Two-Dimensional Composite Mathematical Alluvial Model for the Braided Reach in the Lower Yellow River

Abstract

The fluvial processes are considerably complicated in the braided reach of the Lower Yellow River, and the lateral or transverse channel deformation process is especially pronounced. The state-of-the-art of simulation techniques for the channel deformation in the Lower Yellow River was analyzed in this paper, and such a conclusion was drawn that existing mathematical alluvial models only can simulate the longitudinal channel deformation and cannot simulate such the lateral deformation as lateral erosion and failure of bank. Then a new two-dimensional (2D) composite model was developed herein, consisting of a 2D flow and sediment transport submodel and a riverbank-erosion submodel. This model not only can simulate the longitudinal and lateral channel deformations, but also can be used to simulate the fluvial processes of natural alluvial rivers with complex bed morphology. Through using the proposed composite model, the flood routing and channel deformation processes during the August 1982 flood were simulated. The maximum stage along the reach and the discharge hydrograph at the outlet so obtained were in good agreement with the observed data. Simulated results of the channel deformation processes showed that during the flood season, the main channel scours and the flood plain deposits; during the dry season, the main channel deposits and banks of the floodplain retreat due to lateral erosion by the flow and failure under gravity. Such results accord with the annual varying law of bed scouring and deposition in the braided reach.     

Impact of depth ratio on flow structure and turbulence characteristics of compound open channel flows

Compound open channel flows appear in most natural rivers are of great importance in river management and flood control. In this study, large eddy simulations were carried out to simulate the compound open channel flows with four different depth ratios (h_r = 0.10, 0.25, 0.50, and 0.75). The main flow velocity, secondary flow, Reynolds stress, and bed shear stress were obtained from numerical simulations. The depth-averaged streamwise momentum equation was used to quantify the lateral momentum exchange between the main channel and floodplain. The instantaneous coherent structures were presented by the Q criterion method. The impact of h_r on flow structure and turbulence characteristics was analyzed. The results showed that with the increase of h_r, the high velocity area in the main channel shifted to the floodplain, and the dip phenomenon became more obvious; the Reynolds stress largely contributed to the lateral momentum exchange within the flows near the side walls of floodplain; and the vortex structures were found to significantly increase in the floodplain region.     

明渠均匀流流速横向分布的涡黏性模型

为了研究明渠水流的运动特性,开展了明渠水流流速横向分布数学模型的研究。本文根据量纲分析方法和实验资料,得到水流横向剪切作用下横向涡黏性系数的关系式;基于均匀流的水流运动方程,按照有限差分方法,建立流速横向分布计算模型。该模型具有计算简单、快捷和精度较高的优点,且数值计算不受横向涡黏性系数的结构形式和断面形态的影响。采用明渠水流实验资料验证数学模型,数学模型计算的流速横向分布与实验资料较一致,具有较高的理论意义和应用价值。     

Estimation of the transverse dispersion coefficient for two-dimensional models of mixing in natural streams

Existing equations to predict the transverse dispersion coefficient for the two-dimensional model of mixing and transport in natural streams use the channel aspect ratio and roughness factor as well as the sinuosity of the channel as the controlling parameters, and the performance of the equation varies largely according to the range of each parameter that was studied. To this end, this study suggests the criteria to select the proper method to calculate the transverse dispersion coefficient according to the availability and range of each parameter. The strengths and limitations of existing methodologies were compared against observed data acquired from tracer experiments conducted in natural streams. Further, a flow chart was proposed with the criteria to select a suitable method under specific hydraulic and geometric conditions of the stream.The results of the classification flow chart showed that, at the first step, in the cases where secondary currents data were available for natural streams, the theoretical equation by Baek and Seo (2011) could be used to estimate the transverse dispersion coefficient. At the second step, in the case of large value of P, i.e., P > 0.04, the equation by Baek and Seo (2013) was suitable to estimate the transverse dispersion coefficient, while in the case of a small value of P, equations by Yotukura and Sayer (1976) and Baek and Seo (2013), could be used with little differences. At the third step, for the narrow streams with W/h < 50, those proposed by Bansal (1971) and Deng et al. (2001) were preferable to estimate the transverse dispersion coefficient for two-dimensional mixing models. In wide streams with W/h > 50, the results of Jeon et al. (2007) showed much better agreement with the observed values than the others.     

