Journal of Hydraulic Engineering

Existing models of tidal motion in narrow, uniform channels are improved by incorporating a spatial application of Lorentz' principle of equivalent work into the characteristic velocity and tidal friction factor estimates used to linearize the bottom shear stress. The characteristic velocity is evaluated using numerical integration. A steady flow analogy is involved to relate the tidal friction factor to channel roughness and fluid viscosity. These two parameters in turn yield expressions for the viscous wavenumber, damping modulus and damping frequency which describe the wave motion. The procedure is applied to existing analyses of closed end and sea level canals and models are tested against laboratory and field data with accurate and physically plausible results.

Hydrologic flood‐flow design methods generally require one time parameter, such as the time of concentration, as input, and the accuracy of the estimated peak discharge or flood hydrograph is sensitive to the accuracy of the estimated time parameter. Numerous equations for estimating the time of concentration have been proposed. Eleven equations for estimating $t_c$ are compared using data collected from 48 urban watersheds located in most regions of the country. All the watersheds had areas less than 4,000 acres; the average impervious was 29.1%, and the mean time of concentration was 1.49 hr. Using accuracy and bias as the criteria for comparison, the eleven equations show wide variation in accuracy and bias. Two equations are calibrated with the data; the rainfall intensity is found to be the most important input parameter. The mean time of concentration computed by the velocity method for the 48 watersheds agrees very closely with the mean time computed from rainfall and hydrograph data. However, for individual watersheds the differences are relatively large.

An accurate numerical method for the mathematical modeling of contaminant dispersion in two‐dimensional tidal currents is developed and applied. The method avoids the excessive numerical damping or oscillations associated with most finite difference and finite element schemes for advection by using a characteristics approach with high order Hermite bicubic interpolation. The split‐operator algorithm, incorporating a Crank‐Nicolson operator for diffusion, provides a relatively simple and economic method for accurate simulation of pollutant dispersion on a fixed, Eulerian mesh. A special procedure for Lagrangian calculation of the dispersion of concentration fields which are small compared to the mesh size simulates the early stages of growth of point source plumes. These various procedures are described in detail, and their performance is demonstrated by application to schematic test cases and to the Bay of Saint‐Brieuc, France.

The algorithmic properties of a dissipative Galerkin scheme for openchannel flow are investigated by means of a Fourier analysis based on the linearized equations describing kinematic and dynamic wave motion in shallow water. Optimum dissipation levels are determined so that the kinematic wave speed error is reduced by two orders of magnitude compared to that of the standard Galerkin method. The method is then extended to the equations of dynamic‐wave propagation written in conservation form and the dissipation and phase characteristics of the scheme are determined and compared to the corresponding properties of some well‐known finite‐difference schemes. The dissipative Galerkin scheme exhibits some remarkable characteristics, which include unconditional stability, a highly selective dissipative interface and very satisfactory wave‐speed characteristics. The overall wave deformation characteristics of the method are found to be not only an improvement of the classical Galerkin method but also better than some of the most popular finite‐difference methods used widely in unsteady open‐channel flow.

The dynamic interaction between solids and fluid for homogeneous slurries during the passage of pressure waves is investigated by assuming the solids to be ellipsoidal in shape. An alternative formula for the acoustic wave speed, including the dynamic interaction, is derived from the two governing equations for the mixture. Comparisons of the new formula with the existing ones and with the available experimental data are made. The new formula yields more accurate wave speeds for slurries with heavy solids.

A numerical model for simulating thermal‐ice conditions in a natural river is developed with emphasis on its application to the growth and decay of the ice cover. The model treats the river as a coupled air‐ice‐water‐bed system taking into consideration the heat exchanges at all interfaces in the system. The heat conduction in the ice cover is represented by a one‐dimensional, quasi‐steady state approximation. The temperature distribution in the water is formulated by the longitudinal dispersion equation. The model is applied to a 28‐mile reach of the St. Lawrence River between Iroquois Dam and the Moses‐Saunders Power Dam. Numerical results show good agreement with field data in both the ice thickness and the break‐up dates.

The influence of the Bay of Bothnia sea level on the water stages in a series of interconnected lakes near the city of Lulea in Sweden is studied. Future conditions as a consequence of land elevation and channel improvements are simulated using a mathematical model. It is found that due to landlift the lake system will be divided into two lake systems. The upper lakes will turn to true lakes experiencing no water exchange with the sea. It is also found that a reasonable water depth for boating can be maintained in the lakes, if a dam is built at one of the outfalls to the sea.

For engineering studies with numerical models several digital filters were designed which pass, for practical purposes only, information in the main tidal frequency bands. The filters are designed for data at hourly intervals in the bands of the diurnal, semi-diurnal, quarter-diurnal, sixth-diurnal and eighth-diurnal tides. Examples of their applications are presented.

An equation for predicting water temperature change in a river caused by water abstraction is derived. It requires water temperature data from the abstraction and study points and also average water depth at the natural and reduced flow rates. The equation requires the assumption that water depth change is the primary cause of water temperature change, which is true for small temperature changes only.

A method is presented for interpreting and describing the size distribution and the packing of particles in armor layers formed on the surface of non-uniform bed sediments. An armor-layer thickness is defined in terms of the larger particle-size fraction constituting the armor layer.

A simple, analytical model is proposed for the description of flow and stress characteristics in an open-channel flow with nonuniform distribution of bed-shear stress. The model describes the relationship between the secondary current and the transverse variation in bed-shear stress. The streamwise velocity profile is obtained by superposition of a power law and a second-order defect law. The model simulates the flow behavior measured in a laboratory channel with artificially induced transverse variation of shear velocity.