曹志先
主要从事河流水沙运动与数学模型基本理论研究。
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 姓名：曹志先
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博士生导师
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学科领域：
水力学
 研究兴趣：主要从事河流水沙运动与数学模型基本理论研究。
曹志先，水力学及河流动力学专业博士。现任武汉大学水资源与水电工程科学国家重点实验室教授、博士生导师。曾在英国和日本从事合作学术研究多年。近年持续在相关学科国际主流学术刊物上发表研究成果，于2003 年荣获英国土木工程师学会Telford 奖。主要从事河流水沙运动与数学模型基本理论研究。发现了非耦合数学模型不适用于输沙率高、河床变形快的强冲积河流过程的根源在于所应用的简化控制方程违背了严格的守恒定律，同时发展了普遍适用于强、弱冲积河流过程的全耦合数学模型。建立了基于湍流猝发特征的床面泥沙上扬定量化方法，为水流挟沙力和泥沙数学模型近底边界条件等关键理论问题的研究提供了新途径。揭示了复合明渠洪水临界漫滩时阻力相对于动量通量发生突变而诱导计算困难，发展了新的动量通量与阻力计算模式，从而解决了研究复合明渠洪水传播时河漫滩小水深所引起的理论问题。

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9
【期刊论文】SEDIMENTLADEN FLOW IN OPEN CHANNELS FROM TOWPHASE FLOW VIEWPOINT
曹志先， By Zhixian Cao， ， Liangyan Wei， and Jianheng Xie
，0001，（）：
1年11月30日
Most existing analytical and mathematical models for sedimentladen flows are based on theverning equations for singlephase flows, and are valid only for low sediment concentration situations. This paper presents an analysis, on the basis of the fundamental equations for fluidsolid twophase flows, of the velocity and sediment concentration profiles in openchannel flows. A new diffusion equation is established for suspended sediment concentration from a rigorous derivation of the watersediment mixture's normal velocity in the sense of mass flux conservation. The differences between this new equation and Schmidt's aswell as Hunt's are shown to be attributable to the different approximations of sediment velocity. Previous formulations for velocity and sediment concentration distributions are special cases of the present model for low sediment concentration flows. The developed model is extensively tested against available measurements, and satisfactory or fairly good agreement is obtained.

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【期刊论文】TURBULENT BURSTINGBASED SEDIMENT ENTRAINMENT FUNCTION
曹志先， By Zhixian Cao， ， Associate Member， ASCE
，0001，（）：
1年11月30日
One of the basic impediments to a clear understanding of a variety of fundamental problems in the context of sediment transport has been the lack of a wellgrounded formulation of bed sediment entrainment. This is dealt with herein, physically based on the mechanism that bed sediment particles are actually entrained by the bursting process inherent in wall turbulent flows. A simple theoretical model for sediment entrainment from flat, loose bed is established using the averaged bursting period scaled on inner variables and the spatialscales of turbulent bursts. Sediment entrainment is shown to depend strongly on bedshear velocity. The theoretical entrainment flux is compared to available laboratory data sets covering both hydraulically smooth andtransitional bed situations. Generally good agreement is obtained, representing the best performance of the present model in relation to existing entrainment functions. It appears to characterize a rather encouraging aspect for a new approach to sediment transport, given the enhanced understanding of turbulent bursting.

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【期刊论文】EQUILIBRIUM NEARBED CONCENTRATION OF SUSPENDED SEDIMENT
曹志先， By Zhixian Cao， ， Member， ASCE
，0001，（）：
1年11月30日
A new approach is presented for calculating the equilibrium nearbed concentration of suspended sediment in an alluvial channel flow. It is formulated from the balance between bed sediment entrainment and suspended sediment deposition across the nearbed boundary. The entrainment flux is determined making use of a turbulent bursting outerscalebased function and the flux of deposition by the product of nearbed concentration and hindered settling velocity of sediment. A number of flume data records in the literature are analyzed to calibrate and verify the present approach. The observed nearbed concentrations for the data records are obtained by first isolating the suspended load transport rate from the observed total load transport rate using Engelund and Fredsoe's bedload formula and then equating the suspended load transport rate to the shape integration of Dyer and Soulsby. The present approach is shown to perform satisfactorily compared to the results of data analysis. It is found that the nearbed concentration is evidently dependent on sediment particle size in addition to the Shields parameter due to skin friction. This finding seems to challenge previous relationships that simply represent the nearbed concentration as empirical functions of the purely skinfrictionrelated Shields parameter.

