<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<front>
<journal-meta>
<journal-id journal-id-type="publisher">ADGEO</journal-id>
<journal-title-group>
<journal-title>Advances in Geosciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">ADGEO</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Adv. Geosci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1680-7359</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/adgeo-37-1-2013</article-id>
<title-group>
<article-title>Tracer dispersion in bedload transport</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Lajeunesse</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Devauchelle</surname>
<given-names>O.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Houssais</surname>
<given-names>M.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Seizilles</surname>
<given-names>G.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Institut de Physique du Globe &amp;ndash; Sorbonne Paris Cité, Équipe de Dynamique des fluides géologiques, 1 rue Jussieu, 75238 Paris cedex 05, France</addr-line>
</aff>
<pub-date pub-type="epub">
<day>17</day>
<month>12</month>
<year>2013</year>
</pub-date>
<volume>37</volume>
<fpage>1</fpage>
<lpage>6</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2013 E. Lajeunesse et al.</copyright-statement>
<copyright-year>2013</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://adgeo.copernicus.org/articles/37/1/2013/adgeo-37-1-2013.html">This article is available from https://adgeo.copernicus.org/articles/37/1/2013/adgeo-37-1-2013.html</self-uri>
<self-uri xlink:href="https://adgeo.copernicus.org/articles/37/1/2013/adgeo-37-1-2013.pdf">The full text article is available as a PDF file from https://adgeo.copernicus.org/articles/37/1/2013/adgeo-37-1-2013.pdf</self-uri>
<abstract>
<p>Bedload particles entrained by rivers tends to disperse as they move
downstream. In this paper, we use the erosion-deposition model of
Charru et al. (2004) to describe the velocity and the spreading of a plume of
tracer particles. We restrict our analysis to steady-state transport above a
flat bed of uniform sediment. The transport of tracer particles is then
controlled by downstream advection and particle exchange with the immobile
bed. After a transitional regime dominated by initial conditions, the
evolution of a plume of markers tends asymptotically towards classical
advection-diffusion: its average position grows linearly with time, whereas
it spreads like the square root of time.</p>
</abstract>
<counts><page-count count="6"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Ancey, C., Davison, A., Bohm, T., Jodeau, M., and Frey, P.: Entrainment and motion of coarse particles in a shallow water stream down a steep slope, J. Fluid Mech., 595, 83–114, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112007008774&quot;&gt;https://doi.org/10.1017/S0022112007008774&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Bagnold, R.: Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear, P. Roy. Soc. A-Math. Phy., 49–63, 1954.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bradley, D. N., Tucker, G. E., and Benson, D. A.: Fractional dispersion in a sand bed river, J. Geophys. Res., 115, F00A09, &lt;a href=&quot;http://dx.doi.org/10.1029/2009JF001268&quot;&gt;https://doi.org/10.1029/2009JF001268&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Carretier, S., Regard, V., and Soual, C.: In situ cosmogenic nuclides in river bedload. Implications for catchment-scale erosion rate and surface exposure dating, Geochim. Cosmochim. Ac., 71, A147–A147, 2007.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Carretier, S., Regard, V., and Soual, C.: Theoretical cosmogenic nuclide concentration in river bed load clasts: Does it depend on clast size?, Quat. Geochronol., 4, 108–123, 2009.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Cerling, T. E., Morrison, S. J., Sobocinski, R. W., and Larsen, I. L.: Sediment-water interaction in a small stream: Adsorption of 137Cs by bed load sediments, Water Resour. Res., 26, 1165–1176, 1990.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Charru, F.: Selection of the ripple length on a granular bed sheared by a liquid flow, Phys. Fluids, 18, 121508-1–121508-9, &lt;a href=&quot;http://dx.doi.org/10.1063/1.2397005&quot;&gt;https://doi.org/10.1063/1.2397005&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Charru, F., Mouilleron, H., and Eiff, O.: Erosion and deposition of particles on a bed sheared by a viscous flow, J. Fluid Mech., 519, 55–80, 2004.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Durán, O., Andreotti, B., and Claudin, P.: Numerical simulation of tubulent sediment transport, from bed load to saltation, Phys. Fluids, 24, 2012.