LONGITUDINAL DISPERSION IN SEDIMENT-LADEN OPEN CHANNEL FLOWS

Laboratory experiments on longitudinal dispersion in clear-water and sediment-laden open channel flows are reported. Data from these experiments and those available from previous studies indicate that the suspended sediment present in the flow affects the longitudinal dispersion process. The observed velocity distributions over the depth of sediment-laden flows indicate that the velocity deviates from the mean velocity more in sediment-laden flows than in clear-water flows. The velocity distributions over the cross section and secondary flow in the channel are also expected to be altereddue to the presence of suspended sediments in the flow. For these reasons, more dispersion is found in sediment-laden flows than in corresponding clear-water flows. A predictor for the dispersion coefficient in sediment-laden flows is proposed.     

A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain

An unstructured Godunov-type finite volume model is developed for the numerical simulation of geometrically challenging two-dimensional shallow water flows with wetting and drying over convoluted topography. In the framework of sloping bottom model, a modified formulation of shallow water equations is used to preserve mass conservation during flooding and recession. The key ingredient of the model is the use of this combination of the sloping bottom model and the modified shallow water equations to provide a robust technique for wet/dry fronts tracking and, together with centered discretization of the bed slope source term, to exactly preserve the static flow on irregular topographies. The variable reconstruction technique ensures nonnegative reconstructed water depth and reasonable reconstructed velocity, and the friction terms are solved by semi-implicit scheme that does not invert the direction of velocity components. The robustness and accuracy of the proposed model are assessed by comparing numerical and reference results of extensive test cases. Moreover, the results of a dam-break flooding over real topography are presented to show the capability of the model on field-scale application.     

Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynolds stress model

A Reynolds stress model for the numerical simulation of compound open-channel flows with vegetation on the floodplain is described. The Reynolds stress model consists of various sub-models such as Speziale et al.’s model, Mellor and Herring’s model, and Rotta’s model for the pressure–strain correlation term, the turbulent diffusion term, and the dissipation term, respectively. For validation of the model, plain compound open-channel flows are simulated. The computed results were compared with measured data by [Tominaga A, Nezu I. Turbulent structure in compound open-channel flows. J Hydraul Eng, ASCE 1991;117(1):21–41] and the results show that the Reynolds stress model successfully simulates the mean flow and turbulence structure of plain compound channel flows. The model was then applied to compound open-channel flows with vegetated floodplains. Good agreement between the simulated results and data from an algebraic stress model by [Naot D, Nezu I, Nakagawa H. Hydrodynamic behavior of partly vegetated open channels. J Hydraul Eng, ASCE 1996;122(11):625–33] was found. However, it was shown that the RSM is capable of predicting the velocity dip and lateral shift in the maximum streamwise velocity, which were not observed in the data from algebraic stress modeling. Finally, a depth-averaged analysis of the streamwise momentum equation was performed to investigate the lateral momentum transfer in compound channel flows with vegetated floodplains. Compared with components by the secondary currents and Reynolds stress, the drag force due to the presence of vegetation appears to be a factor in reducing the bottom shear stress in both main channel and floodplain.     

Processes of dike-break induced flows:A combined experimental and numerical model study

Dike breaking is a disaster that could cause extensive damage. It could lead to flood flows outside the dike and induce water level fluctuations in the main channel. Numerical models are increasingly used to simulate flood flows due to dike-break, because direct observations from field surveys and physical models are rather limited. Existing knowledge concerning dam-break flows cannot be applied directly to dike-break flows because the effect of channel discharge cannot be neglected in the latter. In this study,physical experiments are done in a large laboratory flume to simulate the process of dike-break induced flood wave propagation in the floodplain and flow fluctuations in the main channel. The variations of water levels and velocities are measured and recorded using an array of pressure sensors and two acoustic Doppler velocimetry devices. A numerical model has been set up according to the experimental layout. The experiments have high repeatability and the numerical model predictions agree closely with the physical model data. The experimental results provide reliable information for improving the understanding of dike-break flow dynamics and for the verification of numerical models.     

Application of a sigma coordinate sea model to the calculation of wind-induced currents

A three-dimensional numerical sea model is formulated in terms of sigma coordinates in the vertical. The vertical grid spacing in the model is arbitrary and can be refined to give enhanced resolution in high shear regions (e.g., close to the sea surface in wind-driven flows, and/or across the thermocline in stratified flows). A method of accurately determining surface currents and indicating how fine a grid is required in the surface layer is described.The problem of determining a suitable formulation of vertical eddy viscosity to use in a model of wind-induced flow in a tidal sea is considered in detail. A formulation in which surface eddy viscosity depends upon the roughness of the sea surface and the transfer of momentum to depth by surface waves appears reasonable. Below the surface layer turbulence is related to the current at depth.Idealized calculations are performed to demonstrate the accuracy and stability of the sigma coordinate model. Results of these calculations indicate that the formulation of eddy viscosity developed in this paper can explain the high surface shears reported in lake measurements of wind-induced surface currents, and the lack of shear under strong wind conditions in the open sea (GORDON, 1982, Journal of Geophysical Research, 87, 1939–1951).Surface current to surface wind ratio are also computed.     

