A fuzzy dynamic flood routing model for natural channels

A fuzzy dynamic flood routing model (FDFRM) for natural channels is presented, wherein the flood wave can be approximated to a monoclinal wave. This study is based on modification of an earlier published work by the same authors, where the nature of the wave was of gravity type. Momentum equation of the dynamic wave model is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. Hence, the FDFRM gets rid of the assumptions associated with the momentum equation. Also, it overcomes the necessity of calculating friction slope (S_f) in flood routing and hence the associated uncertainties are eliminated. The fuzzy rule based model is developed on an equation for wave velocity, which is obtained in terms of discontinuities in the gradient of flow parameters. The channel reach is divided into a number of approximately uniform sub‐reaches. Training set required for development of the fuzzy rule based model for each sub‐reach is obtained from discharge‐area relationship at its mean section. For highly heterogeneous sub‐reaches, optimized fuzzy rule based models are obtained by means of a neuro‐fuzzy algorithm. For demonstration, the FDFRM is applied to flood routing problems in a fictitious channel with single uniform reach, in a fictitious channel with two uniform sub‐reaches and also in a natural channel with a number of approximately uniform sub‐reaches. It is observed that in cases of the fictitious channels, the FDFRM outputs match well with those of an implicit numerical model (INM), which solves the dynamic wave equations using an implicit numerical scheme. For the natural channel, the FDFRM outputs are comparable to those of the HEC‐RAS model. Copyright © 2009 John Wiley & Sons, Ltd.     

A fuzzy logic based dynamic wave model inversion algorithm for canal regulation

A fuzzy logic based centralized control algorithm for irrigation canals is presented. Purpose of the algorithm is to control downstream discharge and water level of pools in the canal, by adjusting discharge release from the upstream end and gates settings. The algorithm is based on the dynamic wave model (Saint‐Venant equations) inversion in space, wherein the momentum equation is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. The fuzzy rule based model is developed on fuzzification of a new mathematical model for wave velocity, the derivational details of which are given. The advantages of the fuzzy control algorithm, over other conventional control algorithms, are described. It is transparent and intuitive, and no linearizations of the governing equations are involved. Tuning of the algorithm and method of computation are explained. It is shown that the tuning is easy and the computations are straightforward. The algorithm provides stable, realistic and robust outputs. The disadvantage of the algorithm is reduced precision in its outputs due to the approximation inherent in the fuzzy logic. Feed back control logic is adopted to eliminate error caused by the system disturbances as well as error caused by the reduced precision in the outputs. The algorithm is tested by applying it to water level control problem in a fictitious canal with a single pool and also in a real canal with a series of pools. It is found that results obtained from the algorithm are comparable to those obtained from conventional control algorithms. Copyright © 2009 John Wiley & Sons, Ltd.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

结构振动的模糊建模与模糊控制规则提取

模糊振动控制中存在的模糊控制规则的建立大都依赖于主观经验的现状。对此本文提出了一种通过对结构振动模糊建模来产生控制规则的方法。首先，通过对系统运动状态变量的模糊化，建立结构振动的模糊关系模型；其次通过对结构振动的模糊关系模型的分析，提取出模糊控制规则；最后，通过一个单自由度体系的数值仿真方法进行了验证。     

MÉTHODE D'ÉTUDE DES NAPPES LIBRES DANS LES AQUIFÈRES ANISOTROPES

Abstract

The necessary and sufficient conditions for non-zero phase shift and non-zero attenuation in linear flood routing can be derived from the continuity equation alone and are found to depend on the existence of an imaginary part in the expression for frequency or in the expression for wave number. It is shown that in linear flood routing the phase lag between flow rate and area of flow is directly related to the attenuation per unit wave length. The effects of using various forms of the momentum equation, in addition to the continuity equation, are exemplified by deriving analytical expressions in terms of the frequency, both for attenuation per unit channel length and for phase shift, for the kinematic wave, the general diffusion analogy, and the complete St. Venant equation.     

涡激振动下管桥段的模糊动力可靠性研究

本文首先给出了管道在流体作用下的力学模型，并对风力作用下管道产生涡激振动的机理进行了分析，从而建立了管桥在风力作用下的力学模型和相应的振动微分方程，同时给出了管桥的固有特性和动力响应分析结果，然后，在此基础上，提出了首超模糊失效、模糊疲劳失效和混合失效等三类模糊失效准则，并依据这些准则分析给出了动力可靠性的计算公式，最后，给出了具体的算例。     

MODELING UNSTEADY TURBIDITY CURRENTS IN A STEEP NARROW RESERVOIR

1.IN~DUCTIONTurbiditycurrentisoneclassofflowsnameddensitycurrentorgravitycurrent(therHunterRouse(Yih(1980)),whichdePictstheintmsionofheaVyfluidintoalighterone.Usually,thedensitydifferencebetWeentWonuidisrelativelysmallandmixingacrosstheimerfaceoccurs.ThedrivingforceofdensitycurrentsisnotdensitydifferenceitselfbutthedifferenceinspeCmcweights.Turbiditycurrentisnamedwhenthedensitydifferenceisespeciallycausedbysuspendedfinesedimentparticles.Sincesediment-ladenflowcaninteraCtwiththelowerbou…     

