Turbulence Modeling of Surface Water Flow and Transport: Part V
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 9
Abstract
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.
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References
1.
Abbott, M., McCowan, A., and Warren, I. (1981). “Numerical modeling of free surface flows that are two dimensional in plan.” in: Transport models for inland and coastal water, H. Fischer, Ed., Academic Press, New York, N.Y., 222–283.
2.
Abdelwahed, M., and Chu, V. (1981). “Surface jets and plumes in crossflows.” Tech. Rept. No. 81‐1 (FML), McGill University Civil Engrg. Dept., Montreal, Canada.
3.
Adams, E., Stolzenbach, K., and Harleman, D. (1975). “Near and far field analysis of buoyant surface discharges into large bodies of water.” R. Parsons Lab Rept. No. 205, M.I.T., Cambridge, Mass.
4.
Alfrink, B. J., and van Rijn, L. C. (1983). “Two‐equation turbulence model for flow in trenches.” J. Hydr. Div., ASCE, 109(7), 941–958.
5.
Amsden, A. A., and Harlow, F. H. (1970). “The SMAC method: A numerical technique for calculating incompressible fluid flows.” Report LA‐4370, Los Alamos Laboratory, Los Alamos, N.M.
6.
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. (1984). Computational fluid mechanics and heat transfer. Hemisphere Publishing Corp., McGraw Hill Book Co., New York, N.Y.
7.
Babajimopoulos, C., and Bedford, K. W. (1980). “Formulating lake models which preserve spectral statistics.” J. Hydr. Div., ASCE, 106(1), 1–19.
8.
Baker, A. J. (1982). “The CMC: 3DPNS computer program for prediction of three dimensional, subsonic, turbulent aerodynamic juncture region flow, vol. I: Theoretical manual.” NASA Technical Report CR‐3645.
9.
Baker, A. J. (1983). Finite element computational fluid mechanics. Hemisphere Publishing Corp., McGraw Hill Book Co., New York, N.Y.
10.
Baker, A. J. (1984). “A finite element penalty algorithm for the parabolic Navier‐Stokes equations for turbulent three‐dimensional flow.” Computer Meth. in Appl. Mech. and Engrg., 46, 277–293.
11.
Baker, A. J., et al. (1981). “A three dimensional finite element algorithm for prediction of V/STOL jet induced flow fields.” presented at the NATO/AGARD (Advisory Group for Aerospace Research and Development) Symposium on Fluid Dynamics of Jets with Application to V/STOL, Lisbon, Portugal, Nov. 2–5.
12.
Bauer, S. W., and Schmidt, K. D. (1983). “Irregular‐grid finite‐difference simulation of Lake Geneva surge,” J. Hydr. Div., ASCE, 109(10), 1285–1297.
13.
Bedford, K. (1981). “Spectra preservation capabilities of Great Lakes transport models,” in: Transport models for inland and coastal waters, H. Fischer, Ed., Academic Press, New York, N.Y., 172–219.
14.
Bedford, K., Dingman, S., and Yeo, W. (1987). “Preparation of estuary and marine model equations by generalized filtering methods.” in: Three dimensional models of marine and estuarine dynamics, J. Nihoul and B. Jamart, Eds., Elsevier Publ. Co., New York, N.Y., 113–126.
15.
Bennett, J. R. (1974). “On the dynamics of wind‐driven lake currents.” J. Physical Oceanography, 4(3), 400–414.
16.
Benque, J. P., et al. (1982). “New method for tidal current computation.” J. Wtrway., Port, Coast, and Oc. Div., ASCE, 108(3), 396–417.
17.
Berger, M. J., and Oliger, J. (1983). “Adaptive mesh refinement for hyperbolic partial differential equations.” Numerical Analysis Manuscript NA‐83‐02, Computer Science Department, Stanford University, Stanford, Calif.
18.
Bernard, J. P., et al. (1974). “La simulation de la turbulence pour le calcul des ecoulements de convection mixte,” Report ALSTHOM Technique des Fhudes, Grenoble, France.
19.
Betts, P. L., and Haroutunian, V. (1985). “ modeling of turbulent flow over a backward facing step by a finite element‐method. Comparison with finite volume solutions and experiments.” in: Proc. of the 4th Int. Conf. on Numerical Methods in Laminar and Turbulent Flows, Swansea, England, Jul. 9–12.
20.
Blumberg, A. F., and Mellor, G. L. (1978). “A coastal ocean numerical model.” Geophysical Fluid Dynamics Program, Princeton University, Princeton, N.J.
21.
Blumberg, A. F. and Mellor, G. L. (1980). “A coastal numerical model.” in: Mathematical Modeling of Estuarine Physics, J. Sundermann and K.‐P. Holz, eds., Springer‐Verlag, New York, N.Y., 202–218.
22.
Blumberg, A. F., and Mellor, G. L. (1983). “Diagnostic and prognostic numerical circulation studies of the south Atlantic bight.” J. Geophysical Res., 88, 4579–4592.
23.
Blumberg, A. F., et al. (1984). “California shelf physical oceanography circulation model, final report.” Mineral Management Service, U.S. Department of the Interior, pub. by Dynalysis of Princeton, 219 Wall Street, Princeton, N.J.
24.
Blumberg, A. F. and Herring, H. J. (1987). “Circulation modelling using orthogonal curvilinear coordinates.” in: Three‐Dimensional Models of Marine and Estuarine Dynamics, J. Nihoul and B. Jamart, eds., Elsevier Pub. Co., Amsterdam, 55–88.
25.
Boussinesq, T. V. (1877). Mem. press acad. sci., 3rd Ed., Paris XXIII, p. 46.
26.
