Boltzmann Distribution of Sediment Transport.
TL;DR: This work tracks particles in a laboratory flume to relate their statistical behavior to the self-organization of the granular bed they make up, and finds that as they travel downstream, the transported grains wander randomly across the bed's surface, thus inducing cross-stream diffusion.
Abstract: The coupling of sediment transport with the flow that drives it allows rivers to shape their own bed. Cross-stream fluxes of sediment play a crucial, yet poorly understood, role in this process. Here, we track particles in a laboratory flume to relate their statistical behavior to the self-organization of the granular bed they make up. As they travel downstream, the transported grains wander randomly across the bed's surface, thus inducing cross-stream diffusion. The balance of diffusion and gravity results in a peculiar Boltzmann distribution, in which the bed's roughness plays the role of thermal fluctuations, while its surface forms the potential well that confines the sediment flux.
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01 Jan 2006
TL;DR: The mysterious rattleback and its fluid counterpart：Developments in shear instabilities（Patrick Huerre，Falling clouds＋Elisabeth Guazzelli）ＬEcotectural fluid mechanics％Herbert Huppert ）
Abstract: 流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．
767 citations
01 Jan 1988
TL;DR: In this article, it has been shown that suspension by fluid turbulence of mineral solids larger than those of medium sands does not become appreciable until the bed shear stress is increased to a value exceeding 12 times its threshold value for the bed material considered.
Abstract: Owing to observational difficulties the distinction between a ‘suspended’ load of solids transported by a stream and a ‘ bed-load ’ has long remained undefined. Recently, however, certain critical experiments have thrown much light on the nature of bed-load transport. In particular, it has been shown that bed-load transport, by saltation, occurs in the absence of fluid turbulence and must therefore be due to a separate dynamic process from that of transport in suspension by the internal eddy motion of a turbulent fluid. It has been further shown that the forward motion of saltating solids is opposed by a frictional force of the same order as the immersed weight of the solids, the friction coefficient approximating to that given by the angle of slip. The maintenance of steady motion therefore requires a predictable rate of energy dissipation by the transporting fluid. The fluid thrust necessary to maintain the motion is shown to be exerted by virtue of a mean slip velocity which is predictable in the same way as, and approxim ates to, the terminal fall velocity of the solid. The mean thrust, and therefore the transport rate of saltating solids, are therefore predictable in terms of the fluid velocity close to the bed, at a distance from it, within the saltation zone, of a ‘centre of fluid thrust’ analogous to the ‘centre of pressure’. This velocity, which is not directly measurable in water streams, can be got from a knowledge of stream depth and mean flow velocity. Thus a basic energy equation is obtained relating the rate of transporting work done to available fluid transporting power. This is shown to be applicable to the transport both of wind-blown sand, and of water-driven solids of all sizes and larger than that of medium sand. Though the mean flow velocity is itself unpredictable, the total stream power, which is the product of this quantity times the bed shear stress, is readily measurable. But since the mean flow velocity is an increasing function of flow depth, the transport of solids expressed in terms of total stream power must decrease with increasing flow depth/grain size ratio. This considerable variation with flow depth has not been previously recognised. It explains the gross inconsistencies found in the existing experimental data. The theoretical variation is shown to approximate very closely to that found in recent critical experiments in which transport rates were measured at different constant flow depths. The theory, which is largely confirmed by these and other earlier experiments, indicates that suspension by fluid turbulence of mineral solids larger than those of medium sands does not become appreciable until the bed shear stress is increased to a value exceeding 12 times its threshold value for the bed material considered. This range of unsuspended transport decreases rapidly, however, as the grain size is reduced till, at a certain critical size, suspension should occur at the threshold of bed movement.
39 citations
TL;DR: It is shown that, at equilibrium, the river shapes its channel so that the intensity of sediment transport follows a Boltzmann distribution, which selects a well-defined width over which the river transports sediment, while the sediment remains virtually idle on its banks.
Abstract: An alluvial river builds its own bed with the sediment it transports; its shape thus depends not only on its water discharge but also on the sediment supply. Here we investigate the influence of the latter in laboratory experiments. We find that, as their natural counterpart, laboratory rivers widen to accommodate an increase of sediment supply. By tracking individual particles as they travel downstream, we show that, at equilibrium, the river shapes its channel so that the intensity of sediment transport follows a Boltzmann distribution. This mechanism selects a well-defined width over which the river transports sediment, while the sediment remains virtually idle on its banks. For lack of a comprehensive theory, we represent this behavior with a single-parameter empirical model which accords with our observations.
