Journal of Hydraulic Engineering

A spherical coordinate, three-dimensional, nonorthogonal, boundary-fitted circulation model (contravariant formulation) for application to estuarine, coastal sea, and continental shelf waters is presented. The model employs a split mode technique where the equations are decomposed into exterior and interior modes. The exterior mode (vertically averaged) described in an earlier paper (Muin and Spaulding 1996) is solved using a semiimplicit solution technique. The interior mode (vertical structure) is solved explicitly, except for the vertical diffusion terms that are solved implicitly. The temporally and spatially varying eddy viscosity and diffusivity are determined from a turbulent kinetic energy equation and an empirically specified length scale. A series of tests are presented to evaluate model performance where analytical solutions or other numerical solutions are available for comparison. The model's ability to predict the point vertical structure of tidal flow is tested against analytic solutions employing (1) constant viscosity; and (2) an eddy viscosity varying linearly with depth with a no-slip bottom boundary condition. The ability of the model to simulate three-dimensional tidal flow was tested against an exact solution for an annular section channel with quadratically varying bathymetry. The model was also tested against analytic solutions for steady residual flow generated by density gradient, wind, and river flow in a channel. The model predicted turbulent energy distributions generated from a bottom boundary were compared to those from a previous numerical study by Davies and Jones (1990). No-slip and bottom stress formulations at the sea bed, and their effect on the vertical structure of the flow are analyzed. The model was used to predict the salinity distribution in a simple rectangular channel identical to the Rotterdam Waterway. The computational method is very economical, stable, and accurate with the CFL stability condition up to 100.

A three-dimensional boundary-fitted circulation model (Muin and Spaulding 1996b) was applied to simulate tidal and wind driven flow in Upper Narragansett Bay and the Providence and Seekonk Rivers. The model employs a split mode solution technique. The exterior mode (vertically averaged) was solved using a semiimplicit method. The interior mode (vertical structure) was solved explicitly, except for the vertical diffusion term that is implicit. The vertical eddy viscosity was calculated from a one-equation turbulence model. Model predicted tidal currents for the principal constituents were in good agreement with field observations. The M₂ dominated the tidal currents accounting for 80% of the total tidal energy. A combination of bottom friction coefficient of 0.0025 and constant γ= 0.3 in the mixing length formulation of the turbulence model provided the best fit to the available observations. The model predicted a cooscillating wave pattern with the M₂ water elevation about three hours out of phase with the current. An approximate one-hour phase difference between the currents in the deep dredged channel and the shallow water on either side was predicted. Wind-driven flow was simulated under constant wind forcing of 0.01 N/m² (0.1 dyne/cm²) along and across the river axis. The steady-state flow patterns are consistent with observations, showing flows against the wind direction in the dredged channel. The model predicted steady state currents in the dredged channel have maximum values of 3–4 cm/s for winds along the channel axis, and 1 cm/s for winds across the channel axis.

Pearl River is the largest river system in South China with the city of Hong Kong at its mouth. The delta is one of the most rapidly developing regions in the world. With many river-related civil projects in progress there, the water environment is a major concern in recent years. The horizontal two-dimensional (2D) simulation of tides in the Pearl River estuary is presented. The Abbott-Ionescu scheme, a two-level alternate direction implicit (ADI) scheme, is applied in this model and the third-order upwind numerical discretizations of convection terms for inner points are described in detail in this paper. As there exist intertidal flats in the inner bay that occupy substantial area, a simple but efficient drying-flooding procedure is proposed to simulation this process of the flats. The simulated dry situation near the lower low water level is confirmed by satellite image. The computations are calibrated with the field measurement data and the results are also analyzed in this paper.

The development and application of a one-dimensional heat transport model in highly transient streams governed by unsteady flow is described here. The resultant framework consists of two modules called the hydrodynamic and heat transport modules. In the hydrodynamic module, the hydraulic variables such as flow depth and velocity are simulated. Based on this information, the heat transport module is executed to calculate temperatures. A new approach—coupling heat transport in the surface water and diffusion in the sediment zone—is developed and applied for this module. In this approach, an interaction term accounts for the flux of heat energy between the water and sediments, which affects the distribution of water temperature in clear and shallow streams. Implicit finite difference methods called the Preissmann four-point and the Crank-Nicolson schemes are used to solve each module. Application of this framework demonstrates that the model effectively simulates the hydraulic variables and temperatures.