Bobyleva, L. M., Zilitinkevich, S. S., and Laikhtman, D. L. (1965). “Turbulent regime in a thermally stratified planetary atmospheric boundary layer.” Int. Colloq. on the Microstructure of the Atmosphere and the Effect of Turbulence on Radiowave Propagation, Moscow, USSR.
27.
Bradshaw, P. (1971). An introduction to turbulence and its measurements. Pergamom Press, London, U.K.
28.
Bradshaw, P. (1976). Turbulence. Springer‐Verlag, New York, N.Y.
29.
Bradshaw, P., Cebeci, T., and Whitelaw, J. H. (1981). Engineering calculation methods for turbulent flow. Academic Press, London, U.K.
30.
Bradshaw, P., Ferriss, D. H., and Atwell, N. P. (1967). “Calculation of boundary layer development using the turbulent energy equation.” J. Fluid Mech., 28, 593–616.
31.
Brandt, A. (1977). “Multi‐level adaptative solutions to boundary layer problems.” Math. Comp., 31, 333–390.
32.
Brison, J. F., et al. (1985). “Finite element simulation of turbulent flows using a two equation model.” in: Proc. of the 4th Int. Conf. on Numerical Methods in Laminar and Turbulent Flows, Swansea, England, Jul. 9–12.
33.
Brooks, A. N., and Hughes, T. J. R. (1982). “Streamline upwind Petrov‐Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier‐Stokes equations.” Computer Methods in Appl. Mech. and Engrg., 199–259.
34.
Buchak, E. M., and Edinger, J. E. (1984). “Simulation of a density underflow into Wellington Reservoir using longitudinal/vertical hydrodynamics.” Rep. 84/10/R, J. E. Edinger Assoc., Inc., Wayne, Pa.
35.
Buleev, N. J. (1962). “Teploperedacka,” USSR Academy of Sciences, Moscow, USSR (also AERE Translation 957, 1963).
36.
Cebeci, T., and Smith, A. M. O. (1974). Analysis of turbulent boundary layers. Academic Press, New York, N.Y.
37.
Celik, I., and Rodi, W. (1984). “Simulation of free‐surface effects in turbulent channel flow.” Physicochemical Hydrodynamics, 5(3/4), 217–227.
38.
Celik, I., and Rodi, W. (1985a). “Calculation of wave‐induced turbulent flow in estuaries.” Ocean Engrg., 12(6), 531–542.
39.
Celik, I., and Rodi, W. (1985b). “Mathematical modelling of suspended sediment transport in open channels.” in: Proc. 21st IAHR Congress, Melbourne, Australia, IAHR Pub., Delft, the Netherlands.
40.
Celik, I., Rodi, W., and Stamou, A. I. (1985). “Prediction of hydrodynamic characteristics of rectangular settling tanks.” in: Proc. IAHR Int. Symp. on Refined Flow Modelling and Turbulence Measurements, Iowa City, Iowa.
41.
Chorin, A. (1967). “A numerical method for solving incompressible viscous flow problems.” J. Computational Physics, 2, 12–26.
42.
Chou, P. Y. (1945). “On velocity correlations and the solution of the equations of turbulent fluctuation.” Quart. J. Appl. Math., 3(1), 38–54.
43.
Chow, V. Te. (1956). Open channel hydraulics, McGraw Hill Book Co., New York, N.Y.
44.
Crawford, M. E., and Kays, W. M. (1975). “STAN‐5—A program for numerical computation of two‐dimensional internal/external boundary layer flows.” Stanford University, Dept. Mech. Eng., Report HMT‐23, Stanford, Calif.
45.
Creare, Inc. (1984). “FLUENT, An interactive computer program for simulating fluid flow.” and “FLUENT seminar notes.” Creare R&D Inc., Etna Road, P.O. Box 71, Hanover, N.H.
46.
Damaskinidan‐Georgiadon, A., and Smith, K. (1986). “Flow in a curved converging channel.” J. Hydr. Engrg., ASCE, 112(6), 476–496.
47.
DHI (1982). “Danish hydraulics.” Rept. No. 3, Danish Hydraulics Institute, Agern Alle 5, DK‐2970 Horsholm, Denmark.
48.
Delft Hydraulics Laboratory. (1983). “The two‐dimensional depth averaged mathematical model WAWUA.” Delft, The Netherlands.
49.
Demuren, A. (1982). “Computation of three‐dimensional turbulent jets in cross flow.” in: Proc. of the Int. Conf. on Computational Methods and Experimental Measurements, Washington, D.C., Springer‐Verlag Publ. Co., New York, N.Y.
50.
Demuren, A. O. (1983). “Three‐dimensional computation of flow and pollutant dispersion in meandering channels.” in: Proc. 20th IAHR Cong., Moscow, USSR.
51.
Demuren, A. O., and Rodi, W. (1983). “Three‐dimensional calculation of side discharges into open channels.” J. Hydr. Engrg., ASCE, 109(12), 1707–1722.
52.
Demuren, A., and Rodi, W. (1986). “Calculations of flow and pollutant dispersion in meandering channels.” J. Fluid Mech., 172, 63–92.
53.
Dimitriadis, C., and Leschziner, M. (1985). “Computation of three‐dimensional flow in duct‐junctions by a zonal‐approach.” in: Proc. of the 4th Int. Conf. on Numerical Methods in Laminar and Turbulent Flows, Swansea, England, Jul. 9–12.
54.
Ditmars, J., et al. (1987). “Performance evaluation of surface water flow and transport models,” J. Hydr. Engrg., ASCE, 113(8), 961–979.
55.
Dongarra, J. (1983). “Performance of various computers using standard linear equations software in a FORTRAN environment.” Argonne National Laboratory, Technical Memo, Argonne, Ill.
56.
