TECHNICAL PAPERS
Apr 1, 1997

Review of Recent Developments in Tidal Hydrodynamic Modeling. I: Spectral Models

Publication: Journal of Hydraulic Engineering
Volume 123, Issue 4

Abstract

In this paper we present a brief overview, with a comprehensive set of references to recently published papers for detail, of a range of techniques used in tidal hydrodynamic modeling and recent progress in the field. Although the paper aims to introduce the topic to someone new to the area, the main emphasis is on new developments in near coastal (shallow sea) tidal modeling, and consequently we concentrate on three-dimensional modeling, which has progressed significantly in recent years. The paper gives a brief account of methods used to discretize the hydrodynamic equations in the horizontal, namely finite difference, finite element and boundary-fitted coordinates, and through time. The representation of tidal current structure in a three-dimensional model using a spectral method in the vertical is also described. In this method the subgrid scale vertical diffusion of momentum, which has a major influence on tidal current profiles, is parameterized using a flow-dependent eddy viscosity. Recent work on the chaotic behavior of particles released into two-dimensional tidal flow models and the use of adjoint models is also briefly considered.

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References

1.
Abraham, G., and Gerritsen, H.(1990). “Sub-grid transport of matter in two-dimensional tidal flow over an uneven bed.”Continental Shelf Res., 10, 225–242.
2.
Abraham, G., Gerritsen, H., and Lindijer, G. J. H.(1987). “Subgrid tidally induced residual circulations.”Continental Shelf Res., 7, 285–305.
3.
Aldridge, J. N., and Davies, A. M.(1993). “A high resolution three dimensional hydrodynamic tidal model of the eastern Irish Sea.”J. Phys. Oceanography, 23, 207–224.
4.
Amin, M.(1993). “The mutual influence of tidal constituents in the presence of bottom stress.”Estuarine, Coast. and Shelf Sci., 37, 625–633.
5.
Baker, T. F.(1984). “Tidal deformations of the Earth.”Scientific Progress Oxford, Oxford, England, 69, 197–233.
6.
Bakhmetev, B. A. (1932). Hydraulics of open channels. Eng. Soc. Manograph, McGrawhill.
7.
Baptista, A. M., Westerink, J. J., and Turner, P. J.(1989). “Tides in the English Channel and southern North Sea. A frequency domain analysis using model TEA-NL.”Adv. Water Resour., 12, 166–183.
8.
Beckmann, A., and Haidvogel, D. B.(1993). “Numerical simulation of flow around a tall isolate seamount. Part 1: Problem formulation and model accuracy.”J. Phys. Oceanography, 23, 1736–1753.
9.
Bennett, A. F., and McIntosh, P. C.(1982). “Open ocean modelling as an inverse problem in tidal theory.”J. Phys. Oceanography, 12, 1004–1018.
10.
Blumberg, A. F., and Kantha, L. H.(1985). “Open boundary condition for circulation models.”J. Hydr. Engrg., ASCE, 111, 237–255.
11.
Bowden, K. F.(1978). “Physical problems of the benthic boundary layer.”Geophysical Surveys, 3, 255–296.
12.
Bowden, K. F., and Hamilton, P.(1975). “Some experiments with a numerical model of circulation and mixing in a tidal estuary.”Estuarine Coast. Marine Sci., 3, 281–301.
13.
Chapman, D. C.(1985). “Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model.”J. Phys. Oceanography, 15, 1060–1075.
14.
Das, S. K., and Lardner, R. W. (1991). “On the estimation of parameters of hydraulic models by assimilation of periodic tidal data.”J. Geophys. Res., 96, 15,187–15,196.
15.
Das, S. K., and Lardner, R. W.(1992). “Variational parameters estimation for a two-dimensional numerical tidal model.”Int. J. Numer. Methods in Fluids, 15, 313–327.
16.
Davies, A. G. (1989). “A model of the vertical structure of the wave and current bottom boundary layer.”Modeling marine systems, Vol. II, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 263–298.
17.
Davies, A. M.(1983). “Numerical modelling of stratified flow: a spectral approach.”Continental Shelf Res., 2, 275–300.
18.
Davies, A. M.(1986). “A three-dimensional model of the northwest European continental shelf with application to the M4 tide.”J. Phys. Oceanography, 16, 797–813.
19.
Davies, A. M. (1987). “Spectral models in continental shelf sea oceanography.”Three-dimensional coastal ocean models, N. S. Heaps, ed., Am. Geophys. Union, Washington, D.C., 71–106.
20.
