020

Preprint

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We report two rigorous results concerning the emergence of anomalous wave statistics within a truncated KdV statistical-mechanics framework. Together, these results imply necessary conditions for the creation of anomalous waves. We assume a mixed Gibbs ensemble that is microcanonical in energy and macrocanonical in the Hamiltonian. Both results are for the KdV system with finite truncation, but in the limit of large cutoff wavenumber. First, we prove that with zero inverse temperature, surface displacement statistics converge to Gaussian, independent of the relative strength of nonlinearity and dispersion. Second, we prove that if nonlinearity is absent, then surface displacement statistics converge to Gaussian independent of the inverse temperature, as long as it satisfies a certain physically-motivated scaling relationship. Together, these results imply that both nonlinearity and non-zero inverse temperature are necessary to create the non-Gaussian statistics observed in recent numerical and experimental studies.

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A free-boundary model of diffusive valley growth: theory and observation

Cited by 3 publications

References 21 publications

Channelization cascade in landscape evolution

Channelization cascade in landscape evolution

Transient emergence of ramified river channels: simulations of geographical cycle by Erosion-Diffusion Model (EDM)

Rigorous criteria for anomalous waves induced by abrupt depth change using truncated KdV statistical mechanics

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