Hydraulic Modeling

     ·    Alexander, David E.  1990.  Drag Coefficients of Swimming Animals: Effects of Using Different Reference AreasBiological Bulletin .  179(2)

Abstract
The drag coefficient (CD) is useful for comparing the hydrodynamic drag among different swimming animals. However, CD is calculated using an arbitrary reference area for which there is no uniform convention; both total surface area (_‘wetted area’) and maximum cross-sectional area (_‘frontal area’) are widely used. The choice of reference area can have a profound effect on calculations of drag coefficient. To illustrate this problem, drag measurements from two isopod crustacean species were used to calculate CD based on both wetted and frontal areas. Idotea wosnesenskii had a higher mean CD based on wetted area (0.084) than Idotea resecata (0.059), but a lower mean CD based on frontal area (0.95) compared to I. resecata (1.22); both differences are statistically significant. Given that there is no powerful hydrodynamic basis for choosing either reference area, and that conversions between wetted area CD and frontal area CD cannot accurately be made for complex shapes, I suggest reporting both wetted area and frontal area CD’s wherever practical. (Author’s Abstract)
Keywords:
drag; drag coefficient; swimming; wetted area; frontal area; hydraulics

 

     ·    Azzillino, A.  and Vismara, R.  2001 .  Pool Quality Index: New Method to Define Minimum Flow Requirements of High-Gradient, Low-Order StreamsJournal of Environmental Engineering.  127(11):1003-1013.

Abstract
:  High-gradient (>1%), low-order streams, characterized by hydraulically nonuniform and heterogeneous channels, represent a problem for the most widely employed habitat-based in-stream flow methods (IFIM-PHABSIM). In a nonuniform high gradient and turbulent channel, as low-order streams usually are, the classical 1D hydraulic modeling, ordinarily employed by in-stream flow models to simulate the changes in fish habitat with the flow, could be questionable, if not completely inapplicable. Channel morphology in fact plays a major role in association with hydraulics in determining the abiotic environments (biotopes) in which aquatic communities live. Particularly, in low-order river systems, different channel form features shape the biological community that can be hosted in a certain biotope. For this reason, the link between morphology and discharge is important when evaluating possible impacts of flow reduction on aquatic organisms. To represent the relationship between hydraulics and channel morphology quantitatively, a hydraulic diversity concept has been adopted. Studies from the literature have revealed that, in a regulated river, a decrease of the environmental variability including hydraulic diversity quite often resulted in a downstream decrease of the macro-invertebrate diversity, which can consequently affect fish biomass. These considerations create the ground for a hydraulic diversity-dischargebased in-stream flow method with the aim to promote high community diversity in a low-order regulated stream. A statistic ordination technique (correspondence analysis) applied to 370 hydraulic sections helped to identify four main morphological units (pools, deep pools, and slow and fast riffles) in terms of hydraulic diversity. In each morphological unit, the hydraulic diversity-discharge relationship was investigated and modeled by means of best-fit regression curves. Combining the hydraulic diversity-discharge curves from different morphological units (pools and riffles), a simplified model of the stream [pool quality index (PQI)] was obtained. This model has been applied to make recommendations for the minimum flow requirements in six low-order river sites. PQI recommendations were consistent with hydrology and other hydrology-based in-stream flow methodologies. Finally, a multiple regression model indicated that in 12 low-order stream sites a good deal of the variability of macro-invertebrate diversity is explained by the availability of hydraulic environments modeled by means of PQI curves. In conclusion, given the encouraging cues about the ecological meaning of PQI and the possibility to overcome difficulties typically encountered by other methods in the low-order river modeling, PQI can be considered a valid alternative for assessing the in-stream flow needs of low-order streams.  (Author’s abstract)

Keywords:
IFIM; PHABSIM; channel morphology; hydraulics; invertebrate communities

 

     ·    Bao, Yixing, Tung, Yeou-Koung, and  Hasfurther, Victor R.  1987.  Evaluation of uncertainty in flood magnitude estimator on annual expected damage costs of hydraulic structuresWater Resources Research.  23:2023-2029.

