Journal of Hydraulic Engineering

A one‐dimensional mathematical model has been developed to simulate accurately channel characteristics under low flow conditions in alluvial channels. For a given steady discharge, channel geometry, and channel bed particle size distribution, the model predicts the flow depth, the mean velocity, and the flow resistance. Energy losses are assumed to result from flow resistance, as well as from local losses generated by the contractions and expansions occurring through the pool‐riffle sequence. Laboratory and field data were used to calibrate and verify the model, as well as to conduct an in‐depth analysis of the flow characteristics associated with low discharges.

The linear form of the Muskingum model has been widely applied to river flood routing. However, a nonlinear relationship between storage and discharge exists in most actual river systems, making the use of the linear model inappropriate. In this paper, a nonlinear Muskingum model is solved using the state variable modeling technique. Various curve fitting techniques are employed for the calibration of model parameters, and their performances within the model are compared. Both linear and nonlinear models are applied to an example with pronounced nonlinearity between storage and discharge. The results show that the nonlinear Muskingum model is superior to the linear one.

A physical hydraulic model investigation was conducted to evaluate the performance of a stepped overflow spillway. The spillway has a standard ogee profile with continuous steps cut into the spillway face from just below the crest, to the toe. The steps significantly increase the rate of energy dissipation on the spillway face, thus eliminating or greatly reducing the need for a large energy dissipation basin at the spillway toe. Primary objectives of the investigation were to evaluate the effectiveness of the flow transition from the smooth crest profile to the steps, to quantify the energy dissipation on the spillway face, and to define the flow characteristics on the steps. The investigation demonstrated that this stepped spillway is quite effective at dissipating energy and that smooth flow transition from the spillway crest to the stepped face is easily achieved.

The equations which govern the movement of two‐dimensional gradually varied turbidity currents in reservoirs and over beaches are derived and solved numerically. Turbidity currents are sediment‐laden gravity currents that exchange sediment with the bed by erosion or deposition as the flow travels over the downslope. Turbidity currents derive this driving force from the sediment in suspension. They experience a resisting shear force on the bed and entrain water from above. Turbidity currents can be eroding or depositive, accelerating or decelerating, dependent on the combination of initial conditions, bed slope, and size of sediment particles. They can be controlled from upstream (supercritical) or downstream (subcritical). Gravity currents with and without erosion and deposition are examined in order to understand the effects of sediment exchange on the flow.

The characteristics of the second instability related to energy loss for the diffusive explicit method and the characteristic method for one‐dimensional unsteady open channel flow is studied by numerical experiments. The Koren stability criterion is found to be valid not only for the diffusive explicit method but also applicable to the characteristic method. This instability severely restricts the allowable grid size $\Delta t$ and $\Delta x$ when the Froude number is small. By treating the energy loss term in a semi‐implicit manner without complicating the computational procedure, it is possible to significantly improve the stability of the numerical schemes. The accuracy of various numerical schemes is also studied by numerical experiments. It is found that the most stable method is not necessarily the most accurate method.