Davies, A. M.(1988). “On formulating two dimensional vertically integrated hydrodynamic numerical models with an enhanced representation of bed stress.”J. Geophys. Res., 93, 1241–1263.
21.
Davies, A. M. (1990). “On the importance of time varying eddy viscosity in generating higher tidal harmonics.”J. Geophys. Res., 95, 20,287–20,312.
22.
Davies, A. M.(1991a). “On using turbulence energy models to develop spectral viscosity models.”Continental Shelf Res., 11, 1313–1353.
23.
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.
24.
Davies, A. M.(1991c). “Solution of the 3D linear hydrodynamic equations using an enhanced eigenfunction approach.”Int. J. Numer. Methods in Fluids, 31, 235–250.
25.
Davies, A. M.(1992). “Modelling currents in highly sheared surface and bed boundary layers.”Continental Shelf Res., 12, 159–188.
26.
Davies, A. M.(1993a). “A bottom boundary layer-resolving three dimensional tidal model: A sensitivity study of eddy viscosity formulation.”J. Phys. Oceanography, 23, 1437–1453.
27.
Davies, A. M.(1993b). “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.
28.
Davies, A. M. (1994). “Quasi-three-dimensional modelling using mixed finite-difference and spectral models.”Coastal, estuarial and harbour engineer's reference book, M. B. Abbott and W. A. Price, eds., Chapman and Hall, London, U.K., 117–128.
29.
Davies, A. M., and Aldridge, J. N. (1993). “A numerical model study of parameters influencing tidal currents of the Irish Sea.”J. Geophys. Res., 98, 7049–7067.
30.
Davies, A. M., Kwong, C. M., and Flather, R. A.(1996). “Formulation of a variable function three dimensional model, and computation of the M2 tide and overtides on the European Shelf.”Continental Shelf Res., 17, 165–204.
31.
Davies, A. M., and Gerritsen, H. (1994). “An intercomparison of three dimensional tidal hydrodynamic models of the Irish Sea.”Tellus, 46A(2), 200–221.
32.
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.
33.
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.
34.
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.
35.
Davies, A. M., and Jones, J. E.(1993). “On improving the bed stress formulation in storm surge models.”J. Geophys. Res., 98, 7023–7038.
36.
Davies, A. M., Jones, J. E., and Xing, J.(1997). “Review of recent developments in tidal hydrodynamic modeling. II: Turbulence energy models.”J. Hydr. Engrg., ASCE, 123(4), 293–302.
37.
Davies, A. M., and Lawrence, J. (1994a). “A three dimensional model of the M4 tide in the Irish Sea: The importance of open boundary conditions and influence of wind.”J. Geophys. Res., 99(C8), 16,197– 16,227.
38.
Davies, A. M., and Lawrence, J.(1994b). “Examining the influence of wind and wind-wave turbulence on tidal currents, using a three dimensional hydrodynamic model including wave-current interaction.”J. Phys. Oceanography, 24, 2441–2460.
39.
Davies, A. M., and Lawrence, J.(1994c). “Modelling the non-linear interaction of wind and tide: its influence on current profiles.”Int. J. Numer. Methods in Fluids, 18, 163–188.
40.
Davies, A. M., and Lawrence, J.(1995). “Modelling the effect of wave-current interaction on the three dimensional wind driven circulation of the eastern Irish Sea.”J. Phys. Oceanography, 25, 29–45.
41.
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.
42.
Davies, A. M., and Owen, A.(1979). “Three-dimensional numerical sea model using the Galerkin method with a polynomial basis set.”Appl. Math. Modelling, 3, 421–428.
43.
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.
44.
Flather, R. A. (1981). “Results from a model of the north east Atlantic relating to the Norwegian Coastal Current.”The Norwegian Coastal Current, Vol. 2, R. Saetre and M. Mork, eds., Bergen University, Bergen, Norway, 427–458.
45.
Flather, R. A.(1988). “A numerical model investigation of tides and diurnal period continental shelf waves along Vancouver Island.”J. Phys. Oceanography, 18, 115–139.
46.
Flather, R. A., and Hubbert, K. P. (1990). “Tide and surge models for shallow water—Morecambe Bay revisited.”Modeling marine systems, Vol. 1, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 135–166.
47.
Foreman, M. G. G., Henry, R. F., Walters, R. A., and Ballantyne, V. A.(1993). “A finite element model for tides and resonance along the north coast of British Columbia.”J. Geophys. Res., 98, 2509–2531.
48.