Abstract
:  In the risk-based design for hydraulic structures, the major task is the evaluation of the annual expected damage costs caused by floods. Due to the use of a limited amount of data in flood frequency analysis, the computed flood magnitude of a specified return period is subject to uncertainty. A methodology to integrate such uncertainty in the evaluation of annual expected flood damage is developed and illustrated through an example in culvert design. The effect of uncertainty in estimating flood magnitude using different hydrologic probability models with different sample sizes on the annual expected damage cost is examined. Results of the study show that the effect of the uncertainty in a flood magnitude estimate on annual expected damage is quite significant and is sensitive to the sample sizes and the probability distribution models used. (A) 9 refs

Keywords:
risk analysis and design; drainage structure; flood estimation and control; cost and economics; hydraulics; analysis and assessment

 

     ·    Barber, M. E.  and Downs, R. C.  1996.  Investigation of culvert hydraulics related to juvenile fish passage.  Pullman, WA.  Washington State Transportation Center (TRAC), Washington State University.   Final Technical Report.

Abstract
: Culverts often create barriers to the upstream migration of juvenile fish. Fish will not travel upstream under high water velocity conditions. It is hypothesized that low velocity regions exist near culvert boundaries. Therefore, the objective of this study was to determine hydraulic characteristics of culverts with different flow conditions. Methods of predicting flow profiles were developed by both Chiu and Mountjoy. Two equations were compared to experimental results. The Mountjoy equation proved to yield better results for velocity profile predictions. An area of flow corresponding to a predetermined allowable velocity can be calculated using the Mountjoy equation. This can then be used in the design of culverts as fish passage guidelines. The following technical report contains a detailed description of background information, experimental methodology, the results of experimental tests, and an analysis of both the Chiu and Mountjoy equations. (A)

Keywords
: culvert design; fish passage; hydraulics; research methodology; behavior; culvert

 

     ·    Barber, M. E.  and Downs, R. C.  1996.  Investigations of culvert hydraulics related to juvenile fish passage.  Pullman, Washington.  State Transportation Center (TRAC), Washington State University.:  1-54

Abstract
: Culverts often create barriers to the upstream migration of juvenile fish.  Fish will not travel upstream under high water velocity conditions.  It is hypothesized that low velocity regions exist near culvert boundaries.  Therefore, the objective of this study was to determine the hydraulic characteristics of culverts with different flow conditions.  Methods of predicting flow profiles were developed by both Chiu and Mountjoy.  Two equations were compared to experimental results.  The Mountjoy equation proved to yield better results for velocity profile predictions.  An area of flow corresponding to a predetermined allowable velocity can be calculated using the Mountjoy equation.  This can then be used in the design of culverts as fish passage guidelines.  The following report contains a summary of background  information, experimental methodology, the results of experimental tests, and an analysis of both the Chui and Mountjoy equations. (Author’s summary)

Keywords
: culvert; culvert hydraulics; juvenile fish passage; fish passage; upstream migration; barrier; water velocity; flow condition; flow profile; flow equation; Chui equation; Mountjoy equation; research methodology; behavior; hydraulics

 

     ·    Donahue, John P. and Howard, Andrew F.  1987.  Hydraulic design of culverts on forest roadsCanadian Journal of Forest Research.  17:1545-1551.

Abstract
:  Design of drainage structures is an important part of planning forest roads, which usually includes culverts. Determining the appropriate pipe size for a given site involves estimation of expected flows and evaluation of the hydraulic performance of pipes of different sizes. In this paper a review of the hydraulic relationships applicable to the evaluation of pipe hydraulics is presented. A computer model is introduced that incorporates these relationships. The model is used to compare two algorithms for computing headwater depths, given inlet control (supercritical flow). The relative efficiency of four inlet types was also investigated. Results indicate that potential cost savings exist by altering inlet geometry and that computer-   assisted design can facilitate accommodations of conflicting design goals. (A)

Keywords:
hydraulics; road design and construction; forest road ; culvert design; modeling; drainage structure ; culvert; research methodology; road

 

     ·    Geldert, Darrin A., Gulliver, John S., and Wilhelms, Steve C.  1998.  Modeling Dissolved Gas Supersaturation Below Spillway Plunge PoolsJournal of Hydraulic Engineering .  124(5):513-521.