Dunn, W., Policastro, A., and Paddock, R. (1975). “Surface thermal plumes: Evaluation of mathematical models for the near and complete field, part 2.” Argonne National Laboratory Report, Argonne, Ill.
57.
Durst, F., and Rastogi, A. (1979). “Theoretical and experimental investigations of turbulent flows with separation.” in: Turbulent Shear Flows I, Springer‐Verlag Publ. Co., New York, N.Y.
58.
Edinger, J., and Buchak, E. (1979). “A hydrodynamic two‐dimensional reservoir model: Development an test application to Sutton Reservoir, Elk River, West Virginia.” Rep. U.S. Army Engineer Division, Ohio River Div., J. E. Edinger Assoc., Wayne, Pa.
59.
Elghobashi, S., and Launder, B. (1982). “Turbulent time scales and the dissipation rate of temperature variance in the thermal mixing layer.” Physics of Fluids, 26(9), 2415–2419.
60.
Elghobashi, S., and LaRue, J. (1983). “The effect of mechanical strain on the dissipation rate of a scalar variance.” Proc. 4th Symp. on Turbulent Shear Flows, Karlsruhe, F.R.G.
61.
Elliot, R., and Raithby, G. (1981). “A three dimensional finite difference model for the prediction of thermal discharges.” in: Proc. 3d Conf. on Waste Heat Management and Utilization, Miami Beach, Fla.
62.
Elliot, R., and Raithby, G. (1982). “The prediction of a thermal discharge entering a crossflow.” in: Proc. Refined Modeling of Flows, IAHR, Paris, France, Sept. 7–10, 37–46.
63.
Elston, R., et al. (1983). “A study of the present and alternative sewage outfall locations for Sequim, Washington, phase I,” Rep. for the Dept. of Ecology, State of Washington, Battelle Pacific Northwest Laboratory, Richland, Wash.
64.
Eyler, L., Trent, D., and Budden, M. (1983). “TEMPEST, A three‐dimensional, time‐dependent computer program for hydrothermal analysis, volume II: Assessment and verification results.” Battelle Pacific Northwest Laboratory, Richland, Wash.
65.
Feldman, A. (1983). “Software documentation and support: HEC experience.” in: Frontiers in hydraulic engineering, H. T. Shen, Ed., ASCE, New York, N.Y., 318–323.
66.
Ferziger, J. (1981). “Higher level simulations of turbulent flows.” Rep. TF16, Thermosciences Div., Mech. Engrg. Dept., Stanford Univ., Stanford, Calif.
67.
Ferziger, J. (1982). “Morphology of the flows and computational methods.” in: Proc. 1980–81 AFOSR‐HTTM Stanford Conference on Complex Turbulent Flows, S. J. Kline et al., Eds., Stanford Univ., Stanford, Calif.
68.
Ferziger, J. (1987). “Simulation of incompressible turbulent flows.” J. Comp. Physics, 69(1), 1–48.
69.
Findikakis, A., and Street, R. (1982). “Finite element simulation of turbulent stratified flows.” J. Hydr. Div., ASCE, 108(8), 904–920.
70.
Fischer, H., et al. (1979). Mixing in inland and coastal waters. Academic Press, New York, N.Y.
71.
Fortin, M., Peyret, R., and Terman, R. (1971). Lecture notes in physics, 8. Springer‐Verlag, New York, N.Y.
72.
Franke, R., Leschziner, M., and Rodi, W. (1987). “Numerical simulation of wind‐driven turbulent flow in stratified water bodies.” in: Proc. 3d Int. Symp. on Stratified Flows, Pasadena, Calif.
73.
Freeman, N., Hale, A., and Danard, M. (1972). “A modified sigma equation approach to the numerical modeling of Great Lakes hydrodynamics.” J. Geophysical Res., 77(6), 1050–1060.
74.
Freitas, C., et al. (1985). “Numerical simulation of three‐dimensional flow in a cavity.” Int. J. for Numerical Methods in Fluids, 561–575.
75.
Gebhart, B., and Mollendorf, J. (1977). “A new density relation for pure and saline water.” Deep Sea Res., 244, 831–848.
76.
Gibson, M., and Launder, B. (1976). “On the calculation of horizontal, turbulent free shear flow under gravitational influence.” J. Heat Transfer, ASME, 98, 81–87.
77.
Gibson, M., and Launder, B. (1978). “Ground effects on pressure, fluctuations in the atmospheric boundary layer.” J. Fluid Mechanics, 86, 491.
78.
Goussebaille, J., et al. (1985). “A finite element algorithm for turbulent flow possessing a model.” in: Proc. of the 4th Int. Conf. on Numerical Methods in Laminar and Turbulent Flows, Swansea, England, Jul. 9–12.
79.
Gosman, A. O., et al. (1969). Heat and mass transfer in recirculating flows, Academic Press, London, U.K.
80.
Gosman, A. O., and Pun, W. (1973). “Calculation of recirculating flows,” lecture notes, Report No. HTS/74/2, Imperial College, London, U.K.
81.
Gosman, A. O., and Ideriah, F. (1976). “TEACH‐2E: A general computer program for two‐dimensional turbulent, recirculating flows.” Dept. of Mechanical Engineering, University of California, Berkeley, Calif.
82.
Gresho, P., and Lee, R. (1981). “Don't suppress the wiggles—They are telling you something.” Computers and Fluids, 9(2), 17–43.
83.
Gresho, P., et al. (1984). “A modified finite element method for solving the time‐dependent incompressible Navier‐Stokes equations, part I: Theory.” Int. J. for Numerical Methods in Fluids, 4, 557–598.
84.
Grimm‐Strele, J. (1975). “Naturmessdaten zur Quervermischung in Flussen.” Univ. of Karlsruhe Tech. Rept. SFB 80/E/75, Germany, F.R.G.
