Analytic Theory of Equilibrium Fluvial Landscapes: The Integration of Hillslopes and Channels

Smith, Terence R.

doi:10.1002/2016jf004073

Cited by 5 publications

(12 citation statements)

References 65 publications

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“…The dynamics of eroding surfaces and related overland flow (including raindrop impact) can be modeled via different approaches, from mechanistic models that consider coupled overland flow and soil erosion (e.g., Hairsine & Rose, 1992a, 1992bNearing et al, 1989) to catchment scale landscape evolution models (LEMs) (e.g., Howard et al, 1994;Perron et al, 2008;Smith, 2018;Willgoose, 1989). LEMs, which predict channel networks at both the catchment and laboratory scales, are relevant to our experimental results.…”

Section: Resultsmentioning

confidence: 99%

“…The consistency between the laboratory results in Figure and and results for catchment networks (e.g., Rodríguez‐Iturbe & Rinaldo, ) points to an underlying governing principle operating at different scales, such as the principle of minimum energy expenditure (Rodríguez‐Iturbe et al, ) that applies at equilibrium conditions for river networks. Similarly, recent work (Smith, ) on equilibrium landscapes showed that overland flows minimized a Lagrangian function of kinetic and potential energies. For both potential (viscosity dominated) and inviscid flows and for fixed boundary conditions, energy dissipation continues monotonically until the steady flow configuration is achieved; that is, energy dissipation is a minimum (Lord, ).…”

Section: Resultsmentioning

confidence: 99%

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Catchment Drainage Network Scaling Laws Found Experimentally in Overland Flow Morphologies

Cheraghi

Rinaldo

Sander

et al. 2018

Geophysical Research Letters

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The scaling relation between the drainage area and stream length (Hack's law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for channelized fluvial regions. We report here on a laboratory experiment on an eroding unconsolidated sediment for which no channeling occurred. Laser scanning was used to capture the morphological evolution of the sediment. High-intensity, spatially nonuniform rainfall ensured that the morphology changed substantially over the 16-hr experiment. Based on the surface scans and precipitation distribution, overland flow was estimated with the D8 algorithm, which outputs a flow network that was analyzed statistically. The above-mentioned scaling and exceedance probability relationships for this overland flow network are the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of experiment. Plain Language SummaryIn spite of different climates, vegetation, and land properties, the geometry of river networks is characterized by near-identical scaling laws. Can we expect similar statistical metrics for surface flow over unchanneled morphologies at small scales? To answer this question, the morphology of uncohesive sediment was measured at high resolution in a laboratory flume and under nonuniform rainfall. Based on this morphology, the overland flow network was determined. The results showed that even at small scale (2 m by 1 m) and in absence of rills, the flow network has the same statistical characteristics as large-scale river networks. In other words, the shallow overland flow could be represented by a network that dynamically changed while preserving catchment scaling laws.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Catchment Drainage Network Scaling Laws Found Experimentally in Overland Flow Morphologies

Cheraghi

Rinaldo

Sander

et al. 2018

Geophysical Research Letters

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“…The transition between the unchannelization phase and the initiation phase is then expected to be the time of incipient channelization according to the theory by [3]. The latest experimental, numerical and theoretical studies [12]- [14] show that bifurcation generated by overland flow and seepage erosion should be investigated by process-based approaches. Thus, better flow models and erosion functions may be necessary and important for future research.…”

Section: Discussionmentioning

confidence: 99%

Laboratory Experiment of Channel Head Bifurcation by Radial Overland Flow

Pornprommin¹

2020

GEOMATE

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Many studies have shown that incipient channelization can be explained by the interaction between flow and an erodible bed. Our recent theoretical study has shown that an eroding channel head by overland flow can maintain its shape without bifurcation if the flow depth is sufficiently large comparing to the channel head radius. Here, we performed nine experimental runs using three sediment sizes to provide better understanding of the bifurcation. A circular pan was filled with sand except at the center, where there were a sink hole and a drain installed at the pan bottom. When water had been filled over the sand to a desirable level, the drain was opened and unsteady radial overland flow accelerated toward the hole. After a while, water formed a downward-concave profile, leading to strong bed erosion in the vicinity of the hole and, as a result, the hole size expanded. In the initial development where flow depth was sufficiently large, the hole maintained its circular shape without channel incision while expanding. As the flow depth and discharge reduced and the hole radius increased, the hole started to lose its circular shape. Thus, the experimental results confirmed the condition of channel bifurcation proposed by our previous study. Main incised channels with large spacing were firstly initiated and elongated upstream in the radial direction while small rills were generated later between main channels. Using the network circularity as an indicator, we propose the new four phases of channel network development (unchannelization, initiation, extension and abstraction).

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“…A second approach involves deriving solutions to the equations when they are in equilibrium form. This approach is applied in the current paper to a landscape model for which Smith (2018) demonstrated the existence of solutions for both overland and channelized regimes of flow, following a suggestion of Fowler et al (2007) concerning the bistability of the two regimes. An issue with this approach is in selecting appropriate solutions from the many that are consistent with the equations and constraints of a model in equilibrium form.…”

Section: Introductionmentioning

confidence: 98%

A Variational Principle for the Integrated Channels and Slopes of Stable Equilibrium Landscapes

Smith

2021

JGR Earth Surface

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Minimizing a simple functional of slope and channel energy implies the equations and properties of general models of equilibrium landscapes • Channels have minimally stable, symmetric inflows with minimal drainage density if the functional contains a slope stability constraint • Solutions for linear ridges have equal length channels and maximully spaced, symmetrical valleys minimizing slope and channel flow energy

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Analytic Theory of Equilibrium Fluvial Landscapes: The Integration of Hillslopes and Channels

Cited by 5 publications

References 65 publications

Catchment Drainage Network Scaling Laws Found Experimentally in Overland Flow Morphologies

Catchment Drainage Network Scaling Laws Found Experimentally in Overland Flow Morphologies

Laboratory Experiment of Channel Head Bifurcation by Radial Overland Flow

A Variational Principle for the Integrated Channels and Slopes of Stable Equilibrium Landscapes

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