TECHNICAL PAPERS
Apr 1, 1997

Review of Recent Developments in Tidal Hydrodynamic Modeling. II: Turbulence Energy Models

Publication: Journal of Hydraulic Engineering
Volume 123, Issue 4

Abstract

The second part of this review deals with three-dimensional tidal models for homogeneous and stratified sea regions in which the vertical eddy viscosity and diffusivity are computed from turbulence energy submodels. The formulation of a range of turbulence energy models is presented, and the solution of the three-dimensional equations using finite difference methods in the vertical on a number of transformed grid (log, log-linear) is described. The application of turbulence energy models is illustrated using results from a three-dimensional model of tides in the Irish Sea. A comparison of computed tidal current profiles determined using a two-equation turbulence closure model with those derived using a simple flow-dependent eddy viscosity model, and with observations, did not reveal any significant differences between the models. Recent work on the effect of stable stratification on turbulence energy and tidal currents is also considered, as this is the more critical test of the accuracy of turbulence energy models. Processes influencing the internal tide generation in regions of steep topography are also examined using the three-dimensional turbulence energy model with a prognostic density field. The role of the nonlinear terms in the generation of short internal waves at the top of the shelf break, and intense surface and bed mixing in this region is examined together with the effects of an upwelling and downwelling favorable wind.