Foreman, M. G. G., and Walters, R. A.(1990). “A finite-element tidal model for the southwest coast of Vancouver Island.”Atmospheric Oceanography, 18, 261–287.
49.
Gerritsen, H., de Vries, H., and Philippart, M. (1995). “The Dutch Continental Shelf Model.”Quantitative skill assessment for coastal ocean models, D. R. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 425–468.
50.
Gjevik, B., Nøst, E., and Straume, T.(1994). “Model simulations of the tides in the Barents Sea.”J. Geophys. Res., 99, 3337–3350.
51.
Gjevik, B., and Straume, T. (1989). “Model simulations of the M2 and the K1 tide in the Nordic Seas and in the Arctic Ocean.”Tellus, 41A, 73–96.
52.
Gordon, R. B., and Spaulding, M. L.(1987). “Numerical simulations of the tidaland wind-driven circulation in Narragansett Bay.”Estuarine, Coast. and Shelf Sci., 24, 611–636.
53.
Grant, W. D., and Madsen, O. S.(1986). “The continental-shelf bottom boundary layer.”Annu. Rev. in Fluid Mech., 18, 265–305.
54.
Greatbatch, R. G., and Otterson, T. (1991). “On the formulation of open boundary conditions at the mouth of a bay.”J. Geophys. Res., 96, 18,431–18,445.
55.
Greenberg, D. A. (1990). “The contribution of modelling to understanding the dynamics of the Bay of Fundy and the Gulf of Maine.”Modeling Marine Systems, Vol. 2, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 107–140.
56.
Gross, T. F., and Werner, F. E.(1994). “Residual circulations due to bottom roughness variability under tidal flows.”J. Phys. Oceanography, 24, 1494–1502.
57.
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.
58.
Haney, R. L.(1991). “On the pressure gradient force over steep topography in sigma coordinate ocean models.”J. Phys. Oceanography, 21, 610–619.
59.
Häuser, J., Paap, H. G., Eppel, D., and Mueller, A.(1985). “Solution of shallow water equations for complex flow domains via boundary-fitted coordinates.”Int. J. for Numer. Methods in Fluids, 5, 727–744.
60.
Heaps, N. S., and Jones, J. E. (1983). “Development of a three-layered spectral model for the motion of a stratified sea. II. Experiments with a rectangular basin representing the Celtic Sea.”Physical Oceanography of Coastal and Shelf Seas, B. Johns, ed., Elsevier, New York, N.Y., 401–465.
61.
Heaps, N. S., and Jones, J. E.(1985). “A three-dimensional spectral model with application to wind-induced motion in the presence of stratification and a bottom slope.”Continental Shelf Res., 4, 279–319.
62.
Howarth, M. J., and Proctor, R.(1992). “Ship ADCP measurements and tidal models of the North Sea.”Continental Shelf Res., 12, 601–623.
63.
Isaji, T., and Spaulding, M. L.(1984). “A model of the tidally induced residual circulation in the Gulf of Maine and Georges Bank.”J. Phys. Oceanography, 14, 1119–1126.
64.
Jamart, B. M., and Ozer, J. (1986). “Numerical boundary layers and spurious residual flows.”J. Geophys. Res., 91, 10,621–10,631.
65.
James, I. D. (1990). “Numerical modeling of density-driven circulation in shelf seas.”Modeling Marine Systems, Vol. II, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 345–373.
66.
Johnson, B. H. (1980). “VAHM—Vertically averaged hydrodynamic model using boundary-fitted coordinates.”Paper HL-80-3, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.
67.
Johnson, B. H., Kim, K. W., Heath, R. E., Hsieh, B. B., and Butler, H. L.(1993). “Validation of three dimensional hydrodynamic model of Chesapeake Bay.”J. Hydr. Engrg., ASCE, 119(1), 2–20.
68.
Jones, J. E., and Davies, A. M.(1995). “A high resolution three dimensional model of the M2, M4, M6, S2, N2, K1 and O1 tides in the eastern Irish Sea.”Estuarine Coast. and Shelf Sci., 42, 311–346.
69.
Keen, T. R., and Glenn, S. M.(1994). “A coupled hydrodynamic-bottom boundary layer model of Ekman flow on stratified continental shelves.”J. Phys. Oceanography, 24, 1732–1749.
70.
Kent, R. E., and Pritchard, D. W.(1959). “A test of mixing length theories in a coastal plain estuary.”J. Marine Res., 18, 62–72.
71.
Koutitas, C. G. (1987). “Three-dimensional models of coastal circulation: An engineering viewpoint.”Three-dimensional coastal ocean models, N. S. Heaps, ed., Am. Geophys. Union, Washington, D.C., 107–123.