We propose an accurate numerical scheme for calculating advection in the simulations of mass, heat, and momentum transport. The second-order spatial derivatives of the advection-diffusion equation can be discretized more accurately by the usual finite-difference approximation than the first-order spatial derivatives. By taking this feature into account, we can expect that the second-order wave equation is more available for numerical calculation of pure advection than the first-order advection equation. However, the second-order wave equation has two types of propagating wave solutions, one of which is unnecessary. To get a unique solution that shows the downstream advection only, the concept of characteristics method is applied. By minimizing truncation errors in the scheme, the parameters involved could be determined as functions of the Courant number. Comparison of this scheme with several others in model calculations proves its superior accuracy and stability. The proposed scheme uses only three grid points in space in case of one-dimensional problems. In addition, this can be easily applied to multidimensional practical problems.

Individual pine and cedar tree saplings and branches were used to model the resistance to flow in a water flume for nonsubmerged and nonrigid vegetation to determine the amount that streamlining decreases the drag coefficient and reduces the momentum absorbing area. Currently, vegetation on floodplains is commonly assumed to behave as rigid roughness that can lead to large errors in the relationships between velocity and drag force. This presents a basic fluid mechanics problem. An extreme variation of roughness with depth of flow can result due to a large increase in the momentum absorbing area in nonsubmerged vegetation as depth is increased. This deems all the available roughness equations (which generally are based on relative roughness approach) useless for this application. In this paper a dimensional analysis, supported by experimental results, is developed to obtain a relationship between roughness conditions (i.e., density and flexural rigidity) and flow conditions (i.e., velocity and depth) for floodplains and vegetative zones of natural waterways.

Some 30 years ago, John F. Kennedy laid the foundations for the description of the geometry of sand waves on stream beds by the potential flow model. Since then, the analysis has been extensively refined and extended, but no rigorous description of the small features, called ripples, exists. The present study attempts a “stock-taking” of the data and the various behavioral concepts with the aim of encouraging researchers to improve our knowledge of the physics of features called ripples. Various trends are identified from the data. It is deduced that ripples act as roughness elements of the boundary. The ripple troughs are “filled” with the energy-consuming lee vortices. The main flow is over the ripple crests and lee vortices and does not interact with the bed geometry. The “roughness layer” of ripples and vortices is within the constant shear layer and is affected by the flow depth only as far as it affects the velocity distribution and alters the shear stress on the bed.

The effluent discharge from most ocean outfalls is periodic while some others discharge only intermittently. When the rate of discharge falls below a critical level, seawater commences to flow into the deeper end of the diffuser forming a salt water wedge in the bottom of the diffuser section of the outfall. The paper examines two aspects of this phenomenon: the purging of seawater from a simple multiport pipeline outfall at start-up or after partial intrusion of seawater, and the flooding of the outfall following cessation of effluent discharge. Mathematical models are developed that describe each of these processes. It is shown that a certain minimum discharge is required before all ports on a sloping diffuser will be utilized. The flooding of a pipeline is described in terms of the volume fraction of the diffuser section that is flooded and a normalized time parameter. Two programs of hydraulic model testing provided verification for the mathematical models of the flooding and purging processes.

Geomorphology-based instantaneous unit hydrographs have been proposed by several engineers as a tool to produce runoff hydrographs from rainfall for ungauged watersheds. A difficulty in applying the geomorphology-based unit hydrographs is the determination of travel time that is actually a hydraulic problem. In this paper, kinematic-wave theory is used to analytically determine the travel times for overland and channel flows in a stream-ordering subbasin system. The resultant instantaneous unit hydrograph is a function of the time rate of water input (intensity of rainfall excess in application); hence the linearity restriction of the unit hydrograph theory is relaxed. In applying the instantaneous unit hydrographs for hydrograph simulation, the model deals with temporally nonuniform rainfall through convolution integration of the instantaneous unit hydrographs applied to the rainfall excess of varying intensities with time. The proposed model is tested by comparing the simulated and observed hydrographs of an example watershed for several rainstorms with good results. Sensitivity of surface runoff unit hydrographs to the model parameters is also investigated.

An analytical solution of the nonlinear equations of the theory of a directed fluid sheet (which includes vertical inertia) is used to prove that for constant depth at the waterfall's brink and variable far upstream depth, the energy head in steady flow in a free waterfall is minimized when the flow is critical. This result provides additional physical understanding of the special nature of critical flow in a waterfall and supplies further justification for using the free waterfall as a self-calibrated flow meter, as suggested by Rouse (1936). Also, this proof should not be confused with the more common proof of minimum energy head in a uniform stream because here the flow rate is not maintained constant and the fluid depth contracts as gravity accelerates the flow near the waterfall's brink.