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Einstein, H.: The bed-load function for sediment transportation in open channel flows, US Department of Agriculture, Soil Conservation Service, 1950.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Ferguson, R. and Wathen, S.: Tracer-pebble movement along a concave river profile: Virtual velocity in relation to grain size and shear stress, Water Resour. Res., 34, 2031–2038, 1998.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Furbish, D., Ball, A., and Schmeeckle, M.: A probabilistic description of the bed load sediment flux: 4. Fickian diffusion at low transport rates, J. Geophys. Res., 117, F03034, &lt;a href=&quot;http://dx.doi.org/10.1029/2012JF002356&quot;&gt;https://doi.org/10.1029/2012JF002356&lt;/a&gt;, 2012a.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Furbish, D., Roseberry, J., and Schmeeckle, M.: A probabilistic description of the bed load sediment flux: 3. The particle velocity distribution and the diffusive flux, J. Geophys. Res., 117, F03033, &lt;a href=&quot;http://dx.doi.org/10.1029/2012JF002355&quot;&gt;https://doi.org/10.1029/2012JF002355&lt;/a&gt;, 2012b.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Gayer, E., Mukhopadhyay, S., and Meade, B. J.: Spatial variability of erosion rates inferred from the frequency distribution of cosmogenic &lt;sup&gt;3&lt;/sup&gt;He in olivines from Hawaiian river sediments, Earth Planet. Sci. Lett., 266, 303–315, 2008.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Habersack, H.: Radio-tracking gravel particles in a large braided river in New Zealand: A field test of the stochastic theory of bed load transport proposed by Einstein, Hydrol. Process. 15, 377–391, 2001.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Haschenburger, J. K. and Church, M.: Bed material transport estimated from the virtual velocity of sediment, Earth Surf. Proc. Land., 23, 791–808, 1998.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Hassan, M. A. and Ergenzinger, P.: Use of tracers in fluvial geomorphology, Tools in fluvial geomorphology, 397–423, 2003.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Lajeunesse, E., Malverti, L., and Charru, F.: Bedload transport in turbulent flow at the grain scale: experiments and modeling, J. Geophys. Res. Earth Surf., 115, F04001, &lt;a href=&quot;http://dx.doi.org/10.1029/2009JF001628&quot;&gt;https://doi.org/10.1029/2009JF001628&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Martin, R. L., Jerolmack, D. J., and Schumer, R.: The physical basis for anomalous diffusion in bed load transport, J. Geophys. Res., 117, F01018, &lt;a href=&quot;http://dx.doi.org/10.1029/2011JF002075&quot;&gt;https://doi.org/10.1029/2011JF002075&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">McNamara, J. P. and Borden, C.: Observations on the movement of coarse gravel using implanted motion-sensing radio transmitters, Hydrol. Process., 18, 1871–1884, 2004.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Meyer-Peter, E. and Müller, R.: Formulas for Bed-Load Transport, in: Proceedings, 2nd Congress, International Association of Hydraulic Research, edited by: Stockholm, S., 39–64, 1948.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Reid, I., Frostick, L. E., and Layman, J. T.: The incidence and nature of bedload transport during flood flows in coarse-grained alluvial channels, Earth Surf. Proc. Land., 10, 33–44, 1985.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Sayre, W. and Hubbell, D.: Transport and dispersion of labeled bed material, North Loup River, Nebraska, Tech. Rep. 433-C, U.S. Geol. Surv. Prof. Pap., 1965.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Schmidt, K.-H. and Ergenzinger, P.: Bedload entrainment, travel lengths, step lengths, rest periods – Studied with passive (iron, magnetic) and active (radio) tracer techniques, Earth Surf. Proc. Land., 17, 147–165, 2006.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Shields, A. S.: Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung, Mitteilung der Preussischen Versuchsanstalt für Wasserbau und Schiffbau, 26, 1936.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Taylor, G.: Dispersion of soluble matter in solvent flowing slowly through a tube, P. Roy. Soc. A-Math. Phy., 219, 186–203, 1953.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Wilcock, P. R.: Entrainment, displacement and transport of tracer gravels, Earth Surf. Proc. Land., 22, 1125–1138, 1997.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Willenbring, J. K. and von Blanckenburg, F.: Meteoric cosmogenic Beryllium-10 adsorbed to river sediment and soil: Applications for Earth-surface dynamics, Earth Sci. Rev., 98, 105–122, 2010.</mixed-citation>
</ref>
</ref-list>
</back>
</article>