DOCSLIB.ORG

A Generalized Exner Equation for Sediment Mass Balance C

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Generalized Exner Equation for Sediment Mass Balance C JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, F04014, doi:10.1029/2004JF000274, 2005 A generalized Exner equation for sediment mass balance C. Paola1 and V. R. Voller2 St. Anthony Falls Laboratory, Minneapolis, Minnesota, USA Received 13 December 2004; revised 7 June 2005; accepted 6 September 2005; published 30 November 2005. [1] The advance of morphodynamics research into new areas has led to a proliferation of forms of sediment mass balance equation. Without a general equation it is often difficult to know what these problem-specific versions of sediment mass balance leave out. To address this, we derive a general form of the standard Exner equation for sediment mass balance that includes effects of tectonic uplift and subsidence, soil formation and creep, compaction, and chemical precipitation and dissolution. The complete equation, (17), allows for independent evolution of two critical interfaces: that between bedrock and sediment or soil and that between sediment and flow. By eliminating terms from the general equation it is straightforward to derive mass balance equations applicable to a wide range of problems such as short-term bed evolution, basin evolution, bedrock uplift and soil formation, and carbonate precipitation and transport. Dropping terms makes explicit what is not being considered in a given problem and can be done by inspection or by a formal scaling analysis of the terms. Scaling analysis leads directly to dimensionless numbers that measure the relative importance of terms in the equation, for example, the relative influence of spatial versus temporal changes in sediment load on bed evolution. Combining scaling analysis with time averaging shows how the relative importance of terms in the equation can change with timescale; for example, the term representing bed evolution due to temporal change in sediment load tends to zero as timescale increases. Citation: Paola, C., and V. R. Voller (2005), A generalized Exner equation for sediment mass balance, J. Geophys. Res., 110, F04014, doi:10.1029/2004JF000274. 1. Introduction We hope that the proposed general form will be especially useful for geologic problems for which processes such as [2] An analysis of sediment mass balance is fundamental tectonic uplift and subsidence, soil formation and creep, and to solving a wide range of problems in morphodynamics. dissolution and precipitation become important. The relations in common use for expressing sediment mass [3] It is easy to overlook the fact that a model is defined balance take a variety of forms but are all descended from as much by what it leaves out as by what it includes. Using the equation initially presented by Exner and reproduced a general equation as a starting point makes this explicit: we below. The additions and changes that have been made to develop specialized relations for specific problems by Exner’s original equation have mostly been done piecemeal eliminating terms from the general equation. Elimination with the aim of adapting it for a particular problem. A of terms can be done by inspection or by formal scaling summary of the Exner equation including forms appropriate analysis. We give examples of how to estimate the magni- for channelized systems and sediment mixtures is presented tudes of different terms below, after deriving the general by Parker [2005], and detailed derivations of mass balance mass balance equation. Because surface evolution occurs on for soil-mantled hillslopes are presented by Anderson timescales from seconds to millions of years, we then [2002] and Mudd and Furbish [2004]. Both of the latter investigate the behavior of the general equation under time works also explicitly include chemical effects. Nonetheless, averaging. We conclude the paper by returning to one of the each of these mass balance equations includes some terms original motivations for it: the satisfaction of finding unity and leaves out others, according to the problem at hand. in apparently diverse phenomena. We hope that the exam- Here we revisit the Exner equation with the aim of provid- ples that conclude the paper, showing how the general mass ing a complete general form. This generality allows the balance equation can be specialized to a variety of problems equation to be specialized for application to a wide range of from classical morphodynamics to basin dynamics and morphodynamic problems by dropping or combining terms. carbonate precipitation, will illustrate how sediment mass balance can serve as one such unifying theme in surface 1Also at Department of Geology and Geophysics, University of dynamics. Minnesota Twin