Analytical Solution for Anomalous Diffusion of Bedload Tracers Gradually Undergoing Burial

Wu Zi; Foufoula‐Georgiou Efi; Parker Gary; Singh Arvind; Fu Xudong; Wang Guangqian

摘要

Abstract > Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2‐D Exner‐Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection‐diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion‐induced scaling ( type="mathematics"> ∝ t 1 ) and an advection‐induced scaling ( type="mathematics"> ∝ t 3 ) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> >床单运输过程中示踪剂粒子的埋葬是追踪器的重要组成部分在河流中分散。在此提出修改过的有源层制剂，其占埋葬和承认分析解决方案的影响，使床单示踪剂在中间时间尺度上的超光探索能够欣赏探索。使用基于2-D Excer的主方程，近来的数值结果已经观察到这种现象。通过假设有源层中的示踪剂可以在衬底层中与非游客颗粒交换以保持质量，并且进入基底层的示踪剂在分析的时间段期间永久捕获，我们能够推断出两者的示踪浓度的控制方程层。有源层示踪浓度被示出为由具有沉降项的平行扩散方程来控制，并且基板层中的示踪剂的增加由相应的源术语驱动。用于分析示踪群的方差的解决方案，并且可以通过扩散诱导的缩放的总和来近似（<跨度型=“数学”>α T </ i> 1 </ sup> </ span>）和平流诱导的缩放（ type =“数学”>α t 3 </ sup> </ span>）术语，其解释说明超极地的现象。所提出的制剂被证明能够通过与数值模拟的可用结果进行比较来捕获示踪传输的关键特性。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-34664/'>《Journal of geophysical research. Earth Surface: JGR》</a> <b style="margin: 0 2px;">|</b><span>2019年第1期</span><b style="margin: 0 2px;">|</b><span>共17页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Zi&option=202" target="_blank" rel="nofollow">Wu Zi;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Foufoula‐Georgiou Efi&option=202" target="_blank" rel="nofollow">Foufoula‐Georgiou Efi;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Parker Gary&option=202" target="_blank" rel="nofollow">Parker Gary;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Singh Arvind&option=202" target="_blank" rel="nofollow">Singh Arvind;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Fu Xudong&option=202" target="_blank" rel="nofollow">Fu Xudong;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wang Guangqian&option=202" target="_blank" rel="nofollow">Wang Guangqian;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of Civil and Environmental EngineeringUniversity of California IrvineIrvine CA USA;</p> <p>Department of Civil and Environmental EngineeringUniversity of California IrvineIrvine CA USA;</p> <p>Department of Civil and Environmental Engineering and Department of Geology Hydrosystems LaboratoryUniversity of Illinois at Urbana‐ChampaignUrbana IL USA;</p> <p>Department of Civil Environmental and Construction EngineeringUniversity of Central FloridaOrlando FL USA;</p> <p>State Key Laboratory of Hydroscience and Engineering;</p> <p>Department of Hydraulic EngineeringTsinghua UniversityBeijing China;</p> <p>State Key Laboratory of Hydroscience and Engineering;</p> <p>Department of Hydraulic EngineeringTsinghua UniversityBeijing China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span>TP79:P3; </span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=bedload transport&option=203" rel="nofollow">bedload transport;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=tracer burial&option=203" rel="nofollow">tracer burial;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=anomalous diffusion&option=203" rel="nofollow">anomalous diffusion;</a> </p> <div class="translation"> 机译：床单运输;示踪剂埋葬;异常扩散; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704025586786.html">Analytical Solution for Anomalous Diffusion of Bedload Tracers Gradually Undergoing Burial</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wu Zi&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Wu Zi,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Foufoula‐Georgiou Efi&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Foufoula‐Georgiou Efi,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Parker Gary&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Parker Gary,</a> <a href="/journal-foreign-34664/" target="_blank" rel="nofollow" class="tuijian_authcolor">Journal of geophysical research. 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href="/conference-cn-32300/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 中国水利学会勘测专业委员会2000年学术研讨会 </a> <span> <span> . 2000</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020316297887.html">该课题对国内外孕妇装方面的研究成果进行了梳理,基于孕妇装方面的研究成果,结合孕期女性身心的变化特点,开展了职场环境下孕妇装设计方法的探索和实践研究。针对孕妇不同阶段体形、心理变化的特点,以服装学、色彩心理学、服装材料学、纸样设计原理等为理论基础,满足孕妇对服装外部廓形、内部结构、色彩、面料的需求。接着,在职场女性着装特点以及着装规范的基础上,给出职场环境下孕妇装的设计方案,并进行设计实践。该课题的研究可以为孕期女性的职场穿衣问题提供可行的解决方案,并为孕妇装品牌产品线的开发提供设计实践方面的借鉴。</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=孙希璐&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 孙希璐</a> <span> . 2021</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120101406059.html">用于通过示踪剂分析法对复杂异质群落进行微生物株系分析、确定其功能关系及相互作用以及合成包括给药微生物群集和接种微生物群集的微生物群集的方法、设备和系统</a> <b>[P]</b> . <span> 中国专利： CN110352250A </span> <span> . 2019-10-18</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120106220735.html">一种在环境突发事件中利用三维GIS进行扩散模拟分析的系统</a> <b>[P]</b> . <span> 中国专利： CN102013052A </span> <span> . 2011-04-13</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130407426806.html">Method, controller, and magnetic resonance apparatus for model-free determination of image regions with anomalous diffusion using diffusion-weighted magnetic resonance image data</a> <b>[P]</b> . <span> 外国专利：  US10006979B2 </span> <span> . 2018-06-26</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于使用扩散加权磁共振图像数据无模型确定异常扩散的图像区域的方法，控制器和磁共振设备 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130410134799.html">METHOD, CONTROLLER, AND MAGNETIC RESONANCE APPARATUS FOR MODEL-FREE DETERMINATION OF IMAGE REGIONS WITH ANOMALOUS DIFFUSION USING DIFFUSION-WEIGHTED MAGNETIC RESONANCE IMAGE DATA</a> <b>[P]</b> . <span> 外国专利：  US2017234956A1 </span> <span> . 2017-08-17</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：利用扩散加权磁共振图像数据无模型确定含异常扩散图像区域的方法，控制器和磁共振装置 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130441279182.html">Use of molecules as analytical tracers which makes it possible to ensure the tracabilite qualitative and quantitative composition of the incorporation of the first material or of the active substance in any of the finished product</a> <b>[P]</b> . <span> 外国专利：  FR2782386B1 </span> <span> . 2004-05-28</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> 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