Development and Integration of Sub-hourly Rainfall–Runoff Modeling Capability Within a Watershed Model

Increasing urbanization changes runoff patterns to be flashy and instantaneous with decreased base flow. A model with the ability to simulate sub-daily rainfall–runoff processes and continuous simulation capability is required to realistically capture the long-term flow and water quality trends in watersheds that are experiencing urbanization. Soil and Water Assessment Tool (SWAT) has been widely used in hydrologic and nonpoint sources modeling. However, its subdaily modeling capability is limited to hourly flow simulation. This paper presents the development and testing of a sub-hourly rainfall–runoff model in SWAT. SWAT algorithms for infiltration, surface runoff, flow routing, impoundments, and lagging of surface runoff have been modified to allow flow simulations with a sub-hourly time interval as small as one minute. Evapotranspiration, soil water contents, base flow, and lateral flow are estimated on a daily basis and distributed equally for each time step. The sub-hourly routines were tested on a 1.9 km² watershed (70% undeveloped) near Lost Creek in Austin Texas USA. Sensitivity analysis shows that channel flow parameters are more sensitive in sub-hourly simulations (Δt = 15 min) while base flow parameters are more important in daily simulations (Δt = 1 day). A case study shows that the sub-hourly SWAT model reasonably reproduces stream flow hydrograph under multiple storm events. Calibrated stream flow for 1 year period with 15 min simulation (R ² = 0.93) shows better performance compared to daily simulation for the same period (R ² = 0.72). A statistical analysis shows that the improvement in the model performance with sub-hourly time interval is mostly due to the improvement in predicting high flows. The sub-hourly version of SWAT is a promising tool for hydrology and non-point source pollution assessment studies, although more development on water quality modeling is still needed.     

以波尔兹曼理论建立明渠水流数值模型方法

根据文献[1]所论述的以波尔兹曼方程建立明渠水流模型的理论及明渠水流中微、微观变量之间的基本关系，采用有限体积离散方法，探讨了BGK明渠水流数值模型的方法，初步建立了不同于传统方法的、满足熵原理的BGK明渠水流数模型，通过对一系列典型的明渠水流现象的模拟，并对理论解，其它计算方法获得的解决以及公开发表的实验结果相比较，表明所提出的模型计算精度高，、稳定性好，勿须人为的熵修正（如人为增加耗散项）、能准确模拟明渠中不连续水流运动（如溃坝波等），不会出现非物理性的震荡，是一种颇具开发前景的明渠水流模型。     

非对称复式断面明渠中污染物输移扩散的大涡模拟

运用大涡模拟计算了两个非对称复式断面明渠内的水流运动和污染物扩散，其中由亚格子尺度涡运动引起的亚格子应力与物质扩散通过Smagorinsky-Lilly亚网格模型模拟。预测结果与Shiono等使用激光多普勒流速计(LDA)和激光诱导荧光技术(LIF)测量的实验数据进行了对比，计算得到的流场结构和污染物浓度分布均较好地吻合于测量结果。成功地再现了在其中一个复式断面明渠中观测到的横向浓度分布呈现显著双峰值的现象，根据计算的流场得出复式断面明渠中流向交替变化的强烈横向流动是产生这种现象的主要原因。     

