Journal of Hydraulic Engineering

A mathematical method that determines the sensitivity of solute concentration to real-time changes of the loading intensity at a remote source is developed here. The hydrodynamic and mass transport conditions correspond to flow in rivers and shallow estuaries and numerical simulations are performed by a two-dimensional finite-element model. The sensitivities are evaluated by solution of the adjoint equation of the fate and transport problem, which is shown to produce accurate results with increased efficiency when compared to equivalent perturbations of the loading intensity of the contaminant source. The corresponding reduction in computational effort allows the real-time optimal control of a contaminant release, which cannot be accomplished otherwise. The method is validated by comparisons with perturbation solutions in channels of simple geometry. Results are also presented for a practical application corresponding to the upper Potomac estuary.

A numerical method is developed for the optimal design of contaminant releases in shallow rivers and estuaries. The algorithm is based on the hypothesis that the control action, at one or more points of release, can be discretized in time so each of the individual loads can be uniquely identified in an optimal fashion. A finite-element solution of the adjoint equation to the fate and transport problem yields the gradient information necessary for the optimization process, which permits accurate and efficient determination of the mass loading at the sources. The optimization is based on the cumulative effects of the contaminant at one or more targets and is achieved by a Gauss-Newton iteration procedure. The adjoint model is driven by the dynamic difference between the computed and desired concentration at the target nodes and incorporates all physical constraints of the problem. The validity of the model is demonstrated by convergence to a unique control action from different starting vectors. The procedure also provides estimates of the uncertainty associated with operator or mechanical device error, which defines the likelihood of success of the suggested dynamic changes. Practical applications are presented for Fox River and the upper Potomac Estuary.

An entrainment model for fluid mud and soft mud is derived by integrating the equation of turbulent kinetic energy across the mixed layer and introducing some modeling assumptions. The resulting entrainment model is similar to models for mixed-layer deepening in lakes and reservoirs, but in addition accounts for settling and the work needed to entrain bed material. The conditions considered are such that the water layer is flowing, whereas the mud layer is at rest. The former layer is the turbulent mixed layer that erodes the quiescent mud layer. Such conditions may result from wind action or turbulence produced at other locations in the flow. The yield strength of the mud as well as the viscous drag of the mud layer due to the flow in the water layer are taken into account. Most empirical model coefficients are obtained from the literature. A sensitivity analysis shows that settling, bed strength, and viscosity all may substantially reduce entrainment rates. An experimental validation of the entrainment model developed is presented in a companion paper.

A study on the erosion of soft mud layers caused by entrainment is reported. Experiments were carried out in an annular flume with suspensions of kaolinite and natural mud. The results of these experiments compare favorably with the results of an integral entrainment model, described in a companion paper. It can be concluded that the initial entrainment process of fluid mud is identical to the entrainment process of two-fluid systems, that is, the upper part of the fluid mud behaves as a viscous fluid. During this initial phase, the entrainment rate may be affected by the time scale for boundary layer development. At a later phase the entrainment process is hindered by the work required to keep the sediment in suspension and by the strength of the bed accounted for by treating the mud as a Bingham plastic. Values for the settling velocity, the yield strength, and the viscosity, used in the model to obtain a fair agreement with the experiments, are comparable to those obtained from independent measurements.

A series of experiments were conducted in a flume to study the hydraulic characteristics of the turbidity current in a reservoir. Kaolin was used as the suspended material. The plunge points were found to be unstable initially. As the experiment went on, it moved downstream from the incipient plunge location and finally reached a stable location. The densimetric Froude number of the incipient and the stable plunge points are approximately equal to 1.0 and 0.6, respectively. It is found that the length of the plunge region is 15 times the water depth at the stable plunge point. The volumetric flow rates in the plunge region increase 17% during the plunging process. About 70% of the water discharge and 80% of the sediment discharge are confined to the denser layer, a layer close to the channel bed with approximately constant concentration. The thickness of the turbidity current increases while the layer-averaged velocity and concentration decrease in the longitudinal direction; the layer-averaged velocity has the smallest variation rates. Equations for the dimensionless velocity and concentration profiles are obtained.