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References

1.
ASCE Task Committee on Turbulence Models in Hydraulic Computations.(1988). “Turbulence modeling of surface water flow and transport: Part 1.”J. Hydr. Engrg., 114(9), 970–991.
2.
Backhaus, J. O. (1989). “On the atmospherically induced variability of the circulation of the Northwest European shelf sea and related phenomena—A model experiment.”Modelling Marine Systems, Vol. 1, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 93–134.
3.
Baines, P. G.(1982). “On internal tide generation models.”Deep-Sea Res., 29, 307–338.
4.
Baumert, H., and Radach, G.(1992). “Hysteresis of turbulent kinetic energy in nonrotational tidal flows: A model study.”J. Geophys. Res., 97, 3669–3677.
5.
Blackadar, A. K.(1962). “The vertical distribution of wind and turbulent exchange in a neutral atmosphere.”J. Geophys. Res., 67, 3095–3120.
6.
Blumberg, A. F., and Mellor, G. L. (1987). “A description of a three-dimensional coastal ocean circulation model.”Three-dimensional coastal ocean models, N. S. Heaps, ed., Am. Geophys. Union, Washington, D.C., 1–16.
7.
Chen, Y., and Falconer, R. A.(1992). “Advection diffusion modelling using the modified QUICK scheme.”Int. J. Numer. Methods in Fluids, 15, 1171–1196.
8.
Cheng, R. T., and Smith, P. E. (1990). “A survey of three dimensional numerical estuarine models.”Estuarine and coastal modeling, M. L. Spaulding, ed., Newport R.I., ASCE, New York, N.Y., 1–15.
9.
Craig, P. D.(1987). “Solutions for internal tidal generation over coastal topography.”J. Marine Res., 45, 83–105.
10.
Craig, P. D.(1988). “A numerical model study of internal tides on the Australian Northwest Shelf.”J. Marine Res., 46, 59–76.
11.
Crawford, W. R. (1991). “Tidal mixing and nutrient flux in the waters of southwest British Columbia.”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, Inc., New York, N.Y., 855–872.
12.
Davies, A. M.(1991a). “On using turbulence energy models to develop spectral viscosity models.”Continental Shelf Res., 11, 1313–1353.
13.
Davies, A. M.(1991b). “On the accuracy of finite difference and modal methods for computing tidal and wind wave current profiles.”Int. J. Numer. Methods in Fluids, 12, 101–124.
14.
Davies, A. M.(1993). “Numerical problems in simulating tidal flows with a frictional-velocity-dependent eddy viscosity and the influence of stratification.”Int. J. Numer. Methods in Fluids, 16, 105–131.
15.
Davies, A. M., and Gerritsen, H. (1994). “An intercomparison of three dimensional tidal hydrodynamic models of the Irish Sea.”Tellus, 46A(2), 200–221.
16.
Davies, A. M., Grozonka, R. B., and Stephens, C. V.(1992). “Implementation of a three-dimensional hydrodynamic sea model using parallel processing on a CRAY X-MP series computer.”Adv. in Parallel Computing, 2, 145–185.
17.
Davies, A. M., and Jones, J. E. (1990). “Application of a three-dimensional turbulence energy model to the determination of tidal currents on the northwest European shelf.”J. Geophys. Res., 95, 18,143–18,162.
18.
Davies, A. M., and Jones, J. E.(1991). “On the numerical solution of the turbulence energy equations for wave and tidal flows.”Int. J. Numer. Methods in Fluids, 12, 17–41.
19.
Davies, A. M., and Jones, J. E.(1992). “A three dimensional model of the M2, S2, N2, K1 and O1 tides in the Celtic and Irish Seas.”Progress in Oceanography, 29, 197–234.
20.
Davies, A. M., Jones, J. E., and Xing, J.(1997). “Review of recent developments in tidal hydrodynamic modeling.” I: Spectral Models. J. Hydr. Engrg., ASCE, 123(4), 278–292.
21.
Davies, A. M., Luyten, P., and Deleersnijder, E. (1995). “Turbulence energy models in shallow sea oceanography.”Quantitative skill assessment for coastal ocean models, D. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 97–124.
22.
Davies, A. M., and Xing, J. (1995). “An intercomparison and validation of a range of turbulence closure schemes used in three dimensional tidal models.”Quantitative skill assessment for coastal ocean models, D. R. Lynch and A. M. Davies, eds., Geophys. Union, Washington, D.C., 71–95.
23.
Deleersnijder, E., and Luyten, P.(1994). “On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling.”Appl. Math. Modelling, 18, 281–287.
24.
Galperin, B., Kantha, L. H., Hassid, S., and Rosati, A.(1988). “A quasi-equilibrium turbulent energy model for geophysical flows.”J. Atmospheric Sci., 45, 55–62.
25.
Galperin, B., Rosati, A., Kantha, L. H., and Mellor, G. L.(1989). “Modeling rotating stratified turbulent flows with application to oceanic mixed layers.”J. Phys. Oceanography, 19, 901–916.
26.
Gerrity, J. P., Black, T. L., and Treadon, R. E.(1994). “The numerical solution of the Mellor-Yamada level 2.5 turbulent kinetic energy equation in the Eta model.”Monthly Weather Rev., 122, 1640–1646.
27.
Haidvogel, D. B., Beckmann, A., and Hedstrom, K. S. (1991). “Dynamical simulations of filament formation and evolution in the coastal transition zone.”J. Geophys. Res., 96(C8), 15,017–15,040.
28.
Heathershaw, A. D., New, A. L., and Edwards, P. D.(1987). “Internal tides and sediment transport at the shelf break in the Celtic Sea.”Continental Shelf Res., 7, 485–517.
29.
Holloway, P. E. (1991). “On the dissipation of internal tides.”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, New York, N.Y., 449–468.
30.
Holloway, P. E.(1994). “Observations of internal tide propagation on the Australian North West shelf.”J. Phys. Oceanography, 24, 1706–1716.
31.
Huthnance, J. M.(1989). “Internal tides and waves near the continental shelf edge.”Geophys. Astrophys. Fluid Dyn., 48, 81–105.
32.
