Mathematical Analysis of a Model of River Channel Formation

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.     

MORPHOLOGICAL DEVELOPMENT OF ANATURE-LIKE BANK PROTECTION

1 INTRODUCTIONFor the pmpose of river restoration of the river Isar in the city area of Munich several inveshgationswere cAned out at the InshtUte for Hydrosciences, German Armed Forces University Munich. The calculation ofwater level for the differnt planned variants were realized by a 2d mathematical model. Although thesesimulahons were a very helpfol basis for fuIther planing, a physical model was constrUcted in order toinvestigate detalled problems.The main interest was focussed …     

Sediment budget and riverbed deformation in the uppermost part of the lower Yangtze River,China

The Yangtze River(YR), similar to most large rivers in the world, has experienced significant changes in its depositional environment due to anthropogenic disturbances and climatic influences in recent decades. However, knowledge of how the river channel and bed deformation respond to these changes in the uppermost part of the lower YR, a 200-km-long branched channel, is limited. In the current study,historical bathymetric data collected from 1992 to 2013 and high-resolution multibeam echo sound...     

Migration rate of river bends estimated by tree ring analysis for a meandering river in the source region of the Yellow River

Meandering rivers have dynamic evolution characteristics of lateral migration and longitudinal creeping movement, and studies on the migration rate of meandering rivers have both scientific and practical significance for understanding the evolution process. A river source region often is sparsely populated and lacks long-term monitoring data, making it difficult to estimate the migration rate of river bends. In the source region of the Yellow River, located in the northeastern part of the Qinghai-Tibet Plateau, China, meandering rivers have extensively developed. Combined with field investigation and sampling in the source region in 2016 and 2017, 9 river bends in the middle Baihe River were selected to attempt estimation of migration rates of the river bends using tree ring analysis. The tree core and disc samples were collected using an increment borer and a crosscut saw, and the ages of the trees were estimated based on tree ring analysis. A method for estimating the migration rate of river bends based on the relation between positions and ages of trees grown on the point bars in inner banks is proposed. The estimated migration rates of the 9 river bends of the Baihe River ranged 0.38–6.10 m/yr, and the migration rates were found to be related to the flow rate, channel slope, height of the outer bank, and width of the river valley. The maximum migration rate was determined to be at the No. 9 River Bend where the ratio of the meander-bend radius to the channel width (R/W) was 2.31, which is consistent with previous findings that the bend migration is most rapid in the ‘migration phase’. The proposed method for estimating the migration rate of river bends provides a potential alternative option for future study on the morphodynamic process of a meandering river.     

地下采煤情况下地表黄土边坡稳定性分析

针对近年来我国西北黄土地区地下采煤诱发地表变形,从而导致地表黄土边坡失稳及滑坡问题,使用显式有限元、动力学大变形计算方法以及土动力学基本理论进行分析研究,并提出一种适用于地下动态扰动对地表边坡稳定性影响的分析方法。通过计算分析得知,地下采煤对地表边坡稳定性的影响是一个动态的过程,所提方法具有较高的计算效率,且能够分析边坡的渐进破坏过程。     

DEVELOPMENT OF LONGITUDINAL PROFILE OF THE LOWER YELLOW RIVER

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Comment on “Luminescence chronology of the Sankosh river terraces in the Assam–Buthan foothills of the Himalayas: Implications to climate and tectonics” by Quaternary Geochronology 72, 101364

In a study of which the main objective was to assess the impact of climate change and tectonics on the formation of river terraces along the Sankosh River, the eastern foreland of the Himalayas, the authors obtained geochrono-logical data using luminescence technique. Four strath river terraces (T4–T1) were distinguished within the valley bottom, and alluvial sediments from three terraces (T4, T2 and T1) were dated to the age range from 143 to 14 ka. The alluvial mantels of river terraces were then linked to the scheme of glacial-interglacial cycle. The paper, however, suffers from few inconsistent and missing information, and the assessment on the landscape evolution of the river valley is incomprehensive. The authors relied on feldspars and therefore the IRSL method was used, but “OSL ages” are discussed at the end. They state that (i) tectonics creates space for sediment accommodation and (ii) the luminescence ages flank deposition and incision phases. Despite the fact that the statements are questionable, the ways these happen are not elucidated within the paper. Due to the lack of geochronological data for T3 terrace, its formation is very enigmatic. It is even more mysterious in the light of the data for the other terraces, but the authors made no attempt to explain this riddle. However, that certain inability of reconstructing the history of T3 would shed a shadow on the robustness of the ages obtained.     

