Journal of Hydraulic Engineering

This paper is the first of a five part series documenting the structure of turbulence models, their use in various classes of surface water models, the considerations required in selecting or building a turbulence model‐based code, and an evaluation of the impact of such models on surface water modeling. Surface water models are considered in these papers with both hydraulic engineering and environmental hydraulics applications in mind. In the first paper the general model equations for free surface flow and transport are stated for the case of two‐dimensional vertically averaged and two‐dimensional areally averaged situations as well as the general three‐dimensional case. Terms requiring closure are defined and the basic eddy viscosity and diffusivity concept is presented. The various classes of turbulence models are defined and a very brief discussion of constant and mixing length dependent viscosity ensues. The paper concludes with a presentation of the one‐equation and general two‐equation k‐ε turbulence model for multidimensional flows. The constants used in the two‐equation model are summarized and their universality is discussed.

The second in a five part series, this paper begins with a general discussion of the two equation turbulence model for twodimensional vertically integrated models. Special attention is placed upon the proper inclusion of bottom generated turbulence in the formulation. An extensive discussion of turbulent stress/flux equations ensues. The Reynolds stress equation is presented as is a detailed discussion of the method for including the effects of pressure on the calculation. Incorporation of wall effects on the pressure/stress calculation is performed by a damping function. A discussion of turbulent scalar flux and variance equation is presented and pressure and wall effects are again considered. Simplification via algebraic representation of the stress/flux equation is discussed. A particular difficulty in the use of such stress/flux models is the nonavailability of boundary data for the various terms. Various types of boundary condition treatments are summarized including wall and free surface varieties. The paper concludes with the first of three case studies; this one being a heated effluent discharge model of the Bruce A and B nuclear power plants on Lake Huron. Built by G. Raithby, the model is a full 3D formulation with a k‐ε model.

The third of a five part series, this paper presents the final two case studies demonstrating the use of turbulence models in surface water flow computations. The first case study is by W. Rodi and co‐workers and summarizes calculations of heated effluent disposal into the Rhine River. A model chain concept is defined for the calculation. The distinctions between the chains are based upon the strength of recirculation in the hot zone and the upstream propagation of pressure effects. Comparisons with data reveal that the strong three‐dimensional effects for submerged jets required the full 3D model but that surface jets were adequately modeled by the 2D formulation. The second case study in this paper is by L. Oey, G. Mellor and co‐workers and documents the prediction of flow and salt transport in the Hudson/Raritan River Estuary. A three‐dimensional formulation is used, but horizontal diffusion has been neglected as the grid was assumed fine enough to resolve its effects. The level 2.5 turbulence closure developed by Mellor and Yamada is used and is based upon a turbulence length scale as opposed to dissipation. An extensive series of calculations for the Hudson River estuary region is presented.

The fourth in a five part series, this paper discusses the computer, numerical, and personnel requirements for turbulence model based surface water codes. The paper concludes with a brief discussion on suggested evaluation procedures for turbulence models. Hardware resources typically require substantial computing resources particularly for the case of time varying calculations. For the case of 3D flows, the solution of extra equations for turbulence quantities will not add much extra time to the calculation. Codes may be developed or acquired with acquisition of public domain software or proprietary codes possible. Public domain software is often not well‐documented but is inexpensive. Proprietary software is generally more expensive but well‐maintained and documented. The development of a code requires trained personnel, considerable computer resources and a sound numerical solution approach. Seven components or considerations in the numerical solution approach are discussed with the treatment of the advection terms being of considerable importance. Finally, six elements of model performance evaluation are summarized and include a discussion of the types of data for such evaluations.

The last paper in the five part series, this paper presents an evaluation of the status of turbulence model—based surface water models and concludes with the literature citations. Two classes of models are evaluated: hydraulic engineering and environmental hydraulics. A table lists the eight major categories of problems. Also listed are citations for the types of turbulence models used in recent solutions to these problems. From this summary table a number of subjective impressions are discussed. In general, almost all the relevant problem classes have been performed with some form of advanced turbulence model; however, the hydraulic engineering subclass is the most frequently performed. As positive as this impact is it has not been the case that practitioners have adopted turbulence models to any great degree. The reason for this skepticism is the lack of objective methods of performance evaluation and the lack of any data taken with sufficient precision to establish the credibility of one turbulence model formulation over another. Creation of a library of high quality data for flow of relevance to hydraulic engineers is suggested.

The use of the specified time interval (STI) numerical schemes has been popular in applying the method of characteristics (MOC) to unsteady open‐channel flow problems. Studies and analyses of several variants of the STI schemes have led to the derivation of a new scheme, referred to herein as the multimode scheme, which combines implicit, temporal reachback, spatial reachback, and classical schemes into one. Three numerical models have been developed to implement the implicit and multimode schemes. The IMOCDS model uses an implicit scheme, with which the time step is no longer subject to the Courant constraint. The remaining two models, NEWMOC and SPRMOC, are two versions of the multimode scheme. The NEWMOC and SPRMOC models demonstrate all the advantages previously provided by individual STI schemes, cover the combined flow range of the various schemes involved, and, in addition, display newly acquired benefits such as robustness. Numerical analyses, numerical experiments, and field applications that verify, support, and demonstrate the enhanced model capabilities are presented.

For advection‐dominated transport processes, the traditional numerical techniques for solving the advection‐diffusion equation fail because of numerical oscillations. Fractional step solutions, in which the advection and diffusion processes are treated in separate steps, have been proposed as one way of overcoming this problem. Here a solution to the advection step based on the method of characteristics on a fixed grid is used. Interpolation is achieved with the finite element technique. Linear and quadratic elements are evaluated in terms of artificial diffusion, phase, and other errors. It was found that linear interpolation creates too much numerical diffusion, while the quadratic scheme is reasonably accurate, but under certain conditions generates spurious extrema. A method retaining the accuracy of the quadratic interpolation and eliminating its shortcoming is suggested. Boundary conditions and source loadings are considered in detail. An application of the model to salinity distribution resulting from canal discharges in Biscayne Bay is described.

A finite difference mathematical model for the calculation of estuarine flow and transport processes is presented. Due to the emphasis on engineering applications, turbulence closure is formulated on the basis of mixing length and damping functions. The necessary empirical constants were determined from theoretical considerations and from data published in the literature from meteorological, oceanographic, and laboratory experiments, which yielded a set of parameters for eddy viscosity and eddy diffusivity not tuned to a particular system. Similarly, an integral model is derived to account for wind‐induced mixing in the case of highly variable meteorological conditions. Application of the model in a case study of the Trave estuary in northern Germany shows its predictive capability. A long‐term simulation of 85 days reproduced both total mixing events and strong stratification. The model showed good agreement with the extensive field data.

An experimental study examining the generation of internal waves by unsteady inertial outflows from a stratified reservoir is presented. The experiments show that shear waves generated when the outflow is begun are identical to those generated when the outflow is stopped. The amplitudes of the lowest mode shear waves can be calculated by assuming that they combine to form the steady withdrawal‐layer velocity profile at the wall. As R, the parameter governing steady withdrawal behavior, is increased, the observed shear‐wave amplitudes decrease relative to their theoretical values, with, the discrepancy increasing with increasing mode number. When the outflow is repeatedly pulsed, the strength of the average flow towards the sink indicates the existance of a withdrawal layer thicker than that which would have been formed given either the average flow rate or the maximum instantaneous flow rate. This observation suggests that one effect of unsteady withdrawals may be to create thicker withdrawal layers than are found for similar steady withdrawals.