Huthnance, J. M., and Baines, P. G.(1982). “Tidal currents in the north west Africa upwelling region.”Deep-Sea Res., 19, 285–306.
33.
James, I. D.(1995). “Advection schemes for shelf sea models.”J. Marine Sys., 8, 237–254.
34.
Johns, B.(1978). “The modeling of tidal flow in a channel using a turbulence energy closure scheme.”J. Phys. Oceanography, 8, 1042.
35.
Johns, B., Marsaleix, P., Estournel, C., and Vehil, R.(1992). “On the wind-driven coastal upwelling in the Gulf of Lions.”J. Marine Systems, 3, 309–320.
36.
Johns, B., and Oguz, T. (1987). “Turbulent energy closure schemes.”Three-dimensional coastal ocean models, N. S. Heaps, ed., Am. Geophys. Union, Washington, D.C., 17–40.
37.
Johns, B., and Xing, J.(1993). “Three-dimensional modelling of the free-surface turbulent flow of water over a bed form.”Continental Shelf Res., 13, 705–723.
38.
Lamb, K. G.(1994). “Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge.”J. Geophys. Res., 99, 843–864.
39.
Lohrmann, A., Hackett, B., and Roed, L. P.(1990). “High resolution measurements of turbulence, velocity and stress using a pulse-to-pulse coherent sonar.”J. Atmospheric and Oceanic Technol., 7, 19–37.
40.
Luyten, P. J., Deleersnijder, E., Ozer, J., and Ruddick, K. G.(1996). “Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region.”Continental Shelf Res., 16, 101–130.
41.
Maas, L. R. M., and Van Haren, J. J. M.(1987). “Observations on the vertical structure of tidal and inertial currents in the central North Sea.”J. Marine Res., 45, 293–318.
42.
Maze, R.(1987). “Generation and propagation of non-linear internal waves induced by the tide over a continental slope.”Continental Shelf Res., 7(9), 1079–1104.
43.
Mellor, G. L., and Yamada, T.(1982). “Development of a turbulence closure model for geophysical fluid problems.”Rev. Geophys. Space Phys., 20(4), 851–875.
44.
New, A. L.(1988). “Internal tidal mixing in the Bay of Biscay.”Deep-Sea Res., 35, 691–709.
45.
New, A. L., and Pingree, R. D.(1990). “Evidence for internal tidal mixing near the shelf break in the Bay of Biscay.”Deep-Sea Res., 37, 1783–1803.
46.
Noye, J. (1984). “Finite difference techniques for partial differential equations.”Computational techniques for differential equations, North-Holland, Amsterdam, The Netherlands, 295–354.
47.
Rodi, W. (1984). “Turbulence models and their application in hydraulics—a state of the art review.” Int. Assoc. for Hydr. Res. (IAHR), A. A. Balkema, Rotterdam, The Netherlands.
48.
Rodi, W.(1987). “Examples of calculation methods for low and mixing in stratified fluids.”J. Geophys. Res., 92, 5305–5328.
49.
Sherwin, T. J. (1991). “Evidence of a deep internal tide in the Faeroe-Shetland Channel.”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, New York, N.Y., 469–488.
50.
Sherwin, T. J., and Taylor, N.(1989). “The application of a finite difference model of internal tide generation to the NW European Shelf.”Deutsche Hydrographische, Zeitschrift, Hamburg, Germany, 42, 151–167.
51.
Sherwin, T. J., and Taylor, N.(1990). “Numerical investigations of linear internal tide generation in the Rockall Trough.”Deep Sea Res., 37, 1595–1618.
52.
Song, Y., and Haidvogel, D.(1994). “A semi-implicit ocean circulation model using a generalised topography-following coordinate system.”J. Computational Phys., 115, 228–244.
53.
Soulsby, R. L. (1990). “Tidal-current boundary layers.”The sea, Vol. 9A, B. Le Méhauté and D. M. Hanes, eds., Wiley-Interscience, New York, N.Y., 523–566.
54.
Stelling, G. S., and Van Kester, J.(1994). “On the approximation of horizontal gradients in sigma coordinates for bathymetry with steep bottom slopes.”Int. J. Numer. Methods in Fluids, 18, 915–935.
55.
Vager, B. G., and Kagan, B. A.(1969). “The dynamics of the turbulent boundary layer in a tidal current.”Izv. Atmospheric and Oceanic Phys., 5(2), 88.
56.
Wolf, J. (1980). “Estimation of shearing stresses in a tidal current with application to the Irish Sea.”Marine turbulence, Proc., 11th Liege Colloquium on Oc. Hydrodyn., Elsevier Oceanogr. Ser. Vol. 28, J. C. J. Nihoul, ed., Elsevier, Amsterdam, The Netherlands.
57.
Xing, J. (1992). “The numerical modelling of shallow water flow and sediment transport over bedforms in the coastal ocean,” PhD thesis, Dept. Meteorology, Univ. of Reading, U.K.
58.
Xing, J., and Davies, A. M.(1995). “Application of three dimensional turbulence energy models to the determination of tidal mixing and currents in a shallow sea.”Progress in Oceanography, 35, 153–205.
59.
Xing, J., and Davies, A. M.(1996a). “Application of a range of turbulence energy models to the determination of M4 tidal current profiles.”Continental Shelf Res., 16, 517–547.
60.
Xing, J., and Davies, A. M.(1996b). “The influence of mixing length formulation and stratification upon tidal currents in shallow seas.”Estuarine Coast. and Shelf Sci., 42, 417–456.
61.
Xing, J., and Davies, A. M.(1996c). “Application of turbulence energy models to the computation of tidal currents and mixing intensities in shelf edge regions.”J. Phys. Oceanography, 26, 417–447.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 123Issue 4April 1997
Pages: 293 - 302

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Published online: Apr 1, 1997
Published in print: Apr 1997

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A. M. Davies
Sr. Res. Sci., Proudman Oceanographic Lab., Bidston Observatory, Birkenhead, Merseyside L43 7RA, UK.
J. E. Jones
Sr. Res. Sci., Proudman Oceanographic Lab., Bidston Observatory, Birkenhead, Merseyside L43 7RA, UK.
J. Xing
Sr. Res. Sci., Proudman Oceanographic Lab., Bidston Observatory, Birkenhead, Merseyside L43 7RA, UK.

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