Analytical and numerical analysis of tides and salinities in estuaries; part I: tidal wave propagation in convergent estuaries

Analytical solutions of the momentum and energy equations for tidal flow are studied. Analytical solutions are well known for prismatic channels but are less well known for converging channels. As most estuaries have a planform with converging channels, the attention in this paper is fully focused on converging tidal channels. It will be shown that the tidal range along converging channels can be described by relatively simple expressions solving the energy and momentum equations (new approaches). The semi-analytical solution of the energy equation includes quadratic (nonlinear) bottom friction. The analytical solution of the continuity and momentum equations is only possible for linearized bottom friction. The linearized analytical solution is presented for sinusoidal tidal waves with and without reflection in strongly convergent (funnel type) channels. Using these approaches, simple and powerful tools (spreadsheet models) for tidal analysis of amplified and damped tidal wave propagation in converging estuaries have been developed. The analytical solutions are compared with the results of numerical solutions and with measured data of the Western Scheldt Estuary in the Netherlands, the Hooghly Estuary in India and the Delaware Estuary in the USA. The analytical solutions show surprisingly good agreement with measured tidal ranges in these large-scale tidal systems. Convergence is found to be dominant in long and deep-converging channels resulting in an amplified tidal range, whereas bottom friction is generally dominant in shallow converging channels resulting in a damped tidal range. Reflection in closed-end channels is important in the most landward 1/3 length of the total channel length. In strongly convergent channels with a single forward propagating tidal wave, there is a phase lead of the horizontal and vertical tide close to 90^o, mimicking a standing wave system (apparent standing wave).     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

Impact of dissipation and dispersion terms on simulations of open‐channel confluence flow using two‐dimensional depth‐averaged model

The flow patterns in confluence channel and the simulation of confluence flow are more complex than that in straight channel. Additional terms in the momentum equations, i.e. dissipation terms, denoting the impact of turbulence, and dispersion terms, denoting the vertical non‐uniformity of velocity, show great impacts on the accuracy of numerical simulations. The dissipation terms, i.e. the product of eddy viscosity coefficient and velocity gradient, are much larger than those of the flow in straight channel. In this study, the zero equation model and the depth‐averaged k‐ε model are used to analyse the impact of eddy viscosity. Meanwhile, the dispersion terms in the momentum equation, depending on the vertical non‐uniformity of velocity, are usually neglected in routine simulation. With the use of detailed experimental data for verification, this study presents the distribution of parameters of vertical non‐uniformity and the intimated connection between non‐uniformity parameters and accuracy of numerical simulations of confluence flow with depth‐averaged models. The results present that simulation accuracy of confluence flow is very sensitive to the turbulence modes, which cannot be handled by normal, simple turbulence model. On the contrary, the impact of dispersion terms is both flow‐condition‐dependent and place‐dependent, and such impact is negligible when secondary circulation is weak. The results indicate the key elements in modelling confluence flow and are helpful for selecting suitable numerical model and solving engineering problems encountered in confluence channel. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of the direct runoff hydrograph at basin outlet

A simple model describing the transformation of effective rainfall to direct runoff through the overland flow mechanism is presented. The model is based on the classical representation of a watershed by a combination of planes and channels. The dynamics of overland flow in each plane is simulated by the non-linear kinematic wave, but the outflow from a given plane is concentrated in the middle of the corresponding drainage channel. The water routing in the channels is carried out by a piece-wise linearized formulation in space of the kinematic wave approximation. Using synthetic events on 10 watersheds, the model was tested by comparing it with results obtained by applying the non-linear kinematic wave to all the elements of the watershed. The model was found to be adequate, even in a form that simplifies the geometric features of the planes through an averaging procedure based on the Horton–Strahler ordering scheme of the watershed. © 1998 John Wiley & Sons, Ltd.     

Modelling overland flow based on Saint‐Venant equations for a discretized hillslope system

Mathematical modelling of overland flow is a critical task in simulating transport of water, sediment and other pollutants from land surfaces to receiving waters. In this paper, an overland flow routing method is developed based on the Saint‐Venant equations using a discretized hillslope system for areas with high roughness and steep slope. Under these conditions, the momentum equation reduces to a unique relationship between the flow depth and discharge. A hillslope is treated as a system divided into several subplanes. A set of first‐order non‐linear differential equations for subsequent subplanes are solved analytically using Chezy's formula in lieu of the momentum equation. Comparison of the analytical solution of the first‐order non‐linear ordinary differential equations and a numerical solution using the Runge‐Kutta method shows a relative error of 0·3%. Using runoff data reported in the literature, comparison between the new approach and a numerical solution of the full Saint‐Venant equations showed a close agreement. Copyright © 2002 John Wiley & Sons, Ltd.     

