Journal of Hydraulic Engineering

A stochastic theory is developed for predicting flow resistance in natural rivers. Irregularly varying river width and bed elevation are represented as one‐dimensional spatial random fields. Large‐scale random flow acceleration and deceleration in response to boundary variations are described by the stochastic differential flow equation. Analytical stochastic flow solutions are developed for the case when boundary variations are small and statistically homogeneous. In particular, closed‐form expressions for the effective flow resistance coefficient and flow variance are obtained. The results indicate that flow resistance in natural rivers is strongly influenced by cross‐sectional nonuniformity and mean flow condition, in addition to relative boundary roughness and mean cross‐sectional shape. The results also show that effective resistance is always greater than uniform resistance in a corresponding mean straight channel. This difference increases as the mean Froude number increases for a given mean bed slope or as mean bed slope decreases for a given mean Froude number. Part II of this paper will be published in the future.

Determination of scour depth is needed for economical design of bridge pier foundation. Currently, determination of design scour depth is mainly based on use of relationships for maximum scour depth in steady flow along with the design discharge. Computations have revealed that time taken by the design discharge to scour to its full potential is generally larger than the time for which it runs. Hence, the computation of temporal variation of scour depth should form the basis of the design. Experiments are conducted on temporal variation of scour around circular bridge piers placed in uniform, nonuniform, and stratified beds under steady and unsteady clear‐water flows. Considering the primary vortex in front of the pier to be the prime agent causing scour, a procedure is developed for computing the temporal variation of scour depth under these conditions. Since the maximum scour depth is the scour depth at large time, the procedure is logically extended to obtain an expression for the same. Sediment nonuniformity and stratification are shown to have a significant effect on scour depth. The effect of these elements as well as that of unsteadiness of flow on scour depth are studied and taken into account in the proposed method of scour calculations.

The Quail Creek Dike failure flood, near Hurricane, Utah, which occurred December 31, 1988, and January 1, 1989, affords the opportunity to evaluate the hydraulics of a high‐gradient channel. For the first mile (1.6 km) downstream from the dike, this unnamed channel has an average slope of 0.032 until it enters the Virgin River at a point where the average channel slope is 0.003. Model‐computed depths and discharges are compared with field‐measured depths and indirect discharge measurements. Initially, flows are modeled as supercritical in the 1‐mi (1.6‐km) reach having a 0.032 channel slope. However, the field‐measured depths can be reconstructed only by modeling the complete reach as subcritical. This paper questions whether supercritical flows occur in natural channels except for very short distances.

A three‐dimensional hydrodynamic model is applied to flows in open channels. The model incorporates a second‐moment turbulence‐closure model that has demonstrated considerable skill in simulating turbulent flows in laboratory experiments and in various geophysical and engineering boundary layers. The closure model consists of differential equations for turbulence energy and turbulence length scale. The remaining second‐moment equations are reduced to a set of algebraic equations in which tendency, advection, and diffusion terms are omitted. To account for the effect of the free surface on the bulk of the channel flow, a modification of the macroscale equation is introduced; the rest of the model equations and their attendant nondimensional constants remain unchanged. The model performance is assessed using laser‐Doppler anemometer measurements on the centerline of a large number of laboratory, smooth and rough, homogeneous and stratified, open‐channel flows with different values of the aspect ratio. Good agreement is found between the model and data in every case. Because the model is based upon a self‐consistent framework and is able to reproduce the many experiments provided here, the model can be used with confidence in environmental applications.

Because of hydraulic sorting (selective transport of grains by the flow), bed‐load transport of mixtures of sand and gravel in streams is difficult to predict. The transported gradation is generally different from the gradation of bed‐surface material or the upstream imposed load, and should be treated as a new unknown variable. A conceptual transport model for bed‐load mixtures is proposed, in which the transported gradation is predicted using the concept of joint probability. In this approach, instead of using a hiding factor or exposure correction, the relative mobility of each particle size and the availability of each size class on the bed surface are considered. The total transport rate is then determined by mean hydraulic conditions of the flow and properties of the transported material. This approach allows easier calibration procedures for transport of mixtures. The method is verified through comparison with an irreversible overloading and underloading flume experiment.

An analytical solution of St. Venant's equations for tidal flow in alluvial estuaries is presented using a Lagrangian approach. The solution is not fully exact; it is obtained on the basis of an assumed combination of harmonics for the velocity of the moving water particle. In addition, the alluvial estuary is assumed to have an exponentially varying cross section. The assumptions made, however, are few compared to the assumptions needed for earlier analytical solutions. Moreover, they do not impose serious restrictions on application to real estuaries. The accuracy obtained with the analytical method is quite acceptable compared to results obtained with a numerical model which does not require an assumed combination of harmonics. The advantage of an analytical method over a numerical method is that the former method provides insight into the phenomena involved in tidal hydraulics. In addition, the Lagrangian approach enhances understanding, as it forces one to follow the movement of an individual water particle in the vertical, horizontal, and lateral sense.

This paper describes an investigation on a numerical prediction method to estimate local scour due to the cooling‐water jets discharged from power stations. The method presented simulates the unsteady convection and diffusion of the warmed jets with a two‐equation turbulence model within the calculation area being deformed by the local scour. The profile of the scoured sand bed is predicted by computing the amount of both the bed load and the suspended load in parallel with the simulation of the flow itself. The prediction method was applied to three kinds of experiments: a three‐dimensional warm‐jet experiment above a fixed bed, and two local‐scour experiments carried out under two‐ and three‐dimensional flows. The validity of the numerical prediction method was reasonably confirmed by these comparisons of results.

Conceptual models of watershed processes and stochastic models of precipitation and streamflow processes are often needed in the planning and management of hydraulic systems. A number of such models have been proposed in the literature, and many of them are actually used in current practice. This paper focuses on identification of stochastic models for representing storage and streamflow processes of a natural watershed subject to a stochastic precipitation input. More specifically, a natural watershed is considered in which all inputs, state variables, outputs, and parameters vary with the season. Assuming that the precipitation input is uncorrelated with periodic mean and periodic variance, that the ground-water storage is the only significant storage in the watershed, and under further linear reservoir assumptions, it has been shown that the seasonal ground-water storage is represented by a periodic autoregressive moving average process of order (1,0), i.e., a PARMA(1,0) process, and the seasonal streamflow is a PARMA(1,1) process. If surface storage is considered, in addition to ground-water storage, then for the same periodic uncorrelated precipitation input, the seasonal ground water becomes a PARMA(2,0) process, and the model of seasonal streamflow becomes a PARMA(2,1) process. Furthermore, extensions have been made considering the general case of PARMA(p,q) precipitation inputs.