7 citations
TL;DR: In this paper, the authors present measurements of particle motion over bedform topography obtained in a laboratory flume and compare these to particle motions over plane bed topography with otherwise similar conditions.
Abstract: The joint probability distribution of streamwise particle hop distance, lateral particle hop distance, and travel time constrains the relationships between topographic change and sediment transport at the granular scale. Previous studies have investigated the ensemble characteristics of particle motions over plane bed topography; however, it is unclear whether reported distributions remain valid when bedforms are present. Here, we present measurements of particle motion over bedform topography obtained in a laboratory flume and compare these to particle motions over plane bed topography with otherwise similar conditions. We find substantial differences in particle motion in the presence of bedforms that are relevant to macroscopic models of sediment transport. Most notably, bedforms increase the standard deviation of streamwise and lateral hop distances relative to the mean streamwise hop distance. This implies that bedforms increase the streamwise and lateral diffusion lengths and, equivalently, increase diffusive-like fluxes.
7 citations
Cites background from "Boltzmann Distribution of Sediment ..."
...This work is primarilymotivated bymacroscopicmorphodynamicmodeling problems (e.g., Abramian et al., 2019) for which the most important features of these distributions are the statistical moments contained in Equations 3–5....
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TL;DR: In this article, the authors investigated the growth of subaqueous barchans consisting of bidisperse grains and found that the grain distribution within the dune changes with the employed pair.
Abstract: Barchans are dunes of crescentic shape found on Earth, Mars and other celestial bodies, growing usually on polydisperse granular beds. In this Letter, we investigate experimentally the growth of subaqueous barchans consisting of bidisperse grains. We found that the grain distribution within the dune changes with the employed pair, and that a transient stripe appears on the dune surface. We propose that observed patterns result from the competition between fluid entrainment and easiness of rolling for each grain type, and that grains segregate with a diffusion-like mechanism. Our results provide new insights into barchan structures found in other environments.
5 citations
References
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TL;DR: In this paper, algorithms for the solution of the general assignment and transportation problems are presen, and the algorithm is generalized to one for the transportation problem.
Abstract: In this paper we presen algorithms for the solution of the general assignment and transportation problems. In Section 1, a statement of the algorithm for the assignment problem appears, along with a proof for the correctness of the algorithm. The remarks which constitute the proof are incorporated parenthetically into the statement of the algorithm. Following this appears a discussion of certain theoretical aspects of the problem. In Section 2, the algorithm is generalized to one for the transportation problem. The algorithm of that section is stated as concisely as possible, with theoretical remarks omitted.
3,918 citations
TL;DR: First the freefem++ software deals with mesh adaptation for problems in two and three dimension, second, it solves numerically a problem with phase change and natural convection, and finally to show the possibilities for HPC the software solves a Laplace equation by a Schwarz domain decomposition problem on parallel computer.
Abstract: This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.
2,867 citations
01 Jan 2006
TL;DR: The mysterious rattleback and its fluid counterpart：Developments in shear instabilities（Patrick Huerre，Falling clouds＋Elisabeth Guazzelli）ＬEcotectural fluid mechanics％Herbert Huppert ）
Abstract: 流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．
767 citations
"Boltzmann Distribution of Sediment ..." refers background in this paper
...To do so, however, rivers need to transport sediment not only downstream, but also across the flow [18, 19]....
[...]
TL;DR: In this paper, a stability analysis of a sinuous channel with erodible banks allows for delineation of a bend instability that does not occur in straight channels, and differs from the alternate-bar instability.
Abstract: Instability of the alternate-bar type in straight channels has long been identified as the cause of fluvial meandering. The condition of inerodible sidewalls, however, does not allow a meandering channel to develop. Herein a stability analysis of a sinuous channel with erodible banks allows for delineation of a ‘bend’ instability that does not occur in straight channels, and differs from the alternate-bar instability.In the case of alluvial meanders, the two mechanisms are shown to operate at similar characteristic wavelengths. This provides a rationale for the continuous evolution of alternate bars into true bends such that each bend contains one alternate bar.The same bend instability applies to incised meanders. A mechanism for incised alternate bars which differs from that for the alluvial case appears to operate at different characteristic wavelengths than that of bend instability. Analysis of data suggests that meandering in supraglacial meltwater streams is primarily due to the alternate bar mechanism, whereas the meandering of rills incised in cohesive material and of caves is likely due to the bend mechanism.The meander wavelength of incised reaches of meandering streams is often longer than that of adjacent alluvial reaches. An explanation is offered in terms of bend instability.
640 citations