Abstract
:  Excessive supersaturation of dissolved gases, primarily nitrogen and oxygen, can cause gas bubble disease, and eventual mortality, in fish. This potential threat is currently a concern in efforts to aid anadromous fish survival in the northwestern United States. In an effort to better understand dissolved gas supersaturation and assist in its mitigation, physically based relationships have been expanded and developed to predict dissolved gas supersaturation below spillways. This paper discusses the predictive technique as applied to the dissolved gas supersaturation that occurs because of the stilling basin and the river reaches immediately downstream of the structure. Gas transfer across both the water surface and the bubble interface are considered. Extensive field data from three spillways on the Columbia and Snake Rivers is used to fit coefficients that the predictive relationships require. The inclusion of more physically based parameters will allow for the evaluation of the operation and design of the structures and may provide insight for efforts to mitigate high dissolved gas concentrations downstream of such structures. (Author’s Abstract)

Keywords:
dissolved gasses; oxygen; nitrogen; bubble disease; fish; Columbia River; Snake River; hydraulics; water quality

 

     ·    Hess, Timothy G.  2001. Unpublished work.  Research for AASHTO standing committee on highways.  Task 146.  Development of software verification protocol for the hydrologic and hydraulic models for highway planning and design.  Project 20-07, Task 146.

Abstract
: The proposed study will develop a protocol for the verification and validation of software available for watershed,   hydrologic and hydraulic modeling for highway planning and design studies.  (Author's abstract)

Keywords
: Hydrologic cycle; Hydraulics ; Highway planning; Software; Design; Research project; National Cooperative; Highway Research Program; Hydrology; hydraulics; analysis and assessment

 

     ·    Katopodis, C. , Rajaratnam, N., Wu, S., and Tovell, D.  1997.  Denil Fishways of Varying GeometryJournal of Hydraulic Engineering .  123(7):624-631.

Abstract
:  This paper presents the results of an extensive laboratory study aimed at improving the design of Denil fishways.  For the standard design of the simple Denil, and equation has been developed between the dimensionless discharge Q* and the relative flow of d/b for d/b as large as 5.5. The normalized velocity distributions in the centerplane of the Denil fishway, based on the results of about 660 experiments, a method has been found to predict not only the relation between Q* and d/b but also the normalized velocity profiles in the centerplane of the Denil.  The coefficient of friction between the central stream in the Denil and the circulating water on thesidess as well as the bottom has been evaluated along with the equivalent Manning's n for the Denil fishway.  These results are believed to be important in extneding the depth range of the standard Denils as well as making changes to the standard Denil for passing differing species  of fish.  (Author’s Abstract)

Keywords:
Denil fishways; barrier remediation; research methodology; hydraulics

 

   ·    Leopold, Luna B. and Maddock, Thomas Jr.  1953.  The hydraulic geometry of stream channels and some physiographic implications.  Washington.  United States Government Printing Office.:  57 pages.