Two-dimensional modeling of channel evolution under the influence of large-scale river regulation works

In the middle and lower reaches of alluvial rivers, various kinds of river regulation projects affecting natural channel evolution often are distributed due to the requirements of flood control, navigation,and channel stability. However, the influence of large-scale river regulation works on fluvial processes is not fully known. Therefore, a two-dimensional(2D) morphodynamic model has been improved to address this problem. The new detailed procedure is presented in this paper:(i) First, each nod...     

A SYSTEM OF CAPACITIVE HIGH-VOLTAGE PULSE RECHARGE/DISCHARGE AND ITS IMPLICATION ON EXPERIMENTALLY TRIGGERED EARTHQUAKE

An external small disturbance may trigger seismic events when the fault is in a critical state. The problems related with earthquakes triggered by the dynamic stress such as blasting loads, impact loads, volcanic eruptions and strong earthquakes, have usually drawn wide concerns in earthquake science, and the corresponding research contents are quite extensive, including earthquake triggering mechanisms, triggering earthquake uncertainty, aftershock triggering, and so on. Among them, experimental research is an important way to understand the stress triggering conditions and physical mechanisms, such as the influence of load disturbance on fault friction traits, the influence of periodic disturbance of tidal stress on fault instability, etc., all of which can be gained through experimental investigations. Among them, "how to trigger" is a basic scientific problem to increase the understanding of earthquake prediction theory, thus receiving more attention. There are also some studies that focus on "what happened after the trigger", that is, the sliding instability generated by the triggering method, and then the evolution characteristics of the sliding instability process. The well-known experimental study of the super-shear rupture process is conducted by using the electric explosion method to trigger the fault instability, and the high-speed camera records the super-shear rupture during the fault instability. This means that when the trigger source is controllable, it is possible to generate different types of instability processes, and then to explore which earthquakes will be triggered at different time and space positions under different stress states by means of active triggering. The study of stability analysis and instability process has important scientific significance.A stable system of capacitive high-voltage pulse discharge and recharge is one of basic techniques for studying the triggered earthquakes in laboratory. Based on the wire electric explosion method, this paper develops a controllable trigger experiment system. By designing a new capacitive high-voltage pulse charge and discharge system, while considering the actual needs of monitoring and system timing, multiple functions are integrated into one system. Functionally, in addition to realizing the dynamic loading and unloading function of the wire electric explosion method, the discharge process can be monitored, and the triggering, synchronization and timing signal output is performed with other observation systems, thus realizing the whole process monitoring of the dynamic disturbance action. After testing, the following functions are achieved:1)The voltage and current of the high-voltage charging power supply system can be automatically adjusted, and the system can be shut off after charging; 2)Control modes include manual and remote controls. These two modes can control the recharge, release and pulse discharge of the high voltage capacitor; 3)The system can produce multi-channel synchronous output, which satisfy multiple systems working together. In particular, the remote sensing method greatly improves the experimental maneuverability and security; 4)The system has multiple sets of gas discharge tube to trigger discharge, with a wide range of discharge voltage of 500~5 000V; 5)Roche coil resistance integral current detection can meet the transient resistance, large current detection. Test results indicate that this system has good repeatability and stability with the same discharge energy and discharge energy regulator, which is conducive to carry out single channel trigger of high-pressure discharge experiment. In short, the new charging and discharging system can meet the requirements of experimental study of triggering earthquake. In addition, this system can be used to generate the stress disturbance under certain static and dynamic conditions, and then judge whether this kind of mechanical conditions in active fault systems is currently stable.In short, a controllable single-shot discharge system is developed by a capacitive high-voltage pulse discharge system, which provides a good technical basis for experimental research on triggering earthquakes. In addition, the new system also has application significance:1)multiple triggering output can simultaneously start multiple systems and improve the efficiency of observation. Fault instability is a characteristic of transient response, so, its observation requires high-speed acquisition equipment, which is difficult to control on observation; the trigger system is controllable, with active synchronization observation using physical parameters; 2)stress disturbance can be triggered under static and dynamic loads to detect the safety and stability of the fault system with active trigger.     