85.
Grimm‐Strele, J. (1981). “Naturmessungen uber Konzentrationsverteilung von konservativen und suspendierten Wasserinhaltsstoffen unterhalb einer Einleitung in einen Fluss. Bericht.” Univ. Karlsruhe Tech. Rept. No. SFB 80/ME/157, Germany, F.R.G.
86.
Grotzbach, G. (1981). “Spatial resolution requirements for numerical simulation of internally heated fluid layers.” in: Proc. of the 2d Int. Conf. on Numerical Methods in Laminar and Turbulent Flow, Venice, Italy, Jul. 13–16.
87.
Grotzbach, G. (1982). “Direct numerical simulation of laminar and turbulent benard convection.” J. of Fluid Mechanics, 119, 27–53.
88.
Habib, M., and Whitelaw, J. (1979). “Velocity characteristics of a confined coaxial jet.” J. of Fluids Engineering, ASME, 101, 521–529.
89.
Haltiner, G., and Williams, R. (1980). Numerical prediction and dynamic meteorology, John Wiley and Sons, New York, N.Y.
90.
Hamilton, P. (1975). “A numerical model of the vertical circulation of tidal estuaries and its application to the Rotterdam Waterway,” Geophysical J. of the Royal Astr. Soc., 40, 1–21.
91.
Hamming, R. (1973). Numerical methods for scientists and engineers, McGraw Hill Book Co., New York, N.Y.
92.
Han, T., Humphrey, J., and Launder, B. (1981). “A comparison of hybrid and quadratic‐upstream differencing in high Reynolds number elliptic flows.” Computer Methods in Appl. Mech. and Engrg., 29, 81–95.
93.
Hanjalic, K., and Launder, B. (1982). Proc. of the 1980–81 AFOSR‐HTTM‐Stanford Conference on Complex Turbulent Flows: Comparison of Computation and Experiments, S. Kline et al., Eds., Stanford University Press, Stanford, Calif.
94.
Harlow, F., and Welch, J. (1965). “Numerical calculation of time dependent viscous incompressible flow of fluid with a free surface.” Physics of Fluids, 8(12), 2182–2189.
95.
Haq, A., and Lick, W. (1975). “On time‐dependent flow in a lake.” J. Geophysical Res., 180, 431–437.
96.
Hinze, J. (1975). Turbulence, McGraw Hill Book Co., New York, N.Y.
97.
Hirt, C., and Cook, I. (1972). “Calculating three‐dimensional flows around structures and over rough terrain.” J. Computational Physics, 10, 324–340.
98.
Hossain, M. (1980). “Mathematische Modellierung von turbulenten Auftriebsstromungen.” Thesis presented to the University of Karlsruhe, Germany, in fulfillment of the requirements for the degree of Doctor of Philosophy.
99.
Hossain, M., and Rodi, W. (1982). “A turbulence model for buoyant flows and its application to vertical buoyant jets.” in: Turbulent Buoyant Jets and Plumes, W. Rodi, Ed., Pergamon Press, New York, N.Y., 121–178.
100.
Hughes, T. J. R., Ed. (1979). Finite element methods in convection dominated flows, ASME, New York, N.Y.
101.
Imam, E., McCorquodale, J., and Bewtra, J. (1981). “Numerical modelling of sedimentation tanks.” J. Hydr. Engrg., 109(12), 1740–1754.
102.
Imberger, J. (1987). “Introduction to papers from the IUTAM symposium on mixing in stratified fluids.” J. Geophys. Res., 92, 5229.
103.
Johnson, B. (1982). “Numerical modeling of estuarine hydrodynamics on a boundary‐fitted coordinate system.” in: Numerical Grid Generation, J. Thompson, Ed., Elsevier Science, Publ. Co., Inc., Amsterdam.
104.
Jones, W., and McGuirk, J. (1980). “Computation of a round turbulent jet discharging into a confined cross flow.” in: Turbulent Shear Flow 2, Springer‐Verlag, New York, N.Y., 233–245.
105.
Keller, R. J., and Rastogi, A. (1975). “Prediction of flow development on spillways.” J. of the Hydr. Div., ASCE, 102(9), 1171–1184.
106.
Keller, R. J., and Rodi, W. (1984). “Prediction of two dimensional flow characteristics in complex channel cross sections.” Proc. Hydrosoft '84, Portoroz, Yugoslavia, Elsevier Publ. Co., Amsterdam.
107.
King, I. (1985). “Strategies for finite element modeling of three dimensional hydrodynamic systems.” Advances in Water Res., 8, 69–81.
108.
Kline, S. (1982a). “Introduction.” in: 1980–81 AFOSR‐HTTM Stanford Conf. on Complex Turbulent Flows: Comparison of Computation and Experiment, S. Kline et al., Eds., Stanford University Press, Stanford, Calif.
109.
Kline, S. (1982b). “Universal or zonal modeling—The road ahead, a personal opinion.” in: 1980–81 AFOSR‐HTTM Stanford Conf. on Complex Turbulent Flows: Comparison of Computation and Experiment, S. Kline et al., Eds., Stanford University Press, Stanford, Calif.
110.
Kolmogorov, A. (1942). “Equations of turbulent motion of an incompressible fluid.” Izv. Akad. Nauk. SSR, Seria fizicheska Vi., No. 1–2, pg. 56–58, (English translation: Imperial College, Mech. Eng. Dept. Rept. ON/6, 1968).
111.
Koutitas, C., and O'Connor, B. (1980). “Three‐dimensional flows.” J. Hydr. Div., ASCE, 106(11), 1843–1865.
112.
Krishnappan, B. G. (1984). “Laboratory verification of turbulent flow model.” J. Hydr. Engrg., ASCE, 112(4), 251–266.