Abstract
: Some hydraulic characteristics of stream channels - depth, width, velocity, and suspended load - are measured quantitatively and vary with discharge as simple power functions at a given river cross section.  Similar variations in relation to discharge exist among the cross sections along the length of a river under the condition that discharge at all points is equal in frequency of occurrence.  The functions derived for a given cross section and among various cross sections along a river differ only in numerical values of coefficients and exponents.  These functions are:
  w=aQb     d=cQf     v=kQm     L=pQj   where   w=width   d=mean depth   v=mean velocity   L=suspended -sediment load, in units of weight per unit time   Q=water discharge, in cubic feet per second (cfs); a, c, k, p, b, f, m, and j are numerical constants. 
These relationships at a given channel cross section and downstream when plotted on graphs are greatly similar even for river systems very different in physiographic setting.  The relationships are described by term "hydraulic geometry."   In the data studied it appeared that when discharges are of equal frequency at different points along a river, that is, equalled or exceeded the same percent of time, the velocity as well as the width and depth of flow, increases with discharge downstream.  This increase of velocity downstream results from the fact that the increase in depth overcompensates for the decrease in slope.  The tendency for velocity to increase downstream exists on most streams despite the decreasing particle size downstream.  This indicates that the mean velocity in a given reach is not merely a function of the size of particles which must be transported but is governed by a more complex interaction among several factors.     Measurements of suspended-sediment load are available for a number of different river cross sections.  The suspended load is shown to be an index to total load for purposes of explaining the observed average characteristics of natural channel systems.     An empiric quantitative relation among average measurements of width, depth, velocity, discharge, and suspended-sediment load is derived from data on natural rivers.  This relation shows that depth and width, as well as velocity, are functions of the load transported in the channel.     In a simplified example, if the discharge is constant, the empiric relation is: At a given discharge, an increase in width at constant velocity is accompanied by a decrease in suspended-sediment load; conversely, at constant discharge and velocity, an increase in width is accompanied by an increase in bedload.     The writers, like many others, postulate that both discharge and sediment load are factors essentially independent of the stream channel and depend on the nature of the drainage basin.  The typical relations between suspended-sediment load and water discharge are shown in quantitative terms.  Specifically, at a given stream cross section, suspended sediment load per unit of discharge characteristically increases rapidly with increased discharge.  However, suspended load per unit volume of water tends to decrease slightly downstream.     These characteristics are important determinants of the shape of the cross section of a channel and the progressive changes in its shape downstream.  The empiric relation between hydraulic characteristics of the channel and suspended load provides, in semiquantitative terms, a logical explanation of the observed channel shape.     The hydraulic geometry of river channels is presented for several river systems.  It is shown that similar equations apply both to rivers and to stable ("regime") irrigation canals which neither scour or aggrade their beds.  The analogy demonstrates that the average river channel-system tends to develop in a way to produce an approximate equilibrium between the channel and the water and sediment it must transport.  This approximate equilibrium appears to exist even in a given cross section for all discharges up to the bankfull stage.  (Author's abstract)

Keywords
: water discharge; mean depth; width; water depth; suspended-sediment load; sediment load; irrigation canal; channel; hydraulic geometry; stream channel; water velocity; river channel; river system; physiographic implication; hydraulics

 

   ·    Liao, James C., Beal, David N., Lauder, George V., and Triantafyllou, Michael S.  2003.  The Kármán Gait: Novel Body Kinematics of Rainbow Trout Swimming in a Vortex StreetThe Journal of Experimental Biology.  206(6):1059-1073.

Abstract
:  Most fishes commonly experience unsteady flows and hydrodynamic perturbations during their lifetime. In this study, we provide evidence that rainbow trout Oncorhynchus mykiss voluntarily alter their body kinematics when interacting with vortices present in the environment that are not self-generated. To demonstrate this, we measured axial swimming kinematics in response to changes in known hydrodynamic wake characteristics. We compared trout swimming in the Kármán street behind different diameter cylinders (2.5 and 5 cm) at two flow speeds (2.5 and 4.5 L s1, where L is total body length) to trout swimming in the free stream and in the cylinder bow wake. Trout swimming behind cylinders adopt a distinctive, previously undescribed pattern of movement in order to hold station, which we term the Kármán gait. During this gait, body amplitudes and curvatures are much larger than those of trout swimming at an equivalent flow velocity in the absence of a cylinder. Tail-beat frequency is not only lower than might be expected for a trout swimming in the reduced flow behind a cylinder, but also matches the vortex shedding frequency of the cylinder. Therefore, in addition to choosing to be in the slower flow velocity offered behind a cylinder (drafting), trout are also altering their body kinematics to synchronize with the shed vortices (tuning), using a mechanism that may not involve propulsive locomotion. This behavior is most distinctive when cylinder diameter is large relative to fish length. While tuning, trout have a longer body wavelength than the prescribed wake wavelength, indicating that only certain regions of the body may need to be oriented in a consistent manner to the oncoming vortices. Our results suggest that fish can capture energy from vortices generated by the environment to maintain station in downstream flow. Interestingly, trout swimming in front of a cylinder display lower tail-beat amplitudes and body wave speeds than trout subjected to any of the other treatments, implying that the bow wake may be the most energetically favorable region for a fish to hold station near a cylinder. (Author’s Abstract)
Keywords:
Kármán street; vortex street; drag wake; vortex; cylinder; hydrodynamic pertubation; swimming kinematics; rainbow trout; Oncorhynchus mukiss; Kármán gait; drafting; tuning; tacking; entraining; locomotion; hydraulics

