Linear Stability Analysis of Channel Inception

Izumi, Norihiro

doi:10.2208/jscej.1999.614_65

Cited by 31 publications

(109 citation statements)

References 14 publications

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“…In experiments, the step celerity is of the same order of magnitude as in the field. The steps did not only migrate upstream by gradual erosion of the bed as Izumi and Parker (2000) assumed in their model, but also by repeated cantilever or planar failures at the step typical of cohesive sediments (van Eerdt, 1985;Simon and Thomas, 2002). Just downstream of the step, the deepening caused further failure of the banks as reported in Simon and Thomas (2002).…”

Section: Resultsmentioning

confidence: 90%

“…In experiments without an initial channel, the steps also developed; but bifurcated in the upstream direction because the flow was not as focussed as it was by an initial channel, and then stalled because the divided flows could no longer erode sediment. Izumi and Parker (2000) and Parker and Izumi (2000) described an analytical model for the stability of erosive steps. Starting from normal, subcritical flow upstream of the step, the flow becomes critical above the step leading to more intense erosion at the step than upstream of the step.…”

Section: Resultsmentioning

confidence: 99%

“…Given the observed normal flow velocity u, depth h, and slope S far upstream of the steps [that is, one backwater adaptation length upstream, estimated as h / S (in m), where flow is no longer affected by the downstream step], the flow velocity above the step for Fr = 1 is calculated as u 1 = (qg) 1/3 with q = uh = specific flow discharge, and g = 9.81 m/s 2 is the gravitational acceleration. Then Izumi and Parker (2000) defined a nondimensional velocity as u n = u / u 1 (with subscript n denoting nondimensionalisation), which is then used to calculate a Froude number Fr n = u n 3/2 (see Izumi and Parker, 2000, for the details of the derivation). An inverse nondimensional excess shear stress parameter, ψ, is defined as the ratio of critical and actual bed shear stress (far upstream of the step): ψ = τ c / ρC f u 1 2 , where the flow friction…”

Section: Description Of Model Of Step Migrationmentioning

confidence: 99%

“…From the stability analysis, Izumi and Parker (2000) found that the step will migrate infinitely far upstream for ψ N 1. (Note that ψ N 1 is defined far upstream; at the step erosion can nevertheless take place because the local shear stress exceeds the critical shear stress at least at the step even though not farther upstream.).…”

Section: Description Of Model Of Step Migrationmentioning

confidence: 99%

“…The steps excavate the bed and undercut the banks as they migrate upstream along the channels. The model of Izumi and Parker (2000) predicts how fast and how far the step migrate upstream depending on the Froude number far upstream of the step and on the threshold for erosion.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Meandering channel dynamics in highly cohesive sediment on an intertidal mud flat in the Westerschelde estuary, the Netherlands

et al. 2009

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Section: Resultsmentioning

confidence: 90%

Section: Resultsmentioning

confidence: 99%

Section: Description Of Model Of Step Migrationmentioning

confidence: 99%

Section: Description Of Model Of Step Migrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Meandering channel dynamics in highly cohesive sediment on an intertidal mud flat in the Westerschelde estuary, the Netherlands

et al. 2009

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Hydraulics of floods upstream of horseshoe canyons and waterfalls

Lapôtre

Lamb

2015

JGR Earth Surface

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Horseshoe waterfalls are ubiquitous in natural streams, bedrock canyons, and engineering structures. Nevertheless, water flow patterns upstream of horseshoe waterfalls are poorly known and likely differ from the better studied case of a one-dimensional linear step because of flow focusing into the horseshoe. This is a significant knowledge gap because the hydraulics at waterfalls controls sediment transport and bedrock incision, which can compromise the integrity of engineered structures and influence the evolution of river canyons on Earth and Mars. Here we develop new semiempirical theory for the spatial acceleration of water upstream of, and the cumulative discharge into, horseshoe canyons and waterfalls. To this end, we performed 110 numerical experiments by solving the 2-D depth-averaged shallow-water equations for a wide range of flood depths, widths and discharges, and canyon lengths, widths and bed gradients. We show that the upstream, normal flow Froude number is the dominant control on lateral flow focusing and acceleration into the canyon head and that focusing is limited when the flood width is small compared to a cross-stream backwater length scale. In addition, for sheet floods much wider than the canyon, flow focusing into the canyon head leads to reduced discharge (and drying in cases) across the canyon sidewalls, which is especially pronounced for canyons that are much longer than they are wide. Our results provide new expectations for morphodynamic feedbacks between floods and topography, and thus canyon formation.

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Supraglacial channel inception: Modeling and processes

2015

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Supraglacial drainage systems play a key role in glacial hydrology. Nevertheless, physical processes leading to spatial organization in supraglacial networks are still an open issue. In the present work we thus address from a quantitative point of view the question of what is the physics leading to widely observed patterns made up of evenly spaced channels. To this aim, we set up a novel mathematical model describing a condition antecedent channel formation, i.e., the down-glacier flow of a distributed meltwater film. We then perform a linear stability analysis to assess whether the ice-water interface undergoes a morphological instability compatible with observed patterns. The instability is detected, its features depending on glacier surface slope, ice friction factor, and water as well as ice thermal conditions. By contrast, in our model channel spacing is solely hydrodynamically driven and relies on the interplay between pressure perturbations, flow depth response, and Reynolds stresses. Geometrical features of the predicted pattern are quantitatively consistent with available field data. The hydrodynamic origin of supraglacial channel morphogenesis suggests that alluvial patterns might share the same physical controls.

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Linear Stability Analysis of Channel Inception

Cited by 31 publications

References 14 publications

Meandering channel dynamics in highly cohesive sediment on an intertidal mud flat in the Westerschelde estuary, the Netherlands

Meandering channel dynamics in highly cohesive sediment on an intertidal mud flat in the Westerschelde estuary, the Netherlands

Hydraulics of floods upstream of horseshoe canyons and waterfalls

Supraglacial channel inception: Modeling and processes

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