113.
Krishnappan, B. G., and Lau, Y. L. (1986). “Turbulence modelling of flood plain flows.” J. Hydr. Engrg., ASCE, 112(4), 251–266.
114.
Larsson, R. (1986). “Coriolis‐generated secondary currents in channels.” J. Hydr. Engrg., ASCE, 112(8), 750–776.
115.
Lau, B., and Krishnappan, B. (1981). “Ice cover effects on stream flows and mixing.” J. Hydr. Div., ASCE, 107(10), 1225–1242.
116.
Laufer, J. (1951). “Investigation of turbulent flow in a two‐dimensional channel.” NACA Rept. 1053.
117.
Launder, B. E. (1975). “On the effect of a gravitational field on the turbulent transport of heat and momentum.” J. Fluid Mech., 67, 569–581.
118.
Launder, B. E. (1982). “A generalized algebraic stress transport hypothesis.” AIAA J., 20(3), 436–437.
119.
Launder, B. E. (1984). “Second‐moment closure: Methodology and practice.” in: Simulation of turbulence models and their applications, Vol. 2, Collection de la Direction des Etudes et Recherches, Electricite de France, editions Eyrolles, Paris.
120.
Launder, B. E., Reece, G., and Rodi, W. (1975). “Progress in the development of a Reynolds stress turbulence closure.” J. Fluid Mech., 68, 537–566.
121.
Launder, B. E., and Spalding, D. (1972). Lectures in mathematical models of turbulence. Academic Press, New York, N.Y.
122.
Launder, B. E., and Spalding, D. (1974). “The numerical computation of turbulent flows.” Computer Methods in Appl. Mech. and Engrg., 3, 269–289.
123.
Leendertse, J., Alexander, R., and Liu, S.‐K. (1973). “A three‐dimensional model for well mixed estuaries and coastal seas: Volume I, computation procedures.” R‐708‐NYC, The Rand Corporation, Pasadena, Calif.
124.
Leendertse, J., and Liu, S.‐K. (1975). “A three‐dimensional model for well mixed estuaries and coastal seas: Volume II, aspects of computation,” R‐1764‐OWRT, The Rand Corporation, Pasadena, Calif.
125.
Leendertse, J., and Liu, S.‐K. (1977). “A three‐dimensional model for well mixed estuaries and coastal seas: Volume IV, turbulent energy computation.” R‐2187‐OWRT, The Rand Corporation, Pasadena, Calif.
126.
Leonard, B., Vachtsevanos, G., and Abood, K. (1977). “Unsteady two‐dimensional salinity intrusion model for an estuary.” in: Proc. Int. Conf. on Appl. Numerical Modelling, University of Southampton, England.
127.
Leonard, B. (1979a). “A survey of finite differences of opinion on numerical muddling of the incomprehensible defective confusion equation.” in: Proc. Symp. on Finite Element Methods in Convection Dominated Flows, ASME, New York, N.Y.
128.
Leonard, B. (1979b). “A stable and accurate convective modelling procedure based on quadratic upstream interpolation.” Computer Methods in Appl. Mech. and Engrg., 19, 59–68.
129.
LeQuere, P., Humphrey, J., and Sherman, F. (1981). “Numerical calculation of thermally driven two‐dimensional unsteady laminar flow in cavities of rectangular cross section.” Numerical Heat Transfer, 4, 249–283.
130.
Leschziner, M. A. (1979). “Numerical prediction of the internal density jump.” in: Proc. 18th IAHR Congress, Cagliari, Italy, IAHR Pub., Delft, The Netherlands.
131.
Leschziner, M. A., and Rodi, W. (1979). “Calculation of strongly curved open channel flow.” J. Hydr. Div., ASCE, 105(10), 1297–1314.
132.
Leschziner, M. A., and Rodi, W. (1983). “Calculations of a coaxial heated water discharge.” J. Hydr. Engrg., ASCE, 109(10), 1380–1385.
133.
Lin, W.‐L., and Eraslan, A. (1981). “A fast‐transient three‐dimensional discreteelement hydrodynamic model for predicting unstratified flow conditions in lakes, reservoirs, estuaries and coastal zones with geometrically complex shoreline boundaries.” Univ. of Tennessee, Dept. of Engrg. Science and Mech., Knoxville, Tenn.
134.
Liu, S.‐K, and Nelson, A. (1977). “A three‐dimensional model for well mixed estuaries and coastal seas: Volume V, turbulent energy program.” R‐2188‐OWRT, Rand Corp., Pasadena, Calif.
135.
Ljuboja, M., and Rodi, W. (1981). “Prediction of horizontal and vertical turbulent buoyant wall jets.” J. Heat Transfer, ASME, 103, 343–349.
136.
Lumley, J. (1978). “Computational modelling of turbulent flows.” in Advances in Applied Mechanics, Academic Press, New York, N.Y., 18, 123–174.
137.
Maliska, C., and Raithby, G. (1984). “A method for computing three dimensional flows using non‐orthogonal boundary‐fitted coordinates.” Int. J. for Numerical Methods in Fluids, 4, 519–537.
138.
McGuirk, J., and Papadimitriou, C. (1986). “A numerical study of the internal hydraulic jump.” in: Proc. Int. Symp. on Buoyant Flows, Athens, Greece.
139.
McGuirk, J., and Rodi, W. (1976). “Calculation of three dimensional heated surface jets.” in: Proc. 1976 ICHMT Seminar on Turbulent Buoyant Convection, Dubrovnik, Yugoslavia.
140.
McGuirk, J., and Rodi, W. (1977). “A mathematical model for a vertical jet discharging into a shallow lake.” in: Proc. 17th IAHR Congress, Baden‐Baden, IAHR Pub:, Delft, The Netherlands.