 

   ·    Maxwell, A. R. and Papanicolaou, A. N.  2001.  Step-pool morphology in high-gradient streamsInternational Journal of Sediment Research.  16(3):380-390.

Abstract
:  The focus of this study is to examine bed stability and morphology in high-gradient gravel-bed streams, and thus to improve understanding of the various parameters governing the sediment flow characteristics in mountain streams.  Ultimately, this knowledge can be used to design pseudo-natural channels, as in the stream simulation method of culvert design; with this in mind, prototype conditions are evaluated in a flume with slopes ranging from 3% to 7%, and particle relative submergence varying from 0.5 to 2.5 for three bed size distributions.  These experiments are designed to satisfy the conditions of dynamic similarity for flow and sediment, and they are preferred over field measurements since they allow a high degree of control over testing conditions.  It is found that step-pool bedforms are the most ubiquitous features along the gravel bed.  A new formula is developed that correlates step height with the gravel-bed size distribution, relative submergence of particles, and the Froude number.  The step spacing is found to be related to step height and streambed longitudinal slope.  Flow resistance is also examined, and a formula is developed which accounts for the resistance due to the bedforms (form resistance), as well as the individual sediment particles (grain resistance).  (Author's abstract)

Keywords:
mountain stream; step-pool bedform; step height; step-pool morphology; high-gradient stream; hydraulics; geomorphology

 

   ·    Odeh, Mufeed.  2003.  Discharge Rating Equation and Hydraulic Characteristics of Standard Denil FishwaysJournal of Hydraulic Engineering .  129(5):341-348.

Abstract
:   This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables.  A dimensionless discharge coefficient based on the physical slope of the fishway is introduced.  The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes.  Hydraulic characteristics of flow inside these fishways are discussed.  Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway.  Eingineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only.  Discharge capacity was directly proportional to the fishway based on a flow availability in conjunction with the swimming capabilities of target fish species.   (Author's Abstract)

Keywords:
fishways; water discharge; fish management; hydraulics; barrier remediation

 

   ·     Rajaratnam, N. and Katopodis, C.  1990.  Hydraulics of culvert fishways III: weir baffle culvert fishwaysCanadian Journal of Civil Engineering.  17:558-568.

Abstract
:  This paper presents the results of a laboratory study of culvert fishways with weir-type baffles. Baffles with heights equal to 0.15 and 0.1 times the diameter (D) of the culvert were studied with longitudinal spacings of 0.6D and 1.2D. Equations have been developed to describe the relation between the discharge, slope, diameter, and the depth of flow. It has been possible to predict the barrier velocity that would exist at the baffles. The performance of the weir baffles has been found to be as good as that of the slotted-weir baffles. (A) 9 Refs

Keywords:
baffle; culvert fish passage; culvert hydraulics; fishway; hydraulics ; research methodology; barrier remediation

 

   ·     Rajaratnam, N., Katopodis, C., and Lodewyk, S.  1991.  Hydraulics of culvert fishways IV: spoiler baffle culvert fishwaysCanadian Journal of Civil Engineering.  18:76-82.