Cities, Minneapolis, Minnesota, USA. 2Also at Department of Civil Engineering, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA. 2. Exner’s Equation Copyright 2005 by the American Geophysical Union. [4] Felix Exner was a Viennese meteorologist who 0148-0227/05/2004JF000274 worked on a variety of topics in natural science. He F04014 1of8 F04014 PAOLA AND VOLLER: GENERALIZED SEDIMENT MASS BALANCE F04014 projected area of the material interfaces into the x-y plane is Axy and the closed circumference of this area is S. Mass conservation for this disk can be written as Z Z Z d a dV þ a u Á n dA À a ðÞu À v dt I I H I iþ1 V AZside Siþ1 Z Á niþ1dA þ aI ðÞu À vi Á ni dA À GdV ¼ 0 ð3Þ Si V where u =(u, v, w) is the material velocity, nH, the outward pointing unit normal on the area Aside, is in the horizontal x-y plane, and G is a volume rate of mass production or destruction. The unit normal on the ith material interface ni points from material layer I into material layer I-1 and from (2) can be calculated as Figure 1. Definition sketch for mass balance in a layer with arbitrary top and bottom boundaries. Âà rFi Sx; Sy; À1 ni ¼ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jjrFi 2 2 developed his equation for sediment mass balance as part of Sx þ Sy þ 1 a pair of remarkably sophisticated studies of river morphol- ogy [Exner, 1920, 1925]. The equation was brought to the @h @h where S = i and S = i are the material interface attention of the English-speaking world via the book by x @x y @y Leliavsky [1955]. The original equation given by Exner can tangent slopes in the x and y directions respectively. We be written as progress from (3) by noting that following the analysis presented by Crank [1984], @h @U ¼ÀA ð1Þ @t @x @hi 1 vi Á ni ¼À ð4Þ @t jjrFi where h is bed elevation relative to some fixed datum, t is time, A is a coefficient, U is average flow velocity, and x is (use the chain rule to take the total derivative of F in (2)) downstream distance. such that [5] In the text preceding the equation, Exner made clear that he intended the flow velocity U as a proxy for the Wi aI ðÞÁu À vi ni ¼ ð5Þ sediment flux. Thus the ‘‘Exner equation’’ is now written jjrFi with the sediment flux in place of the flow velocity. In addition, it has become standard to include a term repre- where senting temporal changes in sediment concentration. We will provide the standard modern form of the Exner equa- @h W ¼ a i þ uS þ vS À w ð6Þ tion below as a special case of a general mass balance i I @t x y equation. Wi is the mass flux across interface i and by our sign 3. General Derviation of Sediment Mass Balance convention is positive for flow from the Ith layer into the underlying (I-1)th layer. Further, an area element on Si can [6] It is natural to think of the outer part of the Earth in be equated to an area element on the projected area A terms of layers (for instance, rock, soil, water, etc.), noting qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xy 2 2 that these layers can have interfaces with complex geome- through the relationship dAi = 1 þ Sx þ Sy dAxy = try. Consider a layered material with each material layer I jrFijdAxy such that characterized by a distinct density aI and moving material Z Z interfaces defined by equations of the form YdA ¼ YjjrFi dA ð7Þ Si Axy FiðÞ¼x; y; z; t hiðÞÀx; y; t z ¼ 0 ð2Þ where Y(x, y) is an arbitrary function. where the subscript i refers to the material interface at the [7] Using (5) in (3) modifies the single-layer mass bottom of the Ith material layer and layer I + 1 is vertically balance to above layer I. A mass conservation equation for a given Z Z Z material layer in this system can be obtained by arbitrarily d Wiþ1 choosing, at an instant in time, a ‘‘disk’’ from the material aI dV þ aI u Á nH dA À dA dt jjrFiþ1 layer of interest (Figure 1). The volume V of the disk is V Z Asides Z Siþ1 defined by fixed vertical sidewalls of area Aside, a bottom W þ i dA À GdV ¼ 0 ð8Þ material interface of area Si and velocity vi, and a top jjrFi material interface of area Si+1 and velocity vi+1. The Si Vi 2of8 F04014 PAOLA AND VOLLER: GENERALIZED SEDIMENT MASS BALANCE F04014 Applying the divergence theorem to the contour integral around S reduces all terms in (11) to integrals over the projected area Axy Z Zhiþ1 Z @ a À G dz dA þ r Á F dA @t I H h Axy Z i Axy @h þ a iþ1 À W dA I @t iþ1 AZxy @h þ Àa i þ W dA ¼ 0 ð12Þ I @t i Axy hRiþ1 @ @ where rH =[@x, @y, 0] and F = aIudz is a line flux. Since hi the area Axy is arbitrary the sum of arguments in (12) has to be identically zero, leading to Zhiþ1 @ @h @h a dz þr Á F þ a iþ1 À a i À W þ W @t I H I @t I @t iþ1 i hi Zhiþ1 À Gdz ¼ 0 ð13aÞ hi which using the conventional Leibnitz rule is equivalent to Zhiþ1 Zhiþ1 @ a dz þr Á F À W þ W À Gdz ¼ 0 ð13bÞ @t I H iþ1 i hi hi Figure 2.