A similitude relationship for the oxygen transfer that occurs in a vented hydroturbine is developed with reference to scaling between a homologous turbine model and a full-size turbine installation (prototype). Three basic parameters are identified as important for the scaling of oxygen transfer: the liquid film coefficient, the specific surface area, and the contact time. The similitude relation is then developed with existing theories on turbine hydrodynamics, bubble hydrodynamics, and interfacial mass transfer. The only model-prototype data set currently available is used to empirically fit one coefficient and to test the theory. Model-prototype similitude for oxygen transfer is primarily a function of gas-void ratio, rotational speed, and runner diameter with diffusivity, surface tension, and density playing a lesser role.

A research program was conducted at the St. Anthony Falls Laboratory to investigate impulse pressures caused by the collapse of transient cavitation bubbles. The impulsive pressures associated with vibratory as well as hydrodynamic cavitation were measured. Both a stationary specimen subjected to vibratory cavitation and a hydrofoil of NACA 0015 section were instrumented with custom-made pressure transducers using polyvinylidene fluoride (PVDF) piezoelectric polymer film. These transducers provided in situ measurement of impulse pressures. A practical application of this measurement technique was demonstrated in testing the viability of air injection as a means of mitigating cavitation erosion. The high sensitivity, minimal thickness, high frequency response, high spatial resolution, and low cost of the piezoelectric transducers point to their applicability in a wide range of field measurements.

An accurate network linear programming (NLP) algorithm for the hydraulic analysis of water pipe networks is developed and compared with direct equation solving techniques. Accuracy is achieved by the use of a novel iterative scheme in which successive linear approximations to the nonlinear head loss equations are refined for each pipe in the region of the emerging solution. The use of primal-dual and simplex method NLP solvers in the iterative strategy is investigated, with a hybrid scheme being shown to reduce execution times by an order of magnitude. Nevertheless, the direct equation solving algorithm of Todini and Pilati remains much more efficient than the best NLP algorithm. A new algorithm for the analysis of locally controlled feedback devices is developed for inclusion in the NLP strategy. The uniqueness of pipe network hydraulic solutions is also investigated. Although some doubt has been expressed regarding uniqueness of solutions to networks that contain locally controlled feedback devices, evidence of nonuniqueness has not been forthcoming. Arguments in support of unique solutions for such networks are presented.

The unsteady, turbulent flow characteristics behind a two-dimensional vertical fence is investigated numerically by using a weakly compressible-flow computational method. A large-eddy simulation technique together with a subgrid-scale turbulence model is applied in the calculation to account for the turbulence effects in the flow. Numerical results show reasonably correct wake characteristics behind the fence and are in good agreement with available experimental data.

Recently increased emphasis and attention has been given to river management and restoration of modified streams. A variety of restoration techniques and objectives exist, including asymmetrical cross-section construction, point bar development, two-stage channel design, floodplain approaches, pools and riffles re-creation, and sinuosity and meander restoration. Modifications of the planform geometry can induce undesirable morphological and ecological consequences and significant channel adjustments that, depending on the energy of the flow, can result in failure of the restoration design through either erosion or sedimentation. In this study we provide an analysis of the accuracy of empirical relations of meander parameters for use in meander restoration procedures. A case study in central Maryland is used to demonstrate this analysis. It is suggested that the combination of a field reconnaissance and analytical study should be used to determine the appropriateness of using published regression equations for restoration design.

During the afternoon of August 19, 1971, an intense thunderstorm a few miles southwest of Wikieup, Arizona, produced one of the largest known flood peaks for a 49.2-square-km drainage basin. Initial computations of the peak discharge assumed stable flow conditions and a four-section slope area measurement indicated that discharge was 2,082 m³/s. Recent findings based on free-surface instability characteristics at the site suggest that gravitational forces exceeded boundary retarding forces, and flow in the wide sand channel was unstable. Computations for roll or translatory waves indicate that waves crashed into the highway bridge at velocities of as much as 12.5 m/s. The close agreement of free surface instability results, translatory wave computations, estimates of the steady flow on which the translatory waves traveled, and an eyewitness account of the translatory waves suggest the total peak discharge could have been 2,742 m³/s or 32% greater than the published discharge. The occurrence of translatory waves in natural channels may be more common than previously thought, and instability criteria should be considered for hydraulic analysis of flow in steep smooth channels.