Abstract
:  This paper presents the results of an experimental study on the hydraulics of culvert fishways with spoiler baffles. Four designs were studied with the heights of the baffles equal to 0.09D and 0.15D and longitudinal spacings of 0.53D and 1.06D, where D is the diameter of the culvert. Design equations have been developed relating the flow depth to the flow rate, the diameter and the slope of the culvert for each baffle design. Expressions    have also been found for the barrier velocity. (A) 8 Refs

Keywords:
baffle; culvert fish passage; culvert hydraulics; fishway; hydraulics

 

   ·     Rooseboom, A.  1985.  Practical culvert hydraulics: a South African perspectivePapers presented at the 2nd international conference on the hydraulics of floods & flood control.  Cambridge, England.  Cranfield, England.

Abstract
: Culverts and stormwater drains are common and relatively costly items in street and road drainage. They are often designed by persons who are not specialists in hydraulics. The result is that many of these elements are improperly designed. This paper presents a flexible system which has been developed for determining the design flood return period. It also includes a simplified system for performing practical design calculations. These calculations relate to culvert sizing, increasing the capacity of culvert barrels, outlet velocities and erosion protection measures downstream. (A) 4 refs

Keywords
: hydraulics; culvert design; road drainage; surface drainage; culvert; regional

 

   ·    Sands, Stephen R., Harned, James A., Sites, Mark A., and Stahl, James R.  1995.  Conveyance distribution to define flow boundaries at culvertsProceedings of the 22nd annual conference on integrated water resources planning for the 21st century.  Cambridge, MA.  Editor Domenica, M. F.  New York.

Abstract
: This paper presents a method to quantitatively analyze the location of the effective flow areas at culvert/bridge openings using a one-dimensional flow model based on the conveyance distribution in the cross-section contiguous to the culvert/bridge. The conveyance distribution method can be applied to a full spectrum of storm events and associated peak flows to result in independent water surface elevation results and effective flow boundary locations for a particular storm event. A comparison of standard one-dimensional model, one-dimensional model with effective flow boundaries defined using the conveyance distribution method, and two-dimensional hydraulic model results of an actual complex bridge opening is performed to verify the conveyance distribution method of effective flow boundary definition (A)

Keywords
: flow capacity; culvert hydraulics; bridge design; modeling; hydraulics

 

   ·    Scruton, D. A., McKinley, R. S., Kouwen, N., Eddy, W., and Booth, R. K.  2002.  Use of Telemetry in the Development and Application of Biological Criteria for Habitat Hydraulic ModelingHydrobiologia.  483(1-3):83-94.

Abstract
:  Habitat hydraulic modeling has arisen as the preferred tool for the prescription of ecologically acceptable flow regimes for projects that are striving to alter or reduce natural river flows. The biological/habitat components of these models are criticized and require more development. A research study was conducted on the West Salmon River, Newfoundland, Canada, to examine the influence of temporal and spatial elements of habitat selection on habitat hydraulic modeling. Juvenile Atlantic salmon (Salmo salar) were surgically implanted with radio transmitters and habitat selection was determined over varying flows, seasons, and on a diel basis. Experimental manipulation of flows simulated _‘peaking flow’ power generation allowing characterization of micro-habitat selection (depth, velocity, substrate) on a seasonal basis and in relation to flow variation. Habitat criteria (preference indices) were determined over the range of experimental conditions and used in simulations of weighted usable area (WUA). Curves derived at different flows had a large influence on WUA maxima, WUA trends in relation to discharge, and on spatial distribution of habitat suitability. This study has demonstrated the utility of telemetry in collection of data for development of temporally and spatially explicit habitat criteria. The study has also demonstrated the sensitivity of habitat hydraulic simulations to the selection of habitat preference indices.  (Author’s Abstract)

Keywords:
Atlantic salmon; smolts; downstream migration; fish passage; hydroelectric development; louver; fish exclusion system; hydraulics; research methodology

 

   ·     Triantafyllou, M. S., Techet, A. H., Zhu, Q., Beal, D. N., Hover, F. S., and Yue, D. K. P.   2002.  Vorticity Control in Fish-Like Propulsion and ManeuveringIntegrative and Comparative Biology.  42(5):1026-1031.