黄河下游游荡型河段洪水演进与河床变形过程的数值模拟

黄河下游游荡型河段的河床变形过程相当复杂，横向变形尤为突出，现有水沙数学模型一般仅能模拟河床纵向冲淤，不能模拟滩岸横向冲刷与崩塌，本文将平面二维水沙数学模型与粘性河岸冲刷的力学模型相结合，建立河床变形的平面二维混合模型。然后以黄河下游花园口至夹河滩的游荡型河段为例，采用该混合模型，首次较为全面地模拟了1982年汛期的洪水演进与河床变形过程。沿程最高水位、出口断面流量过程等计算值与实测值符合较好。计算结果还表现为大水时主槽冲刷，滩地淤积；小水时主槽淤积，滩地崩塌。该计算结果与游荡型河段的年内冲淤变化规律一致。     

TRANSVERSE MIXING IN A TRAPEZOIDAL COMPOUND OPEN CHANNEL

Transverse mixing characteristics of solute in the open channel flow can provide useful information for river environmental management. The lateral mixing coefficient is a crucial parameter for reproducing the transverse mixing either by numerical simulation or by analytical prediction. Since the solute mixing can be greatly affected by the lateral variations in water depth, mixing coefficient should be determined in each sub-section （i.e., the main channel, side slope and flood plain） separately. In this article, the transverse mixing in a symmetric trapezoidal compound channel was studied based on laboratory measurement of longitudinal and transverse velocity components and lateral distribution of solute concentration. The lateral mixing coefficient was estimated by adopting different Schmidt numbers in different sub-sections divided according to the developing trend of the eddy viscosity, and finally a piecewise linear profile of mixing coefficient was adopted to analytically predict the transverse solute concentration. The comparison between the analytically predicted data and the measuring solute concentration proved that this is an effective way to estimate the lateral mixing in the open channel flow with lateral variations in water depth,     

明渠岸边横向取水口的三维数值计算

本文是在明渠岸边横向取水口的试验研究基础上的配套数值模拟。采用雷诺平均的N—S方程，以各向异性的雷诺应力模型(RSM)封闭方程组，用SIMPLEC算法对压力—速度场求解。计算结果与试验实测结果吻合较好，反映了此项模拟的可信性，可籍以扩大、分析一些运动规律。数值计算结果启示了横向取水口水流的复杂三维流动特性，据之对取水口附近水流各区的划分、水流的分离和反向流动、螺旋流以及床面剪应力的分布等复杂水力和泥沙输移物理现象有了进一步认识。     

Application of Genetic Programming in Stage Hydrograph Routing of Open Channels

Routing is a technique used to simulate and predict changes in water flow along a river or channel. There are several hydraulic flow routing methods that model channel flow with high accuracy using lots of data related to channel geometry and specifications, thus making calculations very expensive. In contrast, hydrologic methods are techniques that simplify the calculation of flow conditions in a channel reach. In this paper, a stage hydrograph is modeled in simple and compound channels by genetic programming (GP) as a hydrologic method that does not depend on channel geometry and specifications, channel shape, and modeling time step. Routed hydrographs for simple and compound channels are then compared with a river analysis system model (HEC-RAS) and a coupled characteristic-dissipative-Galerkin procedure in one-dimension (CCDG-1D) as the hydraulic methods, respectively. Results show that the sum of squared differences (SSD) between a stage hydrograph by GP and modeled hydrographs by HEC-RAS and CCDG-1D methods, respectively, are not considerable in simple and compound channels. Moreover, GP is a capable tool to route an acceptable stage hydrograph even by using less geometry specification and time intervals in the detected stage. Those results indicate that the proposed GP method is effective in routing a stage hydrograph.     