Load more

Recommended publications
  • Preliminary Catalog of the Sedimentary Basins of the United States
    Preliminary Catalog of the Sedimentary Basins of the United States By James L. Coleman, Jr., and Steven M. Cahan Open-File Report 2012–1111 U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior KEN SALAZAR, Secretary U.S. Geological Survey Marcia K. McNutt, Director U.S. Geological Survey, Reston, Virginia: 2012 For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprod To order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner. Suggested citation: Coleman, J.L., Jr., and Cahan, S.M., 2012, Preliminary catalog of the sedimentary basins of the United States: U.S. Geological Survey Open-File Report 2012–1111, 27 p. (plus 4 figures and 1 table available as separate files) Available online at http://pubs.usgs.gov/of/2012/1111/. iii Contents Abstract ...........................................................................................................................................................1
    [Show full text]
  • Modeling Subsurface Flow in Sedimentary Basins by CRAIG M
    129 Geologische Rundschau 78/1 I 129-154 I Stuttgart 1989 Modeling subsurface flow in sedimentary basins By CRAIG M. BETHKE, Urbana*) With 16 figures Zusammenfassung raines qui se manifestent dans les bassins sedimentaires, et qui resultent du relief topographique, de la convection, de la Grundwasserbewegungen in sedimentaren Becken, die compaction des sediments, de la decharge due l'erosio? et von dem topographischen Relief, konvektionsbedingtem a de la combinaison de ces divers facteurs. Dans ces modeles, Auftrieb, Sedimentkompaktion, isostatischen Ausgleichsbe­ on peut prendre en con~ideration les effets d~s tr:'nsferts d,e wegungen in Folge von Erosion und v~n ~mbinati~n~n chaleur et de matieres dlssoutes lors de la migration du pe­ dieser Kriifte gesteuert werden, konnen mit Hilfe quanutattv trole et ceux de I'interaction chimique de I'eau avec les modellierender Techniken beschrieben werden. In diesen roches. Toutefois la precision des previsions que I'on peut en Modellen kann man die Auswirkungen des Transports von deduire est limitee par la difficulte d'estimer I'echelle regia­ Warme und gel osten Stoffen, Petroleum-Migration und die a nale les proprietes hydrologiques des sediments, de reconsti­ chemische Interaktion zwischen Wasser und dem grund­ tuer les conditions anciennes, et de connaitre de quelle wasserleitenden Gestein beriicksichtigen. maniere les processus physiques et chimiques interferent Die Genauigkeit der Modell-Voraussagen ist allerdings a I'echelle des temps geologiques. La modelisation des bassins begrenzt wegen der Schwierigkeit, hydrologische Ei­ progressera dans la mesure ou la recherche hydrogeologique genschaften von Sedimenten in einem regionalen Rahmen ser mieux integree acelles d'autres disciplines telles que la se­ vorauszusagen, dem Schatzen vergangener Bedingungen und dimentologie, la mecanique des roches et la geochimie.