One-dimensional simulation model for steady transcritical free surface flows at short length transitions

A numerical experiment is carried out to investigate the suitability of a Boussinesq-type momentum model for simulating transcritical flows at short length transitions in open channel flow measuring structures. Two one-dimensional Boussinesq-type equation models, which incorporate different degrees of dynamic pressure corrections, are considered for this purpose. A finite difference method is employed to discretise and solve the equations. The models are then applied to simulate different test cases for flows in such channels with predominant non-hydrostatic pressure distribution effects. A comparison of the computed results with the corresponding experimental data is presented. Results of this study reveal that the proposed model, which includes a higher-order correction for the effect of the centrifugal pressure, describes well even relatively abrupt changes from sub- to super-critical flow state.     

非均匀流-固边界耦合介质多参数全波形反演方法

海洋勘探环境可以抽象为下伏固体与上覆流体相互耦合的介质,本文针对流-固边界耦合介质提出了一种高效、稳定的多参数（速度和密度）全波形反演方法.本文采用弹性波一阶位移-应力方程作为过渡层耦合声波压力方程与弹性波位移方程来模拟耦合环境,相比于传统的交错网格建模方法或者构建连续性条件,本文提出的方法在正演精度和稳定性上凸显出很大优势,极大降低了计算内存.反演策略对多参数全波形反演至关重要,由于不同参数之间的相互耦合使得密度在多参数全波形反演中较难获得,因此本文将非均匀流-固边界耦合介质多参数全波形反演分为两个步骤完成：第一步利用变密度声波方程结合推导出的密度梯度算子进行纵波速度和密度的双参数反演;第二步根据链式法则求取横波速度的梯度,结合第一步的反演结果使用流-固边界耦合方程反演横波速度.最后通过与声波动方程数值模拟结果对比证明正演算法的准确性;上覆流体的Marmousi-2模型的数值试验测试说明反演方法的有效性和适应性.

     

A consistent derivation of the wave-energy equation from basic hydrodynamic principles

Based on a decomposition of the velocity into mean flow, turbulent and wave components, momentum and hereafter a wave-energy equation is derived. It contains a turbulent energy dissipation term which is closed by applying a wave-related mixing length model and linear wave theory solutions. This closure produces a non-linear turbulent wave-energy dissipation including the wave energy in a 5/2 power law. The theory is able to predict correctly the shape of deep-water wave spectra according to Phillips' similarity law.Responsible Editor: Hans Burchard     

NUMERCAL COMPUTATION OF VERTICAL TWO-DIMENSIONAL NON-EQUILIBRIUM SEDIMENT MOVEMENT

INON-EQUILIBRIUMMOVEMENTContinualexchangeremainsamongthebedmaterial,bedloadandsuspendedloadinariver.Thebedloadmovesonthebedsurfaceandjumpsinsteps.Itstransportrateperwidthvarieswithvaryingflowintensity;whilethesuspendedloadmoveswithalongstep,evenifthehydraulicfactorsbecomeweaker,itwillnotretUrntothebeduntilfinishingthefallingprocess.ThismeansthatahysteresisexistsbetWeenthechangeofthesuspendedsedimentmovementandflowvelocity.Foruniformandsteadyflow,thesedimentmovementkeepsinequilibriumi…     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

Accuracy of kinematic wave and diffusion wave approximations for space-independent flows on infiltrating surfaces with lateral inflow neglected in the momentum equation

Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included.     

垂直上升管中气液两相流电导波动信号的混沌特性分析

首先以Lorenz混沌方程产生的非线性时间序列为例,讨论了在不同时间序列长度下各种延迟时间算法对噪声的适用性.研究发现,采用C_C算法计算延迟时间的鲁棒性强.在此基础上,给出了垂直上升管中气水两相流电导波动信号混沌表征结果,发现在较低水相表观速度时,随着气相表观速度增加,泡状流及混状流动力学特性变得愈加复杂,而段塞流动力学特性受液相表观速度影响较大;在较高水相表观速度时,随着气相表观速度增加,当流型从泡状流向段塞流转变时,气液两相流动力学特性变得相对简单.但是,由于受液相湍流作用影响,段塞流的动力学特性表现出了涨落现象,呈现不稳定性,当流型从段塞流向混状流转变时,气液两相流动力学特性则变得愈加复杂.研究结果表明：基于电导波动信号的混沌分析可以较好地表征气液两相流流型变化,是理解流型转变机理及其动力学演变特性的有用工具.     

Large-eddy simulation of the turbulent structure in compound open-channel flows

A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow in an asymmetric compound channel. The dynamic sub-grid scale model has been employed in the model, with the partial cell treatment being implemented using a Cartesian grid structure to deal with the floodplain. The numerical model was used to predict the: primary velocity and secondary currents, boundary shear stress, turbulence intensities, turbulent kinetic energy, and Reynolds stresses. These parameters were compared with experimental measurements published in the literature, with relatively close agreement being obtained between both sets of results. Furthermore, instantaneous flow fields and large-scale vortical structures were predicted and are presented herein. These vortical structures were found to be responsible for the significant lateral exchange of mass and momentum in compound channels.