141.
McGuirk, J., and Rodi, W. (1978). “A depth‐averaged mathematical model for the near field of side discharges into open channel flow.” J. Fluid Mech., 86, 861–871.
142.
McGuirk, J., and Rodi, W. (1979a). “Calculation of unsteady mass exchange between a main stream and a dead‐water zone.” in: Proc. 18th IAHR Congress, Cagliari, Italy, IAHR Pub., Delft, The Netherlands.
143.
McGuirk, J., and Rodi, W. (1979b). “Mathematical modelling of three‐dimensional heated surface jets.” J. Fluid Mech., 95, 609–634.
144.
McGuirk, J., and Sadrul Islam, A. (1986). “Selective withdrawal from a stratified flow into a line sink.” in: Proc. Int. Symp. on Buoyant Flows, Athens, Greece.
145.
McGuirk, J., and Spalding, D. B. (1975). “Mathematical modelling of thermal pollution in rivers.,” in: Proc. Int. Symp. on Mathematical Models for Environmental Problems, Southampton, England.
146.
Meakin, R., Street, R., and Findikakis, A. (1986). “Numerical simulation using boundary‐conforming coordinate systems.” in: Adv. Aero. Fluid Mech. and Hydr., ASCE, New York, N.Y., 593–600.
147.
Mellor, G., and Yamada, P. (1982). “Development of a turbulence‐closure model for geophysical fluid problems.” Reviews of Geophysics and Space Physics, 20(4), 851–875.
148.
Mendoza, C., and Chen, H. (1985). “Steady two‐dimensional flow over dunes.” in: Proc. 21st IAHR Congress, Melbourne, Australia, Vol. 2, IAHR Pub., Delft, The Netherlands, 110–113.
149.
Monin, A., and Yaglom, A. (1975). Statistical fluid mechanics, Vols. 1 and 2, MIT Press, Cambridge, Mass.
150.
Munk, W., and Anderson, E. (1948). “Notes on the theory of the thermocline.” J. of Marine Res., 1.
151.
Naot, D., and Rodi, W. (1982). “Calculation of secondary currents in channel flow.” J. Hydr. Div., ASCE, 108(8), 948–968.
152.
Norton, W., King, I., and Orlob, G. (1973). “A finite element model for lower Granitre reservoir,” Water Resources Engineers, Walnut Creek, Calif.
153.
Noye, B. (1978). “An introduction to finite difference techniques.” in: Numerical Simulation of Fluid Motion, North‐Holland Publishing Company, Amsterdam.
154.
Oey, L.‐Y., Mellor, G., and Hires, R. (1985a), “A three‐dimensional simulation of the Hudson‐Raritan Estuary. Part I: Description of the model and model simulations.” J. Physical Oceanography, 15, 1676–1692.
155.
Oey, L.‐Y., Mellor, G., and Hires, R. (1985b). “A three‐dimensional simulation of the Hudson‐Raritan Estuary, Part II: Comparison with observation.” J. Physical Oceanography, 15, 1693–1710.
156.
Oey, L.‐Y., Mellor, G., and Hires, R. (1985c). “A three‐dimensional simulation of the Hudson‐Raritan Estuary. Part III: Salt flux analyses.” J. Physical Oceanography, 15, 1711–1720.
157.
Onishi, Y., and Trent, D. (1985). “Three‐dimensional simulation of flow, salinity, sediment and radionuclide movements in the Hudson River Estuary.” ASCE Hydraulics Division Conf. Proc., Orlando, Fla.
158.
Pasche, E. G., and Evers, P. (1985). “Flow in compound channels with extreme flood‐plain roughness.” in: Proc. 21st IAHR Cong., Melbourne, Australia, IAHR Pub., Delft, The Netherlands, 3, 384–389.
159.
Patankar, S. (1980). Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, McGraw Hill Book Co., New York, N.Y.
160.
Patankar, S., Pratap, V., and Spalding, D. B. (1975). “Prediction of turbulent flow in curved pipes.” J. Fluid Mech., 67(3), 583–595.
161.
Patankar, S., and Spalding, D. (1970). Heat and mass transfer in boundary layers. 2nd ed., Intertext Books Pub., London, U.K.
162.
Patankar, S., and Spalding, D. (1972). “A calculation procedure for heat, mass and momentum transfer in three‐dimensional parabolic flows.” Int. J. of Heat and Mass Transfer, 15, 1787–1806.
163.
Paul, J., and Lick, W. (1974). “A numerical model for thermal plumes and river discharges.” in: Proc. of the 17th Conf. on Great Lakes Res., Int. Assoc., for Great Lakes, Res., 445–455.
164.
Pavlovic, R., and Rodi, W. (1982). “Case studies with a depth‐averaged model for calculating pollutant spreading in rivers.” Wasserwirtschaft, 72, 279–285 (in German).
165.
Pavlovic, R., and Rodi, W. (1985). “Depth‐averaged numerical predictions of velocity and concentration fields in meandering channels.” in: Proc. 21st IAHR Cong., Melbourne, Australia, IAHR Pub., Delft, The Netherlands.
166.
Perrels, P., and Karelse, M. (1981). “A two‐dimensional, laterally averaged model for salt intrusion in estuaries.” in: Transport models for inland and coastal waters, H. Fischer, Ed., Academic Press, New York, N.Y., 483–586.
167.
Peyret, R., and Taylor, T. (1983). Computational methods for fluid flow. Springer‐Verlag, New York, N.Y.
168.
Peyret, R. (1981). “Numerical studies of nonhomogeneous fluid flows.” in: Advances in fluid mechanics, Lecture Notes in Physics, 148, Springer‐Verlag, New York, N.Y., 330–361.