    [Show full text]
  • Palu Colostate 0053A 15347.Pdf
    DISSERTATION FLOODWAVE AND SEDIMENT TRANSPORT ASSESSMENT ALONG THE DOCE RIVER AFTER THE FUNDÃO TAILINGS DAM COLLAPSE (BRAZIL) Submitted by Marcos Cristiano Palu Department of Civil and Environmental Engineering In partial fulfillment of the requirements For the Degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Spring 2019 Doctoral Committee: Advisor: Pierre Julien Christopher Thornton Robert Ettema Sara Rathburn Copyright by Marcos Cristiano Palu 2019 All Rights Reserved ABSTRACT FLOODWAVE AND SEDIMENT TRANSPORT ASSESSMENT ALONG THE DOCE RIVER AFTER THE FUNDÃO TAILINGS DAM COLLAPSE (BRAZIL) The collapse of the Fundão Tailings Dam in November 2015 spilled 32 Mm3 of mine waste, causing a substantial socio-economic and environmental damage within the Doce River basin in Brazil. Approximately 90% of the spilled volume deposited over 118 km downstream of Fundão Dam on floodplains. Nevertheless, high concentration of suspended sediment (≈ 400,000 mg/l) reached the Doce River, where the floodwave and sediment wave traveled at different velocities over 550 km to the Atlantic Ocean. The one-dimensional advection- dispersion equation with sediment settling was solved to determine, for tailing sediment, the longitudinal dispersion coefficient and the settling rate along the river and in the reservoirs (Baguari, Aimorés and Mascarenhas). The values found for the longitudinal dispersion coefficient ranged from 30 to 120 m2/s, which are consistent with those in the literature. Moreover, the sediment settling rate along the whole extension of the river corresponds to the deposition of finer material stored in Fundão Dam, which particle size ranged from 1.1 to 2 . The simulation of the flashy hydrographs on the Doce River after the dam collapse was initially carried out with several widespread one-dimensional flood routing methods, including the Modified Puls, Muskingum-Cunge, Preissmann, Crank Nicolson and QUICKEST.
    [Show full text]
  • Fluvial Sedimentary Patterns
    ANRV400-FL42-03 ARI 13 November 2009 11:49 Fluvial Sedimentary Patterns G. Seminara Department of Civil, Environmental, and Architectural Engineering, University of Genova, 16145 Genova, Italy; email: [email protected] Annu. Rev. Fluid Mech. 2010. 42:43–66 Key Words First published online as a Review in Advance on sediment transport, morphodynamics, stability, meander, dunes, bars August 17, 2009 The Annual Review of Fluid Mechanics is online at Abstract fluid.annualreviews.org Geomorphology is concerned with the shaping of Earth’s surface. A major by University of California - Berkeley on 02/08/12. For personal use only. This article’s doi: contributing mechanism is the interaction of natural fluids with the erodible 10.1146/annurev-fluid-121108-145612 Annu. Rev. Fluid Mech. 2010.42:43-66. Downloaded from www.annualreviews.org surface of Earth, which is ultimately responsible for the variety of sedi- Copyright c 2010 by Annual Reviews. mentary patterns observed in rivers, estuaries, coasts, deserts, and the deep All rights reserved submarine environment. This review focuses on fluvial patterns, both free 0066-4189/10/0115-0043$20.00 and forced. Free patterns arise spontaneously from instabilities of the liquid- solid interface in the form of interfacial waves affecting either bed elevation or channel alignment: Their peculiar feature is that they express instabilities of the boundary itself rather than flow instabilities capable of destabilizing the boundary. Forced patterns arise from external hydrologic forcing affect- ing the boundary conditions of the system. After reviewing the formulation of the problem of morphodynamics, which turns out to have the nature of a free boundary problem, I discuss systematically the hierarchy of patterns observed in river basins at different scales.
    [Show full text]
  • Manuscript, Helped to Motivate the Work
    Long-Profile Evolution of Transport-Limited Gravel-Bed Rivers Andrew D. Wickert1 and Taylor F. Schildgen2,3 1Department of Earth Sciences and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, Minnesota, USA. 2Institut für Erd- und Umweltwissenschaften, Universität Potsdam, 14476 Potsdam, Germany. 3Helmholtz Zentrum Potsdam, GeoForschungsZentrum (GFZ) Potsdam, 14473 Potsdam, Germany. Correspondence to: A. D. Wickert ([email protected]) Abstract. Alluvial and transport-limited bedrock rivers constitute the majority of fluvial systems on Earth. Their long profiles hold clues to their present state and past evolution. We currently possess first-principles-based governing equations for flow, sediment transport, and channel morphodynamics in these systems, which we lack for detachment-limited bedrock rivers. Here we formally couple these equations for transport-limited gravel-bed river long-profile evolution. The result is a new predictive 5 relationship whose functional form and parameters are grounded in theory and defined through experimental data. From this, we produce a power-law analytical solution and a finite-difference numerical solution to long-profile evolution. Steady-state channel concavity and steepness are diagnostic of external drivers: concavity decreases with increasing uplift, and steepness increases with increasing sediment-to-water supply ratio. Constraining free parameters explains common observations of river form: To match observed channel concavities, gravel-sized sediments must weather and fine – typically rapidly – and valleys 10 must widen gradually. To match the empirical square-root width–discharge scaling in equilibrium-width gravel-bed rivers, downstream fining must occur. The ability to assign a cause to such observations is the direct result of a deductive approach to developing equations for landscape evolution.