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曹志先， Zhixian Cao， M.ASCE; Rodney Day; and Shinji Egashira
，0001，（）：
1年11月30日
Existing numerical river models are mostly built upon asynchronous solution of simplified governing equations. The strong coupling between water flow, sediment transport, and morphological evolution is thus ignored to a certain extent. An earlier study led to the development of a fully coupled model and identified the impacts of simplifications in the watersediment mixture and global bed material continuity equations as well as of the asynchronous solution procedure for aggradation processes. This paper presents the results of an extended study along this line, highlighting the impacts on both aggradation and degradation processes. Simplifications in the continuity equations for the watersediment mixture and bed material are found to have negligible effects on degradation. This is, however, in contrast to aggradation processes, in which the errors purely due to simplified continuity equations can be significant transiently. The asynchronous solution procedure is found to entail appreciable inaccuracy for both aggradation and degradation processes. Further, the asynchronous solution procedure can render the physical problem mathematically ill posed by invoking an extra upstream boundary condition in the supercritical flow regime. Finally, the impacts of simplified continuity equations and an asynchronous solution procedure are shown to be comparable with those of largely tuned friction factors, indicating their significance in calibrating numerical river models. It is concluded that the coupled system of complete governing equations needs to be synchronously solved for refined modeling of alluvial rivers.
Numerical models， Alluvial streams， Flow simulation， Morphology， Coupled systems.，

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【期刊论文】Mathematical modelling of alluvial rivers: reality and myth. Part 2: Special issues
曹志先， Z. Cao and P.A. Carling
Water & Maritime Engineering 154 December 2002 Issue 4 Pages 297307，0001，（）：
1年11月30日
The last half a century has seen more and more developments and applications of mathematical models for fluvial flow, sediment transport and morphological evolution. However, the quality of this modelling practice has emerged as a crucial issue for concern, which is widely viewed as the key that could unlock the full potential of computational fluvial hydraulics. The major factors affecting the modelling quality comprise: (a) poor assumptions in model formulations; (b) simplified numerical solution procedure; (c) the implementation of sediment relationships of questionable validity; and (d) the problematic use of model calibration and verification as assertions of model veracity. An overview of mathematical models for alluvial rivers is provided in this and the companion paper 'Part I: General review'. This paper is the second part, dealing with three special issues of mathematical river models. First, turbulence closure models are highlighted, particularly with respect to the role of sediment in modulating turbulence and its implications for adapting turbulence closure models for fluvial sedimentladen flows. Second, the bottom boundary conditions are discussed in detail as one of the main sources of model uncertainty. And third, the commonly used calibration and verification/validation methodology in mathematical river modelling is addressed. It is argued that model calibration can be subjective, verification is impossible because models are not closed systems, and validation does not necessarily establish model truth. Confirmation of observations by models only supports model probability, rather than demonstrating model veracity. It is vital for model developers and endusers to keep aware of what mathematical river models can realistically reflect, and therefore avoid misleading decisionmaking. Additionally, some strategies are proposed which can improve the practice of mathematical river modelling.
hydraulics &， hydrodynamics/， mathematical modelling/， river engineering

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【期刊论文】Mathematical modelling of alluvial rivers: reality and myth. Part 1: General review
曹志先， Z. Cao and P.A. Carling
Water & Maritime Engineering 154 September 2002 Issue 3 Pages 207219，0001，（）：
1年11月30日
Mathematical modelling fluvial flow, sediment transport and morphological evolution started half a century ago and, to date, a variety of mathematical models have been developed and are in widespread use. However, the quality of mathematical river modelling remains uncertain because of: (a) poor assumptions in model formulations; (b) simplified numerical solution procedure; (c) the implementation of sediment relationships of questionable validity; and (d) the problematic use of model calibration and verification as assertions of model veracity. An overview of mathematical models for alluvial rivers is provided in this and the companion paper 'Part 2: Special issues'. This paper is the first part, providing a general review of mathematical river models. The issues addressed comprise what have been obvious since the very beginning of mathematical river modelling and are still open, and also the pertinent components that pose challenges to model developers and endusers pursuing refined modelling practice. In particular the simplified mass conservation equations, asynchronous solution procedures, sediment transport functions, movablebed resistance, numerical difficulty for strong hyperbolic equations, and representation of movable and complex geometry are discussed. A test example is provided to demonstrate the impacts of simplified mass conservation equations and an asynchronous solution procedure in comparison with those of largely tuned friction factors. It is concluded that mathematical models for fluvial flowsedimentmorphology systems are far from being mature, and that considerable expertise, physical insight and experience are vital for meaningful solutions to be acquired and for the limitations of modelling outputs to be properly identified, interpreted and assessed.
hydraulics &， hydrodynamics/， mathematical modelling/， river engineering