基于洪水预报系统误差反演的多河段联合校正方法

提出一种基于洪水预报误差系统反演的多河段联合校正方法.采用马斯京根法矩阵方程描述多河段多区间入流的河道汇流过程,基于动力系统反演理论建立洪水预报误差的递推方程,最后利用修正后的多河段状态变量经演算得到预报断面的洪水过程,进而达到多河段联合校正目的.对大渡河上游的应用示例结果表明：多河段联合校正方法考虑了河系中断面间的水力联系及预报误差在时程上的传递规律,可充分利用上游多断面实测和校正信息进行下游预报断面的误差修正,因此具有更高的校正精度和稳定性.     

Simulating and predicting river discharge time series using a wavelet‐neural network hybrid modelling approach

Accurate simulation and prediction of the dynamic behaviour of a river discharge over any time interval is essential for good watershed management. It is difficult to capture the high‐frequency characteristics of a river discharge using traditional time series linear and nonlinear model approaches. Therefore, this study developed a wavelet‐neural network (WNN) hybrid modelling approach for the predication of river discharge using monthly time series data. A discrete wavelet multiresolution method was employed to decompose the time series data of river discharge into sub‐series with low (approximation) and high (details) frequency, and these sub‐series were then used as input data for the artificial neural network (ANN). WNN models with different wavelet decomposition levels were employed to predict river discharge 48 months ahead of time. Comparison of results from the WNN models with those of the ANN models alone indicated that WNN models performed a more accurate prediction. Copyright © 2011 John Wiley & Sons, Ltd.     

分形与混沌理论在地震学中的应用与探讨

分形与混沌理论的研究与发展，揭示了自然界中一大类无规几何形体物理过程的内在规律性及其动力演化过程的内在随机性。这给我们探索自然界中分形客体的几何形态及其与内部物理本质的关系提供了一条暂新的途径。特别是这一理论给我们探讨地震问题，例如：探讨地震活动时空分布的确定性图像、地震演化过程的动力学行为、临界特征以及未来大地震的发生等问题，带来了某些希望。本文较详细地综述了近年来分形与混沌理论在地震学中的应用研究。全文共分５部分。第１部分是孕震过程的一般概述。第２部分描述单分形与多分形在地震学中的某些应用．文中第３部分介绍了混沌动力学中的某些研究在测震学与模型中的应用。第４部分综述了自组织临界现象和闪变噪声的研究．最后，第５部分是分形理论与混沌动力学在地球科学中的应用前景与展望．     

A decadal-scale numerical model for wandering,cobble-bedded rivers subject to disturbance

Alluvial rivers are composed of self-formed channels which are sensitive to disturbances in their flow and sediment-supply regimes. Regime changes commonly occur over decadal and longer timescales and can be caused by anthropogenic alterations such as dam construction and removal. Advances in numerical modeling have increased our ability to explore geomorphic adjustments over long timescales; however, many models designed to be run for decades or longer assume that banks are immovable or that channel width is constant. Since river channels often respond to disturbance by adjusting their geometry, this is a significant shortcoming. To investigate the impact of long-term sediment supply alterations on channel geometry and stability, we have adapted MAST-1D, a reach-scale bed evolution model, to incorporate functions for bank erosion, vegetation encroachment, and local avulsions. The model is designed for medium-large, coarse multithreaded rivers and can be run over long (decades–centuries) timescales. Bank erosion is a function of the mobility and transport capacity for structurally-important grains which protect the bank toe. Vegetation growth is proportional to point bar width and occurs during conditions of low shear stress. Local avulsions occur when aggradation causes channel depth to drop below a threshold. We apply the model to the Elwha River in Washington, USA with the goal of investigating if and when the river recovers from dam emplacement and removal. The Elwha was dammed for nearly 100 years, and then two dams were removed, releasing a large pulse of sediment. We have modeled the set of reaches between the two dams. Our simulations suggest that channel response to dam emplacement occurs gradually over several decades but that the channel recovers to near pre-dam conditions within about a decade following the removal. The dams leave a lasting legacy on the floodplain, which does not completely recover, even after two centuries. © 2019 John Wiley & Sons, Ltd.     