    [Show full text]
  • Use of Sedimentary Megasequences to Re-Create Pre-Flood Geography
    The Proceedings of the International Conference on Creationism Volume 8 Print Reference: Pages 351-372 Article 27 2018 Use of Sedimentary Megasequences to Re-create Pre-Flood Geography Timothy L. Clarey Institute for Creation Research Davis J. Werner Institute for Creation Research Follow this and additional works at: https://digitalcommons.cedarville.edu/icc_proceedings Part of the Geology Commons, and the Stratigraphy Commons DigitalCommons@Cedarville provides a publication platform for fully open access journals, which means that all articles are available on the Internet to all users immediately upon publication. However, the opinions and sentiments expressed by the authors of articles published in our journals do not necessarily indicate the endorsement or reflect the views of DigitalCommons@Cedarville, the Centennial Library, or Cedarville University and its employees. The authors are solely responsible for the content of their work. Please address questions to [email protected]. Browse the contents of this volume of The Proceedings of the International Conference on Creationism. Recommended Citation Clarey, T.L., and D.J. Werner. 2018. Use of sedimentary megasequences to re-create pre-Flood geography. In Proceedings of the Eighth International Conference on Creationism, ed. J.H. Whitmore, pp. 351–372. Pittsburgh, Pennsylvania: Creation Science Fellowship. Clarey, T.L., and D.J. Werner. 2018. Use of sedimentary megasequences to re-create pre-Flood geography. In Proceedings of the Eighth International Conference on Creationism, ed. J.H. Whitmore, pp. 351–372. Pittsburgh, Pennsylvania: Creation Science Fellowship. USE OF SEDIMENTARY MEGASEQUENCES TO RE-CREATE PRE-FLOOD GEOGRAPHY Timothy L. Clarey, Institute for Creation Research, 1806 Royal Lane, Dallas, TX 75229 USA, [email protected] Davis J.
    [Show full text]
  • Autogenic Cycles of Channelized Fluvial and Sheet Flow and Their
    RESEARCH Autogenic cycles of channelized fl uvial and sheet fl ow and their potential role in driving long-runout gravel pro- gradation in sedimentary basins Todd M. Engelder and Jon D. Pelletier* DEPARTMENT OF GEOSCIENCES, UNIVERSITY OF ARIZONA, 1040 E. FOURTH STREET, TUCSON, ARIZONA 85721, USA ABSTRACT The paleoslope estimation method uses a threshold-shear-stress criterion, together with fi eld-based measurements of median grain size and channel depth in alluvial gravel deposits, to calculate the threshold paleoslopes of alluvial sedimentary basins. Threshold paleoslopes are the minimum slopes that would have been necessary to transport sediment in those basins. In some applications of this method, inferred threshold paleoslopes are suffi ciently steeper than modern slopes that large-magnitude tectonic tilting must have occurred in order for sediments to have been transported to their present locations. In this paper, we argue that autogenic cycles of channelized fl uvial and sheet fl ow in alluvial sedimentary basins result in spatial and temporal variations in the threshold slope of gravel transport that can, under certain conditions, cause gravel to prograde out to distances much longer than previously thought possible based on paleoslope estima- tion theory (i.e., several hundred kilometers or more from a source region). We test this hypothesis using numerical models for two types of sedimentary basins: (1) an isolated sedimentary basin with a prescribed source of sediment from upstream, and (2) a basin dynamically coupled to a postorogenic mountain belt. In the models, threshold slopes for entrainment are varied stochastically through time with an amplitude equal to that inferred from an analysis of channel geometry data from modern rivers.