169.
Philips, R., and Schmidt, F. (1983). “Multigrid techniques for the numerical solution of the passive scalar advection‐diffusion equation.” in: 5th Symp. on Turbulent Shear Flows, Pennsylvania State University, College Station, Pa.
170.
Pinder, G., and Gray, W. (1977). Finite element simulation in surface and subsurface hydrology. Academic Press, New York, N.Y.
171.
Prandtl, L. (1925). “Uber die ausgebildete Turbulenz,” ZAMM, 5, 136.
172.
Prandtl, L. (1942). “Bemerkungen zur Theorie der freien Turbulenz,” ZAMM, 22, 241–243.
173.
Prandtl, L. (1945). “Uber ein heues Formelsystem fur die ausgebildete Turbulenz,” Nachr. Akad. Wiss., Gottingen, Math.‐Phys. Klasse, 6.
174.
Pratap, V., and Spalding, D. B. (1976). “Fluid flow and heat transfer in threedimensional duct flows.” Int. J. of Heat and Mass Transfer, 19, 1183–1188.
175.
Raithby, G. (1976). “A critical evaluation of upstream differencing applied to problems involving fluid flow.” Computer Methods in Appl. Mech. and Engrg. 9, 75–103.
176.
Raithby, G. (1984). “Predictions of thermal plumes at the Bruce nuclear power development.” Rept. Thermal Science Ltd., 187Castlegate Cresc, Waterloo Ontario, Canada.
177.
Raithby, G., Elliott, R., and Hutchinson, B. (1988). “Prediction of three‐dimensional thermal discharge flows.” J. Hydr. Engrg., ASCE, 114(7), 720–737.
178.
Raithby, G., and Schneider, G. (1980). “The prediction of surface discharge jets by a three dimensional finite difference model.” J. Heat Transfer, ASME, 102, 138–145.
179.
Raithby, G., and Torrance, K. (1974). “Upstream weighted differencing schemes and their applications to elliptic problems involving fluid flow.” Computers and Fluids, 2, 191–206.
180.
Rastogi, A., and Rodi, W. (1978). “Predictions of heat and mass transfer in open channels.” J. Hydr. Div., ASCE, 104(3), 397–420.
181.
Reece, G. (1976). “A generalized Reynolds stress model of turbulence.” Thesis presented to the University of London, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
182.
Rhie, C., and Chow, W. (1983). “Numerical study of the turbulent flow past an airfoil with trailing‐edge separation.” AIAA J., 27, 1525–1532.
183.
Roache, P. (1976). Computational fluid dynamics.” Hermosa Publishers, Albuquerque, N.M.
184.
Rodi, W. (1976). “A new algebraic relation of calculating the Reynolds stresses,” ZAMM, 56, 1219–1221.
185.
Rodi, W. (1980). Turbulence models and their application in hydraulics. Monograph, International Association for Hydraulic Research, Delft, The Netherlands.
186.
Rodi, W. (1984). “Examples of turbulence‐model applications.” in: Simulation of turbulence models and their applications, Vol. 2, Collection de la Direction des Etudes et Recherches, Electricite de France, editions Eyrolles, Paris, France.
187.
Rodi, W. (1985). “Calculations of stably stratified shear layer flows with a buoyancy‐extended turbulence model.” in: Proc. IMA Conf. on Models of Turbulence and Diffusion in Stable Environments, J. C. R. Hunt, Ed., Oxford University Press, London, U.K., 111–140.
188.
Rodi, W. (1987). “Examples of calculation methods for flow and mixing in stratified fluids,” J. Geophys. Res., 92, 5305–5328.
189.
Rodi, W., Pavlovic, R., and Srivatsa, S. (1981). “Predictions of flow and pollutant spreading in rivers.” in: Transport models for inland and coastal waters, H. Fischer, Ed., Academic Press, New York, N.Y., 63–111.
190.
Rodi, W., and Srivatsa, S. (1980a). “A mathematical model for the flow in channels containing groynes.” Rept. SFB 80/T/160, University of Karlsruhe, Germany.
191.
Rodi, W., and Srivatsa, S. (1980b). “A locally elliptic calculation procedure for three‐dimensional flows and its application to a jet in a cross flow.” Computer Methods in Appl. Mech. and Engrg., 23, 67–83.
192.
Rogallo, R. (1981). “Numerical experiments in homogenous turbulence.” Rept. NASA TM 81315.
193.
Rouse, H. (1976). Advanced mechanics of fluids, Robert E. Krieger Publishers, Huntington, N.Y.
194.
Schamber, D. R., and Larock, B. E. (1981). “Numerical analysis of flow in sedimentation basins.” J. Hydr. Div., ASCE, 107(5), 575–591.
195.
Schuman, U. (1976). “Readability of Reynolds stress models.” Physics of Fluids, 20, 721–725.
196.
Sheng, Y. (1983). “Mathematical modeling of three‐dimensional coastal currents and sediment dispersion.” Rept. U.S. Army Corps of Engineers Waterways Experiment Station, CERC‐83‐2, Vicksburg, Miss.
197.
Sheng, Y. (1986). “Second‐order closure modelling of turbulent flow and sediment dispersion in coastal and estuarine waters.” in: Proc. 3rd Int. Symp. on River Sedimentation, The University of Mississippi, Jackson, Miss.
198.
Sheng, Y. (1987). “On Modelling three‐dimensional estuarine and marine hydrodynamics.” in: Three‐dimensional models of marine and estuarine dynamics, J. Nihoul and B. Jamart, Eds., Elsevier Publ. Co., Amsterdam, 35–54.
199.
Sheng, Y., Parker, S., and Henn, D. (1985). “A three‐dimensional estuarine hydrodynamic model (EHSM3D).” Rept. Water Resources Division, U.S. Geological Survey.
