Chih Ted Yang

Unit stream power equations for total load

Abstract A dimensionless unit stream power equation for the computation and prediction of total sediment concentration is obtained without using any criterion for incipient motion. This equation is compared with a similar dimensionless unit stream power equation proposed by the author in 1973 with the inclusion of criteria for incipient motion. Comparisons between the measured results from laboratory flumes and natural rivers and the computed results from these two unit stream power equations indicate that they are equally accurate in predicting the total sediment concentration in the sand size range. For the 1259 sets of data compared, the average computed result from these equations is only 3% higher than the measured result.

On river meanders

A review of the important stream morphologic theories and hypotheses published before 1971 indicates that none provides a satisfactory explanation to the formation of meandering streams. The law of least time rate of energy expenditure introduced by Yang1) is used to explain the formation of meandering streams. This law can explain why stable unbraided channels always follow a smooth sinuous course. It also explains how the variation in water discharge, sediment concentration, channel geometry, channel slope, valley slope, geological constraints, etc., should change the characteristics of meandering channels. The arguments made in this paper are strongly supported by laboratory and field observations.

Downstream hydraulic geometry relations: 1. Theoretical development

An edited version of this paper was published by AGU. Copyright 2003 American Geophysical Union.

Estimating overland flow erosion capacity using unit stream power

Abstract Soil erosion caused by water flow is a complex problem. Both empirical and physically based approaches were used for the estimation of surface erosion rates. Their applications are mainly limited to experimental areas or laboratory studies. The maximum sediment concentration overland flow can carry is not considered in most of the existing surface erosion models. The lack of erosion capacity limitation may cause over estimations of sediment concentration. A correlation analysis is used in this study to determine significant factors that impact surface erosion capacity. The result shows that the unit stream power is the most dominant factor for overland flow erosion which is consistent with experimental data. A bounded regression formula is used to reflect the limits that sediment concentration cannot be less than zero nor greater than a maximum value. The coefficients used in the model are calibrated using published laboratory data. The computed results agree with laboratory data very well. A one dimensional overland flow diffusive wave model is used in conjunction with the developed soil erosion equation to simulate field experimental results. This study concludes that the non-linear regression method using unit stream power as the dominant factor performs well for estimating overland flow erosion capacity.

Downstream hydraulic geometry relations: 2. Calibration and testing

An edited version of this paper was published by AGU. Copyright 2003 American Geophysical Union.

Force, Energy, Entropy, and Energy Dissipation Rate

The science of mechanics has been developed along two parallel lines, that is, the vectorial and the variational approaches. The vectorial approach is based on force and momentum while the variational approach is based on entropy, energy, or energy dissipation rate. This paper provides a review and comparison of the basic characteristics, strengths and weaknesses, and interrelationships between the two approaches. Some of the basic difficulties of solving hydraulic problems from the vectorial approach alone are cited to indicate the need for the variational approach. Examples of applications of principles and theories based on variational approach are given to demonstrate the flexibility and applicability of the approach to solve or explain complicated and diversified phenomena from a simple and unified point of view. This paper provides a brief review of the concepts and theories derived from the variational approach and compares them with those used in the vectorial approach. Basic difficulties and deficiencies in solving hydraulic and water resources engineering problems from the vectorial approach alone are explained. This paper shows that fundamental laws and equations used in Jiydraulics from the vectorial approach can also be derived from the variational approach. Entropy and energy dissipation rate theories are derived and compared in this paper. Selected examples are summarized to illustrate the strength and flexibility of applying the entropy and energy dissipation rate theories to explain and solve complex phenomena in hydraulics and water resources engineering.

Energy dissipation rate and sediment transport

There are three schools of thought in the study of sediment transport based on the concept that rate of energy dissipation of flowing water should be related to the rate of sediment transport or concentration. They are the unit stream power by Yang, the stream power by Bagnold, and the gravitational theory by Velikanov. Theoretical analyses are made to compare the validity of these theories. Laboratory and river data are used to test the assumptions used in the derivation of sediment transport equations based on these theories.

GSTARS computer models and their applications, Part II: Applications

Abstract In part 1 of this two-paper series, a brief summary of the basic concepts and theories used in developing the Generalized Stream Tube model for Alluvial River Simulation (GSTARS) computer models was presented. Part 2 provides examples that illustrate some of the capabilities of the GSTARS models and how they can be applied to solve a wide range of river and reservoir sedimentation problems. Laboratory and field case studies are used and the examples show representative applications of the earlier and of the more recent versions of GSTARS. Some of the more recent capabilities implemented in GSTARS3, one of the latest versions of the series, are also discussed here with more detail.

GSTARS computer models and their applications, part I: theoretical development

Abstract GSTARS is a series of computer models developed by the U.S. Bureau of Reclamation for alluvial river and reservoir sedimentation studies while the authors were employed by that agency. The first version of GSTARS was released in 1986 using Fortran IV for mainframe computers. GSTARS 2.0 was released in 1998 for personal computer application with most of the code in the original GSTARS revised, improved, and expanded using Fortran IV/77. GSTARS 2.1 is an improved and revised GSTARS 2.0 with graphical user interface. The unique features of all GSTARS models are the conjunctive use of the stream tube concept and of the minimum stream power theory. The application of minimum stream power theory allows the determination of optimum channel geometry with variable channel width and cross-sectional shape. The use of the stream tube concept enables the simulation of river hydraulics using one-dimensional numerical solutions to obtain a semi-two- dimensional presentation of the hydraulic conditions along and across an alluvial channel. According to the stream tube concept, no water or sediment particles can cross the walls of stream tubes, which is valid for many natural rivers. At and near sharp bends, however, sediment particles may cross the boundaries of stream tubes. GSTARS3, based on FORTRAN 90/95, addresses this phenomenon and further expands the capabilities of GSTARS 2.1 for cohesive and non-cohesive sediment transport in rivers and reservoirs. This paper presents the concepts, methods, and techniques used to develop the GSTARS series of computer models, especially GSTARS3.

Numerical modeling of sediment flushing from Lewis and Clark Lake

Abstract Lewis and Clark Lake is located on the main stream of the Missouri River. The reservoir is formed behind Gavins Point dam near Yankton, South Dakota, U.S.A. The Lewis and Clark Lake reach extends about 40 km from the Gavins Point dam. The reservoir delta has been growing since the closure of Gavins Point dam in 1955 and has resulted in a 21% reduction of storage within the maximum pool of the reservoir. Among several sediment management methods, drawdown flushing has been recommended as a possible management technique. The engineering viability of removing sediments deposited in the lake should be examined by numerical modeling before implementing a drawdown flushing. GSTARS4 was used for this study and calibrated by using measured data from 1975 to 1995. Channel cross-section changes and amount of flushed sediment were predicted with four hypothetical flow scenarios. The flushing efficiencies of all scenarios were estimated by comparing the ratios between water consumption and flushed sediment during flushing.