A theoretical analysis of discontinuous flow with mobile bed

Sieben, J. W.

doi:10.1080/00221689909498306

Cited by 23 publications

(8 citation statements)

References 6 publications

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“…[]. In a decoupled model [e.g., Cunge et al ., ; Cui et al ., ; Sieben , ; Di Cristo et al ., ], the effects of sediment density and bed deformation on the flow are neglected, whereas a fully coupled model incorporates those effects into the flow mass and momentum conservation. A partially coupled model [ Phillips and Sutherland , ; Capart and Young , ; Fraccarollo and Capart , ; Lesser et al ., ; Rosatti and Fraccarollo , ; Canestrelli et al ., ; Garegnani et al ., ] falls in between the decoupled and fully coupled models.…”

Section: Introductionmentioning

confidence: 99%

Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme

Vriend

Wang

et al. 2013

Water Resour. Res.

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[1] High-resolution morphological modeling of fluvial processes with complex, rapidly varying flows has been limited so far by model accuracy or computational efficiency. One of the most widely used numerical algorithms is based on the total variation diminishing method, solved by either upwind or centered approaches. An upwind scheme preserves high accuracy but is complex and computationally demanding, whereas the simplicity and efficiency of a centered approach compromise the accuracy. The present paper extends a recent upwind-biased centered scheme originally developed for clear water and scalar transport over a rigid bed, to sediment-laden flows over an erodible bed. It does so by developing a fully coupled 2-D mathematical model using a finite volume method for structured grids. The complete set of noncapacity-based governing equations, involving the effects of bed deformation and sediment density variation, as well as the influences of turbulence and sediment diffusion, and the temporal and spatial scales needed for sediment adaptation, is solved at one time to obtain synchronous solutions for the entire computational domain. For stability, a two-stage splitting approach together with a secondorder Runge-Kutta method is employed for the source terms. The model is verified in a number of tests covering a wide range of complex (sediment-laden) flows. The model is demonstrated to accurately simulate shock waves and reflection waves, but also rapid bed deformations at high sediment transport rates. The combination of high numerical accuracy and computational efficiency makes the model an important tool to forecast flood events in morphologically complex areas.

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Section: Introductionmentioning

confidence: 99%

Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme

Vriend

Wang

et al. 2013

Water Resour. Res.

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“…It follows that the hyperbolic nature of the governing equations is universally appropriate for accommodating bed material waves found in the real world including both field sites and laboratory experiments, irrespective of the sediment transport function implemented. Additionally it is necessary to point out that special treatment is required to model the evolution of shock waves based upon hyperbolic equations (Chu, 1985;Needham and Hey, 1991;Sieben, 1999;Toro, 2001).…”

Section: Discussionmentioning

confidence: 99%

On evolution of bed material waves in alluvial rivers

Cao

Carling

2003

Earth Surf Processes Landf

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Field and laboratory measurements have shown distinct characteristics of bed sediment waves under differing conditions, whilst their theoretical interpretation has emerged to be equivocal. This note aims to clarify the interpretation of evolution of bed material waves. The complete set of governing equations for the flow-sediment-morphology system is deduced to demonstrate its universally hyperbolic nature, irrespective of the sediment transport functions implemented to close the equations. The hyperbolic nature can admit not only attenuating bed material waves, but also shock-like waves that are not unusual in the real world. It is suggested that the theory of dispersion/diffusion is not universally appropriate for evolution of bed material waves.

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“…Far from critical conditions, j1 À Fr 2 j $ Oð1Þ or larger, the celerity of a bed wave is considerably smaller than those of surface waves; the bed interacts only weakly with the water surface, thus justifying an approach in which the equations that govern the dynamics of the liquid phase are solved separately from those governing the solid phase (decoupled approach). Near critical conditions, however, a transcritical region exists, 0.8 < % Fr < % 1.2 (Sieben, 1999), in which two of the three characteristic celerities have the same order of magnitude and the third one is much larger; in this region surface waves strongly interact with bed waves (Lyn and Altinakar, 2002;Lanzoni et al, 2006). In order to cope with situations in which the Froude number may be significantly variable and critical conditions can be encountered we adopt the fully coupled (synchronous) approach and Equations (1), (2) and (3) are solved simultaneously at each time step.…”

Section: Formulation Of the One-dimensional Mathematical Modelmentioning

confidence: 96%

River bed evolution due to channel expansion: general behaviour and application to a case study (Kugart River, Kyrgyz Republic)

Siviglia

Repetto

Zolezzi

et al. 2008

River Research & Apps

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We study the effect of spatial variations of river width on bed aggradation and degradation processes, making use of a one-dimensional numerical model of channel morphodynamics. We refer to a peculiar case, the downstream reach of the Kugart River (Kyrgyzstan). The river has been partly channelized in the recent past with the aim of reducing the flooding risk for the surrounding villages; the consequent reduction of channel width in some reaches was also expected to improve channel conveyance with respect to the high sediment load produced in the upper river basin. The resulting longitudinal sequence of relatively sharp channel expansions and contractions has, however, triggered rapid siltation rates, especially in the narrowest reaches. This motivated the application of a 1-D numerical model of river morphodynamics.Abrupt channel expansions are found to be the main driving forces for aggrading processes, which may extend for long distances from where they are generated. In order to obtain a thorough understanding of the morphodynamics of channel expansions, we first apply the model to simple test cases. This allows us to characterize the basic features of the problem and the dependence of bed evolution on the upstream Froude number Fr and on the expansion ratio r b , which are the most relevant controlling parameters. We invariably find that deposition occurs in expansion regions with bed aggradation observed both upstream and downstream. The deposition prism progressively increases its height and lengthens both in the upstream and downstream directions. The deposition process is particularly intense, in terms of deposition prism height, in super-critical conditions. Moreover, it is found that higher values of Fr strongly reduce the time scale of morphological processes and faster deposition rates are further facilitated by abrupt expansions.The present outcomes are relevant for assessing the expected altimetric response of river bed to the implementation of localized channelization works and to local river widening, a practise which is increasingly being employed within river restoration projects, with the aim of enhancing habitat diversity.

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A theoretical analysis of discontinuous flow with mobile bed

Cited by 23 publications

References 6 publications

Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme

Morphological modeling using a fully coupled, total variation diminishing upwind-biased centered scheme

On evolution of bed material waves in alluvial rivers

River bed evolution due to channel expansion: general behaviour and application to a case study (Kugart River, Kyrgyz Republic)

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