    [Show full text]
  • Introduction to Morphodynamics of Sedimentary Patterns
    MORPHODYNAMICS OF SEDIMENTARY PATTERNS Paolo Blondeaux, Marco Colombini, Giovanni Seminara, Giovanna Vittori Introduction to Morphodynamics of Sedimentary Patterns DIDATTICARICERCA RICERCA Genova University Press Monograph Series Morphodynamics of Sedimentary Patterns Editorial Board: Paolo Blondeaux, Marco Colombini Giovanni Seminara, Giovanna Vittori Advisory Board: Sivaramakrishnan Balachandar (University of Florida U.S.A.) Maurizio Brocchini (Università Politecnica delle Marche, Italy) François Charru (Université Paul Sabatier, France) Giovanni Coco (University of Auckland, New Zealand) Enrico Foti (Università di Catania, Italy) Marcelo H. Garcia (University of Illinois, U.S.A.) Suzanne J.M.H. Hulscher (University of Twente, NL) Stefano Lanzoni (Università di Padova, Italy) Miguel A. Losada (University of Granada, Spain) Chris Paola (University of Minnesota, U.S.A.) Gary Parker (University of Illinois U.S.A.) Luca Ridolfi(Politecnico di Torino, Italy) Andrea Rinaldo (École Polytechnique Fédérale de Lausanne, Switzerland) Yasuyuki Shimizu (Hokkaido University, Japan) Marco Tubino (Università di Trento, Italy) Markus Uhlmann (Karlsruhe Institute of Technology, Germany) Introduction to Morphodynamics of Sedimentary Patterns Paolo Blondeaux, Marco Colombini, Giovanni Seminara, Giovanna Vittori Introduction to Morphodynamics of Sedimentary Patterns is the bookmark of the University of Genoa On the cover: The delta of Lena river (Russia). The image was taken on July 27, 2000 by the Landsat 7 satellite operated by the U.S. Geological Survey and NASA (false-color composite image made using shortwave infrared, infrared, and red wavelengths). Image credit: NASA This book has been object of a double peer-review according with UPI rules. Publisher GENOVA UNIVERSITY PRESS Piazza della Nunziata, 6 16124 Genova Tel. 010 20951558 Fax 010 20951552 e-mail: [email protected] e-mail: [email protected] http://gup.unige.it/ The authors are at disposal for any eventual rights about published images.
    [Show full text]
  • Macro-Roughness Model of Bedrock–Alluvial River Morphodynamics
    Earth Surf. Dynam., 3, 113–138, 2015 www.earth-surf-dynam.net/3/113/2015/ doi:10.5194/esurf-3-113-2015 © Author(s) 2015. CC Attribution 3.0 License. Macro-roughness model of bedrock–alluvial river morphodynamics L. Zhang1, G. Parker2, C. P. Stark3, T. Inoue4, E. Viparelli5, X. Fu1, and N. Izumi6 1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, China 2Department of Civil & Environmental Engineering and Department of Geology, Hydrosystems Laboratory, University of Illinois, Urbana, IL, USA 3Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA 4Civil Engineering Research Institute for Cold Regions, Hiragishi Sapporo, Japan 5Dept. of Civil & Environmental Engineering, University of South Carolina, Columbia, SC, USA 6Faculty of Engineering, Hokkaido University, Sapporo, Japan Correspondence to: L. Zhang ([email protected]) Received: 14 April 2014 – Published in Earth Surf. Dynam. Discuss.: 27 May 2014 Revised: 6 January 2015 – Accepted: 6 January 2015 – Published: 11 February 2015 Abstract. The 1-D saltation–abrasion model of channel bedrock incision of Sklar and Dietrich (2004), in which the erosion rate is buffered by the surface area fraction of bedrock covered by alluvium, was a major advance over models that treat river erosion as a function of bed slope and drainage area. Their model is, however, limited because it calculates bed cover in terms of bedload sediment supply rather than local bedload transport. It implicitly assumes that as sediment supply from upstream changes, the transport rate adjusts instantaneously everywhere downstream to match. This assumption is not valid in general, and thus can give rise to unphysical consequences.