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【期刊论文】Role of suspendedsediment particle size in modifying velocity profiles in open channel flows
曹志先， Zhixian Cao， Shinji Egashira， Paul A. Carling
WATER RESOURCES RESEARCH, VOL. 38, NO.0, XXXX, 2001 WR 000934, 2002，0001，（）：
1年11月30日
Previous experimental and analytical studies have revealed that suspended particles can attenuate or enhance turbulence, depending on the particle size in relation to turbulence scales. Incorporating this mechanism, an empirical turbulent eddy viscositybased closure model is proposed for the mean velocity structure of suspended sedimentladen flow in open channels. The model integrates the sediment particle Stokes number, the ratio of particlesizetoturbulence microscale, the ratio of particle settling velocity to bed shear velocity, and local sediment concentration. Its good performance is demonstrated in comparison with available laboratory observations. It is characterized that singlephase turbulence closure models can be adapted for sedimentladen flows by implementing sediment particle size effects.
sediment transport,， turbulence modulation,， velocity profile,， particle size,， fluvial hydraulics,， twophase flow

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【期刊论文】Numerical modelling of alluvial rivers subject to interactive sediment mining and feeding
曹志先， Zhixian Cao*， ， Gareth Pender
Advances in Water Resources 27(2004)533546，0001，（）：
1年11月30日
Instream sediment mining and feeding inevitably change the sediment budget of an alluvial river, and may substantially alter its hydraulics and morphology. These alterations can have variable effects on fluvial habitat. Minimization of the detrimental effects and maximization of the beneficial impacts require a quantitative understanding of the complicated interaction between flow, sediment transport and morphological evolution. However, existing numerical river models have been developed for purely natural fluvial processes, and are rarely, if ever, applicable where interactive sediment mining and feeding take place. This paper presents numerical models for alluvial rivers subject to interactive sediment mining and feeding, within the context of shallow water hydrodynamics. The theoretical framework of twoand onedimensional models is provided from conservation laws, and closure requirements are briefly addressed. The present models are distinguished from previous ones because of the complete continuity equations for the water and sediment phases and bed material, which are scrutinized under idealized scenarios with known analytical features. The continuity equations contain terms arising from mass exchange, which, though less known to the majority of fluvial hydraulics community, may be significant not only scientifically but also under regimes of practical interests. To demonstrate the applicability of the present models, a numerical study is provided on the dynamics of an otherwise aggrading channel in response to sediment mining, showing the role of sediment mining in mitigating river aggradation.
Sediment transport， Sediment mining， Sediment feeding， River engineering， Fluvial hydraulics， Fluvial morphology

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【期刊论文】Computational DamBreak Hydraulics over Erodible Sediment Bed
曹志先， Zhixian Cao; Gareth Pender; Steve Wallis; and Paul Carling
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1年11月30日
This paper presents one of the first dedicated studies on mobile bed hydraulics of dambreak flow and the induced sediment transport and morphological evolution. A theoretical model is built upon the conservative laws of shallow water hydrodynamics, and a highresolution numerical solution of the hyperbolic system is achieved using the totalvariationdiminishing version of the secondorder weighted average flux method in conjunction with the HLLC approximate Riemann solver and SUPERBEE limiter. It is found that a heavily concentrated and eroding wavefront first develops and then depresses gradually as it propagates downstream. In the early stage of the dambreak, a hydraulic jump is formed around the dam site due to rapid bed erosion, which attenuates progressively as it propagates upstream and eventually disappears. While the backward wave appears to migrate at the same speed as over a fixed bed, the propagation of the forward wavefront shows a complex picture compared to its fixedbed counterpart as a result of the domination of rapid bed erosion initially, the density difference between the wavefront and the downstream ambient water in the intermediate period, and the pattern of the deformed bed profile in the long term. It is also found that the free surface profiles and hydrographs are greatly modified by bed mobility, which has considerable implications for flood prediction. The computed wave structure in the intermediate period exhibits great resemblance to available experiments qualitatively, and yet the existence of a shear wave is found in lieu of a secondary rarefaction postulated in an existing analysis. Finally, the use of the complete, rather than simplified, conservation equations is shown to be essential for correct resolution of the wave and bed structures, which suggests that previous models need reformulating.
Dam failure， Flood routing， Sediment transport， Erosion， Shock waves， Shear waves， Fluvial hydraulics.，

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