Journal of Hydraulic Engineering

A model is presented for the simulation of shallow water flow and, specifically, flood waves propagating on a dry bed. The governing equations are transformed to an equivalent system valid on a deforming coordinate system and are solved by a dissipative finiteelement technique. A second‐order difference scheme is employed for the integration in time. The implicit nonlinear equations resulting from the weak formulations are solved by the Newton‐Raphson method, and the set of linear algebraic equations generated is solved by a frontal algorithm. A deforming grid generation scheme is introduced in the dissipative finite‐element formulation to account for the effects of the propagating or receding wave fronts on dry land. The accuracy and stability of the model is examined by comparing the model results with observed data from an experimental field test. Results of trial runs for the simulation of overland flow are also presented.

A method to simulate the withdrawal of water from a stratified water body is introduced. The method can handle large withdrawals within a single time step and therefore allows the use of relatively long time steps, considerably reducing computational expense. Good agreement with the experimental work of other researchers is found. The results of simulations incorporating the algorithm into the dynamic reservoir model DYRESM are shown for Wellington Reservoir in Western Australia.

A three‐dimensional model is presented that has been extensively used to predict the motion and mixing of thermal discharges entering lakes. The model uses a computational mesh that conforms to the bottom of the lake, the surface, and the shoreline, and is concentrated in the vicinity of the discharge. The $k-\epsilon$ urbulence model is used to estimate the turbulent stresses and fluxes. The effects of bottom surface roughness as well as the enhanced mixing due to turbulence generation by an ice cover or wind are included, and either floating (summer) or sinking (winter) plumes can be predicted. New solution algorithms makes the three‐dimensional model relatively economical to run. The model, presents verification checks, and reports predictions for a single discharge and for two interacting discharges, is described herein.

Equations based on the entropy concept have been derived for describing the two‐dimensional velocity distribution in an openchannel cross section. The velocity equation derived is capable of describing the variation of velocity in both the vertical and transverse directions, with the maximum velocity occurring on or below the water surface. Equations for determining the location of mean velocity have also been derived along with those, such as the entropy function, that can be used as measures of the homogeneity of velocity distribution in a channel cross section. A dimensionless parameter of the entropy function named the M number has been found useful as an index for characterizing and comparing various patterns of velocity distribution and states of open‐channel flow systems. The definition and demonstrated usefulness of this parameter indicate the importance and value of the information given by the location and magnitude of maximum velocity in a cross section, and suggest the need for future experimental and analytical studies about maximum velocity.

All hydraulic computations involving flow in open channels require an evaluation of energy‐loss parameters. A fundamental approach is to assess the different types of energy loss separately. Methods of doing this are described, including a new method using the concept of friction distance and dummy boundaries for computing flow through vegetation. Dummy boundaries are also useful where there is dead water or a large eddy, but care is needed in assessing form losses to account for the assumed flow pattern in the reduced cross section. The parameters used are reasonably easy to assess and are less variable with depth than Manning's n‐values. The method described is less subject to limitations due to lack of measurements in a given river. This is because each parameter is based on a physical feature that can be measured or estimated.

Dispersion in open‐channel flow is significantly affected by boundary roughness. The analysis of data generated in the present experimental program shows that the dimensionless dispersion coefficient is a function of two interacting mechanisms, namely, resistance and blockage effect due to roughness elements. The dispersion characteristics of channels with rough beds are found to be analogous to those of channels with rough sides. The proposed parameter P, which incorporates the influence of resistance and blockage effect, yields a good correlation with the available dispersion data. The empirical model developed in the present study may be used to predict dispersion coefficients in straight laboratory and field channels.

Cavitation damage is often observed near the downstream end of the flip buckets of many high‐head outlet works. To analyze and mitigate the problem, many research efforts now focus on the development of the boundary layer along the bucket surface. In this paper, the centrifugal‐force effect on flow characteristics over a bucket is discussed. The boundary‐layer momentum and energy integral equations are derived by incorporating the effect of the bucket curvature. The surface shear stresses are calculated based on the theory of wall layers. The turbulent boundary‐layer thickness and the exponential velocity distribution are obtained by applying the finite‐difference method. It was found that higher velocity occurs near the bucket surface throughout its entire length, and the skin‐friction coefficient increases significantly in the downstream half of the bucket. The cavitation inception number approaches its maximum value at the end of the bucket, and, therefore, cavitation damage is most likely to occur near the downstream end of the flip bucket of high‐head outlet works.

The usual procedure for determining discharge in a stream involves a numerical integration of depth-averaged velocities. In most instances, the depth-averaged velocity is based on the average of the measured velocities at depths 0.2D and 0.8D, measured from the water surface, where D is the total depth o low. Based on the logarithmic velocity profile, a general 2-point method is derived. Given velocity measurements at two arbitrary but known positions in a given vertical section, the method can be used to determine the depth-averaged velocity. To assess the applicability to natural channels, the method was applied to an average non-dimensional vertical velocity profile based on profiles in 48 natural channels. For many measurement location combinations, the difference between the computed and observed depth-averaged velocities is within 1%. For a few extreme cases where the two measurement depths are very close together, the discrepancies exceed 2%. Provided the measurement locations are properly selected, the general 2-point method will yield acceptable results.

Sediment concentration measurements of particulate slurry flow provide new insights into intense movement of both bed load and suspended load at high concentrations. The submerged weight of the bed-load (contact-load) solids is transferred downward by means of the normal intergranular stress. Associated with this normal stress there is a granular component of the shear stress resisting motion. Only the remaining, fluid-based, component of the shear stress produces the fluid shear velocity which is involved in velocity distribution and other features of turbulent flow. Turbulent support of suspended load entails a dispersive force which can be evaluated on the basis of the usual flux analysis. This force involves a transfer of weight from the particles to the surrounding fluid, which has been measured experimentally. Combined with the inter-granular stresses mentioned above, this dispersive force gives a new method of linking bed-load and suspended-load components to calculate total-load concentration profiles.

Scour downstream of a vertical gate develops slowly. Therefore, for a river in which peak flows are of short duration, the time history of scour development is of major importance. The channel scours created by the flow of water under, over, and simultaneously under and over a vertical gate are investigated with a hydraulic model. Although the scour is less, more water can be discharged when there is simultaneously flow under and over the vertical gate compared with the cases when flow is only under or over the gate. Various relationships characterizing the scour phenomenon are found on the basis of experimental results.