Transfer Function Formulation of Saint-Venant’s Equations for Modeling Drainage Channel Flow: An Experimental Evaluation

Space constraints in developed urban cities necessitate utilizing existing capacity of the drainage system for actively controlling and optimizing the flow during a flood event. This is mainly achieved by the use of non-structural control measures (in the form of suitable controllers and control strategies) for controlling existing structures such as gates in the drainage system. However, the timely opening and closing of gates is fully governed by the rapid feedback and real time control of these structures. Hence, for an extreme rainfall event and flooding, it is necessary to rapidly model the peak flow and time to peak in the drainage system, the results of which can be used for the timely operation of the control structures. Owing to the fact that the conventional modeling methods are quite time consuming and cumbersome, a simplified approach based on transfer function formulation of Saint-Venant’s equations have been proposed in this study. The simplified approach has been validated with the help of carefully planned laboratory experiments in which a test setup consisting of a model drainage channel with upstream and downstream gates have been developed. This laboratory model was used to simulate different flow conditions by the appropriate opening and closing of upstream and downstream gates. It was noted that the results obtained using the simplified approach matches well with the experimentally observed trends. This demonstrates the robustness of the new simplified approach for modeling flow conditions in drainage system.     

How does oil and gas behave when released in deepwater?

Deepwater oil and gas releases have come to greater attention of the scientists as well as general public in the recent past, especially after the Deepwater Horizon spill in Gulf of Mexico in 2010. In this short paper we show the general behavior of an oil and gas spill in deepwater. A model, CDOG, developed by Zheng et al. (2003) and had undergone successive improvements is used for the simulations to illustrate the oil behavior. The impact of the oil droplet sizes are demonstrated. Although cases are not specific to a particular spill, through the use of a state-of-the-art model, we show the key parameters that affect the behavior of oil. In this paper we show oil and gas behavior that has not been clearly explained in previous papers and address newly found concerns brought on by the recent awareness. This paper also shows how the oil behavior changes when additives like dispersants are applied. Results of the simulations reveal that the “underwater plumes” with low concentrations of oil can be formed and stay submerged for long periods of time when very small (less than 0.5 mm in diameter) oil droplets are present.     

复式断面河槽流速横向分布及其对滩唇形成的影响

通过对水流微小控制体进行受力分析,建立了复式断面流速横向分布模型,该模型考虑了侧向副流惯性力的影响。采用实验资料对该模型进行检验,模型计算值与实测值符合较好。运用该模型计算了不同条件下复式断面流速和挟沙力的横向分布,并定量分析了横向分布特性对滩唇形成的影响。分析表明,水流漫滩时,复式断面的横向挟沙力变幅较大,尤其是在主槽和河漫滩交界处,挟沙力减小迅速,而含沙量减小相对较小,泥沙发生淤积,容易形成滩唇。单从水流挟沙力角度考虑,水流漫滩后水深越小、滩槽的糙率差越大,越容易形成滩唇。     

顺坡渐扩矩形明渠水跃计算公式

顺坡渐扩矩形明渠常被用在排水工程中作为排水口与河道的连接段。由于河道水位变化,水跃将发生在连接段。本文从动量守恒原理出发推导了顺坡渐扩矩形明渠水跃方程,在假定水跃水质点作二维运动和水跃段内质点垂向加速度近似为常量的基础上推导了水跃长度近似计算公式。并与扩散角为9°、水平坡度角为6°特定条件的模型试验结果进行了对比,结果吻合良好,可供类似工程参考。     

Numerical simulation of undular jumps on graveled bed using volume of fluid method

Undular hydraulic jumps are characterized by a smooth rise of the free surface, followed by a train of stationary waves. These jumps sometimes occur in natural waterways and rivers. Numerical difficulties are especially distinct when the flow condition is close to the critical value because of the high sensitivity of the near-critical flow field to flow and channel conditions. Furthermore, the free surface has a wavy shape, which may indicate the occurrence of several transitions from supercritical to subcritical states and vice versa (i.e., undular hydraulic jumps). In this study, a flow model is used to predict an undular hydraulic jump in a rectangular open channel. The model is based on the general two-dimensional, Reynolds-averaged, Navier-Stokes flow equations. The resulting set of partial differential equations is solved using the FLOW-3D solver. The results are compared with the experimental data to validate the model. The comparative analysis shows that the proposed model yields good results. Several types of undular hydraulic jumps occurring in different situations are then simulated to prove the potential application of the model.     