Basic Principles of the Hydraulic Theory of Formation and Development of River Channel Mesoforms

A closed system of equations was obtained which describes the formation of river channel mesoforms. The conditions were found which cause recurrent restructuring of the flow velocity field which governs the shape and dimensions of the channel mesoforms. The evolution of the longitudinal profile of a mesoform is considered and the parameters that control this process are evaluated. A numerical solution of the problem of river channel mesoform development is given. An interpretation of the hydraulic theory in terms of energy is given.     

ONE D AND TWO D COMBINED MODEL FOR ESTUARY SEDIMENTATION

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Random stability for lateral vibration on footbridge based on IEVIE–PDE method

The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration. Accordingly, bridge vibration stability falls within the field of nonlinear stochastic vibration stability. At present, the Lyapunov method is mainly used to analyze such stability. However, this method is qualitative, and it cannot quantitatively analyze the vibration stability probability. In this study, a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE) is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge. The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge. A combination of the IEVIE method and the probability density evolution(PDE) method is then proposed, in which the IEVIE method is utilized to determine vibration stability. The PDE method is used to obtain the reliability of vibration stability. The proposed method is successfully applied to the Millennium Bridge, and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods. The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.     

Magnetospheric substorm: Loss of the magnetoplasma equilibrium as a nonlinear dynamical bifurcation

The fast onset of a substorm—a substorm “explosion”—is usually associated with the moment of stability loss of the magnetoplasma equilibrium in the geomagnetic tail. The origination of such a process either from the near-Earth part of the plasma sheet or from its remote part, which is highly stretched into the tail, is now being studied theoretically and verified experimentally (at the present time, in the THEMIS project). In the first case, the resulting disturbance must have the form of a ballooning mode; in the second case, of tearing perturbation. However, in both cases, this stability loss, i.e., a quick breakdown in the balance, replacing the slow quasi-static evolution of configuration, can only occur as a nonlinear process. Taking into account the specific properties of the configuration and possible disturbances in it, we indicate why such a process cannot be the previously proposed “substorm detonation.” It is shown that a suitable mathematical model is a nonlinear dynamical bifurcation occurring on a small time scale, with a delay relative to the moment of passing the marginally stable state.     

水库诱发地震时空演化与库水加卸载及渗透过程的关系 ——以紫坪铺水库为例

为了解水库蓄水过程中,水库诱发地震活动的动态响应机制,本文建立了针对水库诱发地震(Reservoir-induced seismicity,RIS)定量化研究的数理模型,并以紫坪铺水库为例,对库区地质构造及水文地质结构条件、水库蓄水后库区小震活动时空演化特征进行了详细的研究.在此基础上,利用有限元方法计算了水库蓄水过程中弹性附加应力场、有效附加应力场、孔隙压力和断层稳定性的动态变化,讨论了RIS时空演化与库水加卸载及渗透过程的动态响应关系.结果表明:(1) RIS诱发机制的定量化模型可分为2个层次:一是以孔隙介质为载体的流体渗流对岩体变形和稳定性的影响,由流-固耦合形式的岩体变形与孔隙渗流模型进行描述;二是对断层相关的RIS定量研究可将水库附加水头压力沿断层面(区)的扩散与断层库仑应力变化联系起来.两种形式模型方法的结合能为RIS定量研究提供一个相对宏观的力学框架;(2) 断裂渗透结构对孔隙压力变化下断裂的力学响应具有重要的影响,研究区主干断裂可能属于一种上盘破碎带导水、下盘地层及断层核阻水的"下阻上导型"的渗透结构类型,不同程度的具有使地表水体向深部渗流的通道性.库区深部岩体渗透稳定性的差异在很大程度上导致了诱发地震活动对岩性条件的依赖.(3) 紫坪铺水库蓄水后,小震活动在空间分布上呈现出条带状分布、丛集分布和地震迁移的特点,小震震源深度优势分布在地下4~10 km范围内,在通济场断裂与安县-灌县断裂的深部汇聚区域震源分布最为密集.同时,小震活动主要集中发生在脆性程度高、渗透稳定性低的碳酸盐岩地层中,而在岩性较软弱、渗透稳定性高的三叠系须家河组砂泥岩和煤系地层中很少有地震发生.在水库蓄水后地震活动的时间响应特征上,水库西南侧和东北侧两个丛集区的小震活动可能属于"快速响应型"RIS,而都江堰小震群活动可能属于"滞后响应型"诱发地震活动;(4) RIS的发生与库水加卸载及渗透过程中库底岩体有效应力的变化密切相关.在以挤压为主的构造应力环境中,库体荷载作用的结果一般会使库底断层更趋向稳定,而水库附加水头压力扩散的效应则是促使断层趋向失稳,正是这个矛盾双方相互制约与平衡的动态过程,控制了断层库仑应力变化的取向,从而决定了RIS时空演化的规律.     

