Journal of Hydraulic Engineering

A model for simulating the flow and bed topography in a meandering alluvial channel is developed. The basis is a solution to the equations for conservation of mass and momentum and for lateral stability of the streambed. The bed‐stability equation is a transverse force balance for bed‐sediment particles relating the transverse bed slope to primary flow variables. The main controlling parameters are the channel's width‐depth ratio, radius‐width ratio, resistance characteristics (or gradient), and sediment Froude number. An innovative feature is the use of a simple mass‐flux balance (mass conservation) to link the equation for bed stability to the momentum equations. The mass‐flux balance relates the net lateral transport of flow volume to the streamwise variation of transverse bed slope. Thereby, the equations governing the secondary‐current velocity and the transverse bed slope become those of a damped oscillating system subjected to a driving force, the change in channel curvature. The model is tested with both laboratory and field data.

An analytical model for simulating the flow and bed topography in a meandering alluvial channel is tested with data from two field studies. One set of data is used for testing a technique which involves discretizing the river channel into a number of straight and constant‐radius reaches, and solving a set of governing equations for each reach, using appropriate boundary conditions. The other set of data is used for testing a solution for a sequence of sine generated meander curves. In both cases the simulated flow and bed features are in good agreement with those measured. The agreement is obtained without use of calibration factors. With its ability to predict both magnitude and location of bed scour near outer banks in meander curves, the model should be a useful tool for the design of bank‐protection structures.

In calculating water surface profiles, the average friction slope is estimated from conditions at the ends of a reach. Methods used to approximate the average slope include use of the arithmetic, geometric, and harmonic means of reach‐end friction slopes, and the arithmetic mean of the reach‐end conveyances. Systematic variations exist in the slopes, and consequently the water levels, calculated by the various methods. Previous known investigations of the methods are limited, in their application, to prismatic channels. For irregular channels, the true friction slope line can be approximated by a third degree polynomial. Differences between the various approximations and the true average slope of such a curve show that the arithmetic mean of the reach‐end friction slopes has the lowest maximum error but does not always give the smallest error. Its use is suggested, coupled with systematic selection of cross section locations and occasional use of the geometric mean of reach‐end slopes.

A procedure is developed for a rational design of a system of submerged vanes for depth control in alluvial‐river channels. The vanes are vertical, small‐aspect ratio foils installed on the channel bed at an angle of attack of 10–15° with the flow. Their height is 0.2–0.5 times the water depth at design flow (stage). The design procedure is based on a calculation of the transverse bed slope generated by the vane‐induced transverse component of the nearbed velocity vector. The streamwise extent of the vanes' impact is governed by the momentum equation. The effectiveness of the technique is tested in a series of laboratory experiments.

The record St. Clair River ice jam of April 1984 produced major impacts on the levels and flows of the Great Lakes, and on navigation throughout the system. Following the onset of the jam, Lake St. Clair water levels dropped about 0.6 m as the inflow was decreased by the jam. At the peak of the jam the flows were reduced by approximately 65%. The jam had a duration of 24 days. Following the jam breaking on April 29, 1984, the waters of Lake St. Clair rose rapidly, recovering approximately 75% of the drop in levels in four days. Computer simulations indicate that it will take about a year for most and at least 3 years for all the excess water stored in Lakes Michigan and Huron during the jam to be dissipated and for levels in those lakes (and Lakes St. Clair and Erie, downstream) to return to prejam conditions.

A general methodology is presented for use in the design of water distribution networks. The proposed approach is conceptually useful for certain applications. The approach is based on recasting the basic set of hydraulic network equations in terms of selected design parameters for specified operating conditions. The reformulated, network equations are then solved using a modified linear method. In order to demonstrate the feasibility of the approach, two different algorithms are developed and applied to an example network.