    [Show full text]
  • Comparing 2-D and 1-D/2-D Modelling of Agly River Bed Change During a Flood S
    Comparing 2-D and 1-D/2-D modelling of Agly River bed change during a flood S. Mezbache, André Paquier, M. Hasbaia To cite this version: S. Mezbache, André Paquier, M. Hasbaia. Comparing 2-D and 1-D/2-D modelling of Agly River bed change during a flood. River Flow 2020, Jul 2020, Delft, Netherlands. pp.704-710, 10.1201/b22619. hal-03107142 HAL Id: hal-03107142 https://hal.archives-ouvertes.fr/hal-03107142 Submitted on 12 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Comparing 2-D and 1-D/2-D modelling of Agly River bed change during a flood S. Mezbache M’sila University, M’sila, Algeria A. Paquier INRAE, U.R. RiverLy, Villeurbanne, France M. Hasbaia M’sila University, M’sila, Algeria ABSTRACT: The authors discuss the use of a 1-D model or a 2-D model for the evolution of the bed between the levees while the spreading of water and sediment over the floodplains is simu- lated using a 2-D model. A 1-D model cannot represent the asymmetrical behaviour of the flow in the bends but makes easier the estimate of the variations of the sediment transport capacity along the river if the bed geometry is complex.
    [Show full text]
  • The Evolution of Sedimentary Basins
    802 Nature Vol. 292 27 August 1981 intracellular metabolic processes and the potentials'' or radial propagation along In the session on basin formation, A.B. binding of charged dye molecules might muscle fibre T -tubules12 • These, together Watts (Lamont-Doherty Geological interfere with important membrane with the elegant studies of Kamino, Hirota Observatory) discussed the role of crustal processes mediating biological responses. and Fujii', suggest that such techniques flexure, showing that this becomes a major In addition, dyes may react with the have an important future in many factor in basins more than 200 km wide and exogenous reagents, whose effects are investigations involving molecular that the best overall fit to the observations being examined, to form non-fluorescent mechanisms at the cellular level. [] is an elastic plate model with crustal complexes. This would make dose­ strength increasing with age. This predicts response curves difficult to interpret and l. Kamino, K., Hirota, A. & Fujii, S. Nature 290, 595 a sedimentary geometry with coastal on lap would complicate kinetic calculations. (1981). and it seems that Vail's eustatic sea-level 2. Cohen. L.B. eta/. J. Membrane Bioi. 19,1 (1974). Furthermore, even with modest 3. Ross, W.N. eta/. J. Membrane Bioi. 33, 141 (1977). changes based on evidence of onlap may in illuminations, some dyes can cause cellular 4. Hoffman, J.F. & Laris, P.C. J. Physiol., Lond. 239, reality be a record of basin subsidence. The 519 (1974). photodynamic damage. These con­ 5. Sims, P.J. et al. Biochemistry 13, 3315 (1974). thermal effects of subsidence were siderations have prompted intensive work 6.
    [Show full text]
  • Three Dimensional Mobile Bed Dynamics for Sediment Transport Modeling
    THREE DIMENSIONAL MOBILE BED DYNAMICS FOR SEDIMENT TRANSPORT MODELING DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Sean O’Neil, B.S., M.S. ***** The Ohio State University 2002 Dissertation Committee: Approved by Professor Keith W. Bedford, Adviser Professor Carolyn J. Merry Adviser Professor Diane L. Foster Civil Engineering Graduate Program c Copyright by Sean O’Neil 2002 ABSTRACT The transport and fate of suspended sediments continues to be critical to the understand- ing of environmental water quality issues within surface waters. Many contaminants of environmental concern within marine and freshwater systems are hydrophobic, thus read- ily adsorbed to bed material or suspended particles. Additionally, management strategies for evaluating and remediating the effects of dredging operations or marine construction, as well as legacy pollution from military and industrial processes requires knowledge of sediment-water interactions. The dynamic properties within the bed, the bed-water column inter-exchange and the transport properties of the flowing water is a multi-scale nonlin- ear problem for which the mobile bed dynamics with consolidation (MBDC) model was formulated. A new continuum-based consolidation model for a saturated sediment bed has been developed and verified on a stand-alone basis. The model solves the one-dimensional, vertical, nonlinear Gibson equation describing finite-strain, primary consolidation for satu- rated fine sediments. The consolidation problem is a moving boundary value problem, and has been coupled with a mobile bed model that solves for bed level variations and grain size fraction(s) in time within a thin layer at the bed surface.
    [Show full text]