200.
Shir, C. (1973). “A preliminary numerical study of atmospheric turbulent flow in the idealized planetary boundary layer.” J. Atmospheric Science, 30, 1327.
201.
Simons, T. (1973). “Development of three‐dimensional numerical models of great lakes.” Environment Canada, Inland Waters Directorate, Scientific Series No. 12, Canada Centre Inland Waters, Burlington, Ontario, Canada.
202.
Smith, T., and Dyer, K. (1979). “Mathematical modelling of circulation and mixing in estuaries.” in: Mathematical modelling of turbulent diffusion in the environment, C. J. Harris, Ed., Academic Press, London, U.K., 301–342.
203.
Smith, T., and Takhar, H. (1977). “The calculation of oscillatory flow in open channels using mean turbulence energy models.” Rept. Simon Engineering Lab, University of Manchester, U.K.
204.
Spalding, D. B. (1972). “A novel finite difference formulation for differential expressions involving both first and second derivatives.” Int. J. for Numerical Methods in Engrg., 4, 551–559.
205.
Spalding, D. B. (1977). GENMIX—A general computer program for two‐dimensional parabolic phenomena. HMT Series, Vol. 1, Pergamon Press, Oxford, U.K.
206.
Spraggs, L., and Street, R. (1975). “Three‐dimensional simulation of thermally influenced hydrodynamic flows.” Rept., Dept. of Civil Engrg., Stanford Univ., TR‐190, Stanford, Calif.
207.
Stolzenbach, K., and Harleman, D. (1969). “An analytical and experimental investigation of surface discharges of heated water.” M.I.T., R. Parsons Lab Rept. No. 135, Cambridge, Mass.
208.
Svensson, U. (1976). “Flow investigation on the Orsund with a mathematical model (in Swedish), “Rept. No. 3001, University of Lund, Dept. of Water Resour. Engrg., Sweden.
209.
Svensson, U. (1978). “Mathematical model of the seasonal fhermocline.” Rept. No. 1002, University of Lund, Dept. of Water Resour. Engrg., Sweden.
210.
Tanaka, H. (1986). “Turbulence structure and bed friction under waves and current‐interacted motion.” in: Proc. 3d Int. Symp. on River Sedimentation, The University of Mississippi, Jackson, Miss.
211.
Tatom, F., and Smith, S. (1979). “Three‐dimensional computer simulation of cold water and inflow.” prepared for the U.S. Army Engineer, Waterways Experiment Station, Vicksburg, Miss.
212.
Tennekes, H., and Lumley, J. (1972). A first course in turbulence. MIT Press, Cambridge, Mass.
213.
Thomasset, F. (1981). “Implementation of finite element methods for Navier‐Stokes equations,” Springer‐Verlag, New York, N.Y.
214.
Thompson, J., and Warsi, A. (1982). “Boundary‐fitted coordinate systems for numerical solution of partial differential equations—A review.” J. Computational Physics, 47, 1–108.
215.
Tong, G. (1982). “Computation of recirculating flows in two dimensions using finite elements and the model,” in: Proc. Int. Symp. on Refined Modeling of Flows, IAHR, Piesses Pont et Chaussees, Paris, France, 1, 343–354.
216.
Tong, G. (1986). “Turbulent flow computations relevant to sediment transport and bed formation,” in: Proc. 3rd Int. Symp. on River Sedimentation, The University of Mississippi, Jackson, Miss.
217.
Trent, D., Eyler, L., and Budden, M. (1983). “TEMPEST, a three‐dimensional, time‐dependent computer program for hydrothermal analysis, volume 1: Numerical methods and input instructions.” Battelle Pacific Northwest Laboratory, Richland, Wash.
218.
Trent, D., Foote, H., and Eliason, J. (1974). “Determination of the near field excess temperature distribution for the San Onofre generation station cooling water discharge units 2 and 3.” Battelle Pacific Northwest Laboratory, Richland, Wash.
219.
Tropea, C. (1982). “Die turbulente Stufenstromung in Flaschkanälen und offenen Gerinnen.” Thesis presented to the University of Karlsruhe, W. Germany, in fulfillment of the requirements for the degree of Doctor of Philosophy.
220.
Van Doormaal, J., Raithby, G., and Strong, A. (1981). “Prediction of natural convection in non rectangular enclosures using orthogonal curvilinear coordinates.” J. Numerical Heat Transfer, 4, 21–38.
221.
Viollet, P. (1985). “The modelling of turbulent recirculating flows for the purpose of reactor thermal‐hydraulic analysis.” Rept. E44/R05, Electricite de France, Chatou, France.
222.
Voke, P., and Collins, M. (1983). “Large‐eddy simulation: Retrospect and prospect.” Physicochemical Hydrodynamics, 4, 119–161.
223.
Vreugdenhil, C. (1979). “Two‐layer shallow water flow in two dimensions, a numerical study.” J. Computational Physics, 33(2), 169–184.
224.
Waldrop, W., and Farmer, R. (1974). “Three‐dimensional computation of buoyant plumes.” J. Geophysical Res., 79(2).
225.
Waldrop, W., and Tatom, F. (1976). “Analysis of the thermal effluent from the Gallatin Stream plant during low river flows.” Rept. Tennessee Valley Authority, No. 33–30.
226.
Yotsukura, N., Fischer, H., and Sayre, W. (1970). “Measurement of mixing characteristics of the Missouri River between Sioux City, Iowa and Plattmuth, Nebraska.” U.S. Geo. Survey Prof. Paper 1899‐G.
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Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 9 • September 1988
Pages: 1052 - 1073
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Copyright © 1988 ASCE.
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Published online: Sep 1, 1988
Published in print: Sep 1988
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