Abstract
:  Vorticity control is employed by marine animals to enhance performance in maneuvering and propulsion. Studies on fish-like robots and experimental apparatus modelling rigid and flexible fins provide some of the basic mechanisms employed for controlling vorticity. (Author’s Synopsis)
Keywords:
vorticity control; fins; kinematics; locomotion; hydraulics

 

   ·    Ye Jian and McCorquodale, J. A.  1997.  Three-Dimensional Numerical Modelling of Mass Transport in Curved ChannelsCanadian Journal of Civil Engineering.  24(3):471-479.

Abstract
:  A three-dimensional hydrodynamic model has been developed to study the flow and mass transport in curved channels. A curvilinear coordinate system is used in the horizontal xy-plane. In the vertical z direction, the σ-transformation is introduced to fit the free surface and variable bed bathymetry. The collocated grid system is adopted. To reduce the numerical diffusion, the second-order upwind scheme of Roe is incorporated to discretize the convection terms. The k-ε model is used to estimate the turbulent eddy viscosity and diffusivity. The governing equations are solved by a fractional three-step implicit algorithm. Two curved channels are considered: a 180° curved channel and a meandering channel. Some results are compared with the available data, which show that the secondary currents have a strong influence on the mixing of mass in curved channels. (Author’s Abstract)

Keywords:
hydrodynamic model; three dimensions; fractional step algorithm; curvilinear coordinates; collocated grid; curved channel; meanders; hydraulics

 

   ·    Zelensky, Paul N.  1976.  Approximate method for computing backwater profiles in corrugated metal pipes.  U.S. Department of Commerce, National Technical Information Service.   Final Report.

Abstract
: The determination of the shape and characteristics of a backwater profile in a closed conduit is generally a lengthy and tedious procedure without the use of a computer.  Utilizing the charts and tables of this publication and a few simple calculations, it is possible to completely define an M2 profile in a circular structural plate corrugated metal pipe with 6 x 2 inch corrugations.  The depth of flow, velocity head, and specific head may be determined at various points along the backwater curve, and the total length of the backwater curve may be defined.  Use of the publication will also provide the user with a better understanding of the effects of flow parameter variations on the shape and extent of the backwater profile.  (Author's abstract)

Keywords
: backwater; culvert; corrugated metal pipe; resistance slope; critical depth; specific head; full flow; normal depth; backwater profile; conduit; flow; flow parameter variation; hydraulics

 

   ·    Zhang Guang-Hui, Liu Bao-Yuan, Liu Guo-Bin, He Xia-Wu, and Nearing, M. A.  2003.  Detachment of Undisturbed Soil by Shallow FlowSoil Science Society of America Journal .  67(3):713-719.

Abstract
: Quantification of soil detachment rates is necessary to establish a basic understanding of soil erosion processes and to develop fundamental-based erosion models. Many studies have been conducted on the detachment rates of disturbed soils, but very little has been done to quantify the rates of detachment for natural soil conditions. This study was conducted to evaluate the influence of flow discharge, slope gradient, flow velocity, shear stress, stream power, and unit stream power on detachment rates of natural, undisturbed, mixed mesic typical Udorthent soil. Flow rates ranged from 0.25 to 2.0 L s -1 and slope gradient ranged from 8.8 to 46.6%. This study was compared with a previous study that used disturbed soil prepared by static compression. The results indicated that the detachment rates of disturbed soil were 1 to 23 times greater than the ones of natural undisturbed soil. It was necessary to use natural undisturbed soil samples to simulate the detachment process and to evaluate the influence of hydraulic parameter on detachment rate. Along with flow rate increasing, detachment rate increased as a linear function. Detachment rate also increased with slope gradient, but the functional relationship between the two variables depended on flow rate. Stepwise regression analysis indicated that detachment rate could be well predicted by a power function of flow rate and slope gradient (R2 = 0.96). Mean flow velocity was closely correlated to detachment rate (r2 = 0.91). Flow detachment rate was better correlated to a power function of stream power (r2 = 0.95) than to functions of either shear stress or unit stream power.  (Author’s Abstract)

Keywords:
soil detachment rates; erosion; models; matural soil conditions; hydraulics