Journal of Hydraulic Engineering

The current state of knowledge of density currents caused by negatively (dense) or positively (light) buoyant flows entering stratified or unstratified lakes and reservoirs is reviewed and evaluated. Emphasis is given to heavier than ambient flows that plunge below the surface and move along the lower boundary of the receiving water in their initial stage of propagation. The behavior of entering flow, plunging flow, density current, separating flow, and interflow is briefly described. Methods commonly used in the analysis of various flow regimes (zones) are presented. Selected references and examples of the application of density currents are provided to assist the practicing hydraulic and environmental engineering community. Finally, gaps in the current knowledge and research needs are identified for the hydraulic engineering research community.

A computer simulation method is developed to predict the temporal variations of debris‐flow discharge, solids concentration, and vertical mean particle‐size distribution. A single finite step in the simulation is divided into two stages: In the first stage, a sediment bed composed of a well‐graded mixture is eroded by surface water introduced at the head of a channel, thereby generating a debris flow. In the second stage, larger particles in the debris flow move upward because of dispersive force and are then transported forward faster than smaller particles, which remain in the lower part of the flow because the velocity is slower in the lower layer. Another numerical simulation method is also developed to predict simultaneously the shape of the debris‐deposit area, the distribution of the deposit thicknesses within the area, and the three‐dimensional distribution of the mean diameters of the deposited particles. Both simulation methods are verified using laboratory experiments.

Field surveys and experiments in a tilting flume on hyperconcentrated sand‐water mixture (SWM) flows were conducted. At slopes slightly smaller than the equilibrium slope, a rapid development of sand bars propagating upstream was observed. These bars consist of an almost horizontal terrace with subcritical flow, a steep lee‐side slope with supercritical flow, and a hydraulic jump between subsequent bars. The erosion processes on the bar are limited by the high sand concentrations and flow velocities on the steep slopes. As a result, the erosion rate is more moderate than predicted by the pickup functions used in classical sediment‐transport theory. A simple one‐dimensional model is presented to study the behavior of triangular schematized bars. From an analysis of the equations it is concluded that an increase in erosion rate requires an increase in bed slope to maintain equilibrium flow conditions. Finally, simulations with the model are compared with observations in the field and in the tilting flume. The agreement appears to be reasonable.

Surge oscillations in a differential surge chamber have two degrees of freedom and are characterized by nonlinearities. The linear approximation provides stability criteria for small perturbations around the equilibrium state, and the Thoma stability criterion applies to the differential chamber. Large surge oscillations are investigated with direct numerical integration on two phase planes. The analysis indicates that the system reveals itself as a supercritical Hopf bifurcation—the exchange of stability from an asymptotically stable spiral to an unstable spiral approaching a stable limit cycle. The total chamber area is the controlling parameter. The bifurcation point corresponds to the Thoma criterion. For a surge chamber with an‐area larger than the Thoma value, an unstable limit cycle may exist around the equilibrium state on each phase plane, and it defines the domain of asymptotic stability. If the chamber area is less than the Thoma value, the case of soft self‐excitation with a stable limit cycle inside and an unstable one outside may occur, Stability in the large and instability in the small dominate the system.

Some simple relationships derived from a generalized reservoir‐routing analysis provide a sound basis for the preliminary sizing of stormwater detention reservoirs. The analysis indicates that the ratio of required storage to flood volume (the flood‐storage factor) is determined primarily by the ratio of peak outflow to peak inflow (the peak‐discharge factor), the type of outlet, and the shape of the inflow hydrograph. A submerged outlet is more efficient than an overflow outlet in that considerably less detention storage is needed to achieve the same reduction in peak discharge for the same inflow hydrograph. Two algebraic formulas approximate the relationships between the flood‐storage and peak‐discharge factors for detention reservoirs with submerged outlets and overflow outlets. Use of the graphical relationships of U.S. Soil Conservation Service leads to underestimation of detention‐storage requirements.

A simple and methodical strategy is presented for estimating the parameters of a catchment. The method makes use of rainfall‐runoff records to construct response surfaces of the peak flow in terms of eight calibration parameters. The eight calibration parameters are assumed to vary between certain physically meaningful limits and to be random and uniformly distributed between the limits. Experimental design techniques and the response surface methodology are used here. The response surfaces are fitted within the limits. Optimal values on the response surfaces that match the observed peak flows are then obtained using a probabilistic algorithm. The values obtained are optimal since at that point on the response surface the probability density is the highest. The average of the optimal sets obtained for various rainfall‐runoff records is an estimate of the catchment parameters. The estimated values are then verified on other storm runoff. The results obtained matched very well with the observed peak flow values.

The theoretical momentum coefficient (β) and energy coefficient (α) for turbulent shear flow in circular pipes and wide channels are derived from the power law, then compared with their counterparts on the basis of the logarithmic law. For such unidirectional flows, the exponent (m) of the power‐law velocity distribution is the sole parameter that determines the values of β and α. A comparison of the corresponding expressions for β and α derived using both laws shows that their values differ only slightly within a valid range of small m's. Use of a power‐law‐based β expression along with a power‐law resistance formula in the cross‐section‐averaged equation of momentum cannot only eliminate the theoretical incompatibility that results from mixing logarithmic and power laws in the equation but also remove the inconsistent assumption of $\beta =1$ made in the equation. Improvement on the accuracy of the flow computation by incorporating a power‐law‐based p expression in the equation of momentum is demonstrated through an example in which a new stability limit for the Froude number for turbulent shear flow in wide channels can be accurately derived without assuming $\beta =1\text{.}$