Bar dynamics and bifurcation evolution in a modelled braided sand‐bed river

Morphodynamics in sand‐bed braided rivers are associated with simultaneous evolution of mid‐channel bars and channels on the braidplain. Bifurcations around mid‐channel bars are key elements that divide discharge and sediment. This, in turn, may control the evolution of connected branches, with effects propagating to both upstream and downstream bifurcations. Recent works on bifurcation stability and development hypothesize major roles of secondary flow and gradient advantage. However, this has not been tested for channel networks within a fully developed dynamic braided river. A reason for this is a lack of detailed measurements with sufficient temporal and spatial length, covering multiple bifurcations. Therefore we used a physics‐based numerical model to generate a dataset of bathymetry, flow and sediment transport of an 80 km river reach with self‐formed braid bars and bifurcations. The study shows that bar dissection due to local transverse water surface gradients is the dominant bifurcation initiation mechanism, although conversion of unit bars into compound bars dominates in the initial stage of a braided river. Several bifurcation closure mechanisms are equally important. Furthermore, the study showed that nodal point relations for bifurcations are unable to predict short‐term bifurcation evolution in a braided river. This is explained by occurrence of nonlinear processes and non‐uniformity within the branches, in particular migrating bars and larger‐scale backwater‐effects, which are not included in the nodal point relations. Planform morphology, on the other hand, has predictive capacity: bifurcation angle asymmetry and bar‐tail limb shape are indicators for near‐future bifurcation evolution. Remote sensing data has predictive value, for which we developed a conceptual model for interactions between bars, bifurcations and channels in the network. We conducted a preliminary test of the conceptual model on satellite images of the Brahmaputra. Copyright © 2015 John Wiley & Sons, Ltd.     

断层水平错动下河流演变过程的数值模拟研究

在活动构造区, 河流地貌对构造活动具有明显的响应, 地貌形态和水系形态能够很好地记录构造活动信息。 基于地貌演化理论, 考虑断层的左旋错动作用及降雨等因素, 利用数值模拟方法, 定量研究河流形态在断层水平错动及流水侵蚀内外力作用下的动力学演变过程。 初步的计算结果显示了河流形态与断层走滑运动的耦合效应。 断层发生水平左旋滑动促使该处河道两侧的陡坎发生相对错动, 形成弯转水系, 伴随河流的侧向侵蚀作用, 河道上下游连续被拓宽, 河道下游右侧堆积了较厚的沉积物, 而河道上游左侧由于受到较强流水侵蚀作用很难堆积沉积物。 分别对河道上游和河道下游的横剖面形态进行对比分析, 表明由于断层水平错动效应, 使得河道下游两侧呈现不对称特征, 而河道上游依然保持着明显对称性。 同时, 河道剖面形态对断层水平错动作用有积极的响应, 由于断层持续左旋走滑运动, 断层处剖面的高程突然增加, 坡度也随之突然变陡。 数值模拟结果与实际地质考察结果有着很好的一致性, 证明了理论和数值模型的可靠性。