A MATHEMATICAL MODEL OF MIGRATION AND EXPANSION OF MEANDER LOOPS

This article presents a mathematical model of the plane evolution of alluvial meandering streams,through downstream migration and lateral expansion of meander loops.Under the conditions prevailing in natural streams,the channel centerlines follow sine-generated curves,with an assumed steady-state turbulent and subcritical flow,of large width-to-depth ratio(≥ 15,for example) and small Froude number(Fr ).The plane deformation of the channel is caused by the action on the banks of the convective vertically-averaged meandering flow.The growth(migration and expansion) of meander loops is attributed to the regime-trend.The computational results of the model show that the obtained migration and expansion patterns of the meander loops are in good agreement with those of observations and measurements in similar meandering streams.     

植被作用下的复式河槽漫滩水流紊动特性

分别选取塑料吸管、鸭毛和塑料大草模拟乔木、灌木和野草,通过水槽试验,探讨了不同滩地植物作用下的浸滩水流紊动特性。试验结果表明,纵向、横向和垂向三个方向的脉动流速基本满足正态分布;时均流速与采样时间的长短有关;横向动量交换比垂向动量交换大,横向动量基本上是主槽向滩地传递;不同的滩地植物对水流的紊动强度的影响不同。滩地种植植物后,水流的紊动强度增强。纵向和垂向的紊动强度相当,都服从S型分布。     

Not all breaks are equal: Variable hydrologic and geomorphic responses to intentional levee breaches along the lower Cosumnes River,California

The transport of water and sediment from rivers to adjacent floodplains helps generate complex floodplain, wetland, and riparian ecosystems. However, riverside levees restrict lateral connectivity of water and sediment during flood pulses, making the re‐introduction of floodplain hydrogeomorphic processes through intentional levee breaching and removal an emerging floodplain restoration practice. Repeated topographic observations from levee breach sites along the lower Cosumnes River (USA) indicated that breach architecture influences floodplain and channel hydrogeomorphic processes. Where narrow breaches (<75 m) open onto graded floodplains, archetypal crevasse splays developed along a single dominant flowpath, with floodplain erosion in near‐bank areas and lobate splay deposition in distal floodplain regions. Narrow breaches opening into excavated floodplain channels promoted both transverse advection and turbulent diffusion of sediment into the floodplain channel, facilitating near‐bank deposition and potential breach closure. Wide breaches (>250 m) enabled multiple modes of water and sediment transport onto graded floodplains. Advective sediment transport along multiple flow paths generated overlapping crevasse splays, while turbulent diffusion promoted the formation of lateral levees through large wood and sediment accumulation in near‐bank areas. Channel incision (>2 m) upstream from a wide levee breach suggests that large flow diversions through such breaches can generate water surface drawdown during flooding, resulting in localized flow acceleration and upstream channel incision. Understanding variable hydrogeomorphic responses to levee breach architecture will help restoration managers design breaches that maximize desired floodplain topographic change while also minimizing potential undesirable consequences such as levee breach closure or channel incision.     

Rainfall-Runoff Model Considering Microtopography Simulated in a Laboratory Erosion Flume

A comprehensive process-based rainfall-runoff model for simulating overland flow generated in rills and on interrill areas of a hillslope is evaluated using a laboratory experimental data set. For laboratory experiments, a rainfall simulator has been constructed together with a 6.50 m × 1.36 m erosion flume that can be given adjustable slopes changing between 5 % and 20 % in both longitudinal and lateral directions. The model is calibrated and validated using experimental data of simulated rainfall intensities between 45 and 105 mm/h. Results show that the model is capable of simulating the flow coming from the rill and interrill areas. It is found that most of the flow occurs in the form of rill flow. The hillslope-scale model can be used for better prediction of overland flow at the watershed-scale; it can also be used as a building block for an associated erosion and sediment transport model.