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.     

Emplacement conditions of the c. 1,600-year bp Collier Cone lava flow, Oregon: a LiDAR investigation

A long-standing question in lava flow studies has been how to infer emplacement conditions from information preserved in solidified flows. From a hazards perspective, volumetric flux (effusion rate) is the parameter of most interest for open-channel lava flows, as the effusion rate is important for estimating the final flow length, the rate of flow advance, and the eruption duration. The relationship between effusion rate, flow length, and flow advance rate is fairly well constrained for basaltic lava flows, where there are abundant recent examples for calibration. Less is known about flows of intermediate compositions (basaltic andesite to andesite), which are less frequent and where field measurements are limited by the large block sizes and the topographic relief of the flows. Here, we demonstrate ways in which high-resolution digital topography obtained using Light Detection and Ranging (LiDAR) systems can provide access to terrains where field measurements are difficult or impossible to collect. We map blocky lava flow units using LiDAR-generated bare earth digital terrain models (DTMs) of the Collier Cone lava flow in the central Oregon Cascades. We also develop methods using geographic information systems to extract and quantify morphologic features such as channel width, flow width, flow thickness, and slope. Morphometric data are then analyzed to estimate both effusion rates and emplacement times for the lava flow field. Our data indicate that most of the flow outline (which comprises the earliest, and most voluminous, flow unit) can be well explained by an average volumetric flux ～14–18?m³/s; channel data suggest an average flux ～3?m³/s for a later, channel-filling, flow unit. When combined with estimates of flow volume, these data suggest that the Collier Cone lava flow was most likely emplaced over a time scale of several months. This example illustrates ways in which high-resolution DTMs can be used to extract and analyze morphologic measurements and how these measurements can be analyzed to estimate emplacement conditions for inaccessible, heavily vegetated, or extraterrestrial lava flows.     

A nested model of the Cariaco Basin (Venezuela): description of the basin’s interior hydrography and interactions with the open ocean

A high-resolution (1/60°), three-dimensional numerical circulation model of the Cariaco Basin (Venezuela) is constructed by nesting the Regional Ocean Modeling System (ROMS) in the 1/12° global Hybrid Coordinate Ocean Model (HYCOM). A new bathymetry, computed by merging DBDB2 data and in situ depth measurements using optimal interpolation, is described. This new bathymetry corrects the depth of the channels that connect the Cariaco Basin with the open ocean and which play a very important role in the basin circulation. Results from a 2004 ROMS hindcast are presented. Observations (temperature, salinity, and currents) are used to validate the model results before using the model to describe the annual cycle of the Cariaco Basin and the interactions between the basin and the open ocean. Two modes of interaction are described, the first being the meanders and eddies that travel westward with the Caribbean Current, and the second being a subsurface eastward current that flows along the north coast of South America. The circulation path within the basin is directly related to the intensity of this current. Both mechanisms described play a role in the ventilation of the basin. The present study is also an example of the feasibility of one of the objectives of GODAE (Global Ocean Data Assimilation Experiment): downscaling from a large-scale model to a regional model. In particular, the nesting ratio of 5 used in this work demonstrates that a high-resolution model can be successfully nested in HYCOM.     

Numerical solution of the dispersion equation using a variable dispersion coefficient: method and applications

ABSTRACT

The study presented herein forms part of a wider research project on dispersion prediction in open channel flows which include laboratory, field and numerical investigations. In this paper, a numerical model which uses finite elements in space and finite differences in time for the solution of the convective-dispersion equation is developed and verified. In the model, the dispersion coefficient is considered as a function of time (or distance) during the initial period. It is represented by a modified Fickian type model which has been calibrated by the authors using laboratory data. The numerical model has been used to predict concentration profiles of tracer studies carried out in the laboratory as well as in the field.     

A quasi-geostrophic numerical model of a rotating internally heated fluid

Abstract

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.     

Assessing the credibility of a series of computational fluid dynamic simulations of open channel flow

Recent developments in numerical algorithms have enabled the construction of three‐dimensional models for the prediction of flows in open channels. These advances encompass improvements in both numerical solutions and the process representation required for an accurate system definition. However, to date, there is still little agreement on how to assess systematically and report the credibility of these simulations. This paper addresses this problem by adopting a Grid Convergence Index approach. The results indicate, for two simple hypothetical cases, a zero‐degree confluence and a meander bend, that the numerical code can be verified to an acceptable numerical standard. However, it is shown that this does not mean that verification is complete, as the literature implies, as whilst the discretization resolution may be sufficient to verify one of the model variables it does not imply that every variable has converged. Furthermore, the scheme may still be insufficient to capture all the processes of interest that are operating within the chosen environment. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of sizes and shapes of gravel particles on sediment transports and bed variations in a numerical movable-bed channel

The paper presents a numerical movable-bed channel capable of simulating three-dimensional motions of flows and gravel particles in different shapes. At first, the numerical channel was tested against results of fixed-bed channel experiments in which gravel particles were transported. Simulated particle motions were validated in comparison with those in the laboratory experiment. Next, numerical movable-bed experiments with sphere particles and gravel particles were conducted. The results of these experiments clearly elucidated the difference in motion between the large and the small particles, effects of shapes of gravel particles on sediment-transport rates, and hydrodynamic forces and contact forces at incipient motion and at settling.     

A semi-implicit three-dimensional numerical model for non-hydrostatic pressure free-surface flows on an unstructured,sigma grid

A semi-implicit 3-D numerical formulation for solving non-hydrostatic pressure free-surface flows on an unstructured,sigma grid is proposed.Pressure-splitting and 9 semi-implicit methods are inherited and reformed from Casulli’s z-coordinate formulation.The non-orthogonal sigma-coordinate transformation leads to additional terms. The resulting linear system for the non-hydrostatic correction is diagonally dominant but unsymmetric,and it is solved by the BiCGstab method.In contrast with z-coordinate non-hydrostatic models,the new model fits vertical boundaries much better,which is important for the long-time simulation of sediment transport and riverbed deformation.A lock-exchange density flow is computed to determine whether the new scheme is able to simulate non-hydrostatic free-surface flows.The new model is further verified using the field data of a natural river bend of the lower Yangtze River.Good agreement between simulations and earlier research results,field data is obtained, indicating that the new model is applicable to hydraulic projects in real rivers.     

Time-mean structure of secondary flows in open channel with longitudinal bedforms

Secondary motions are commonly present in open channel flows. This study aims to investigate, both experimentally and analytically, time-mean characteristics of cellular secondary flows generated by longitudinal bedforms. Experiments were conducted in a tilting, rectangular flume with six different longitudinal bedforms, including alternate bed strips with different roughness heights and bed ridges of wavy and rectangular shapes. Various flows were sampled using a two-dimensional laser Doppler anemometer (LDA) and a one-dimensional ultrasonic Doppler velocimeter (UDV). Experimental results demonstrate secondary flows appearing basically in cellular fashion over the modeled longitudinal bedforms. It is also shown that the cellular structures can be described analytically with kinematic considerations. The discrepancies between theoretical and measurement results are discussed. An empirical relationship between maximum vertical velocity and bed configuration is finally proposed based on the experimental data.     

Sensitivity of bed shear stress estimated from vertical velocity profiles: the problem of sampling resolution

Bed shear stress in open channel flows is often estimated from the logarithmic vertical velocity profile. However, most measuring devices used in the field do not allow for flow velocity to be measured very close to the bed. The lack of near-bed measurements is a critical loss of information which may affect bed shear stress estimates. Detailed velocity profiles obtained from a field acoustic Doppler velocimeter over three different bed roughnesses clearly show that the inclusion of near-bed points is critical for the estimation of bed shear stress in a shallow river environment. Moreover, the results indicate that using the full flow depth instead of the bottom 20 per cent of the profile generates an underestimation of the shear stress when flow is uniform. © 1998 John Wiley & Sons, Ltd.     

Modeling parametric uncertainty in optimal open channel design using FORM-PGSL coupled approach

Optimal design of artificial open channels is essential for the planning and management of irrigation projects. In this paper a modified formulation is presented for the comprehensive design of open channels considering the seepage loss, evaporation loss and land acquisition cost along with the lining and excavation cost. The resulting formulation is solved using a recent meta-heuristic optimization technique namely probabilistic global search Lausanne (PGSL). The uncertainty associated with channel design parameter may lead to the failure of canals (channels). The parametric uncertainty in open channel design is modeled using first order reliability method (FORM). A bi-objective optimization model is presented in the study which minimizes the cost and minimizes the probability of overtopping considering a probabilistic cost function as the objective function. A new approach is proposed to solve the model in a meta-heuristic environment following PGSL as the solution method. Also a chance constrained optimization model which considers overtopping probability constraint and channel capacity constraint simultaneously along with the objective of minimization of cost is propounded and solved using PGSL. The solutions obtained using coupled FORM-PGSL approach is encouraging and the method can be used for optimal and reliable design of artificial open channels.