72.
Koutitas, C. G., and O'Connor, B. A.(1980). “Modelling three dimensional wind-induced flows.”J. Hydr. Div., ASCE, 106, 1843–1865.
73.
Lardner, R. W. (1990). “Numerical solution of the linearised three-dimensional tidal equations using eddy viscosity eigenfunctions.”J. Geophys. Res., 95, 22,269–22,274.
74.
Lardner, R. W., and Das, S. K.(1994). “Optimal estimation of eddy viscosity for a quasithree-dimensional numerical tidal and storm surge model.”Int. J. Numer. Methods in Fluids, 18, 295–312.
75.
Lardner, R. W., and Song, Y.(1992a). “A comparison of spatial grids for numerical modelling of flows in near coastal seas.”Int. J. Numer. Methods in Fluids, 14(1), 109–124.
76.
Lardner, R. W., and Song, Y.(1992b). “A hybrid spectral method for the three dimensional numerical modelling of nonlinear flows in shallow seas.”Int. J. Numer. Methods in Fluids, 14, 109–124.
77.
Le Provost, C., and Fornerino, M.(1985). “Tidal spectroscopy of the English Channel with a numerical model.”J. Phys. Oceanography, 15, 1009–1031.
78.
Le Provost, C., Genco, M. L., and Lyard, F. (1995). “Modeling and predicting tides over the World ocean.”Quantitative skill assessment for coastal ocean models, D. R. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 175–202.
79.
Le Provost, C., and Lyard, F.(1994). “Towards a detailed knowledge of the world ocean tides: The example of the Kerguelen Plateau.”Geophys. Res. Letters, 20(14), 1519–1522.
80.
Loder, J. W.(1980). “Topographic rectification of tidal currents on the sides of Georges Bank.”J. Phys. Oceanography, 10, 1399–1416.
81.
Loder, J. W., and Wright, D. G.(1985). “Tidal rectification and frontal circulation on the sides of Georges Bank.”J. Marine Res., 43, 581–604.
82.
Luettich, R. A., and Westerink, J. J.(1991). “A solution for the vertical variation of stress, rather than velocity, in a three-dimensional circulation model.”Int. J. Numer. Methods in Fluids, 12, 911–928.
83.
Luettich, R. A., and Westerink, J. J. (1994). “Continental shelf scale convergence studies with a barotropic tidal model.”Quantitative skill assessment for coastal ocean models. D. R. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 349–372.
84.
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.
85.
Lynch, D. R., Ip, J. T. C., Naimie, C. E., and Wernere, F. E. (1995). “Convergence studies of tidally-rectified circulation on Georges Bank.”Quantitative skill assessment for coastal ocean models, D. R. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 153–174.
86.
Lynch, D. R., and Naimie, C. E.(1993). “The M2 tide and its residual on the outer banks of the Gulf of Maine.”J. Phys. Oceanography, 23, 2222–2253.
87.
Lynch, D. R., and Werner, F. E.(1987). “Three-dimensional hydrodynamics on finite elements. Part I: Linearized harmonic model.”Int. J. Numer. Methods in Fluids, 7, 871–909.
88.
Lynch, D. R., and Werner, F. E.(1990). “Three-dimensional hydrodynamics on finite elements. Part II: Nonlinear time-stepping model.”Int. J. Numer. Methods in Fluids, 12, 507–534.
89.
Lynch, D. R., and Werner, F. E. (1991). “Three-dimensional velocities from a finite-element model of the English Channel/Southern Bight tides.”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, New York, N.Y., 183–200.
90.
Lynch, D. R., Werner, F. E., Greenberg, D. A., and Loder, J. W.(1992). “Diagnostic model for baroclinic, wind-driven and tidal circulation in shallow seas.”Continental Shelf Res., 12, 37–64.
91.
Martinsen, E. A., and Engedahl, H.(1987). “Implementation and testing of a lateral boundary scheme as an open boundary condition in barotropic ocean model.”Coast. Engrg., 11, 603–627.
92.
Mellor, G. L., Ezer, T., and Oey, L.-Y.(1994). “The pressure gradient conundrum of sigma coordinate ocean models.”J. Atmospheric and Oceanic Technol., 11, 1126–1134.
93.
Munk, W. H., and Anderson, E. R.(1948). “Notes on a theory of the thermocline.”J. Marine Res., 7, 276–295.
94.
Naimie, C. E., Loder, J. W., and Lynch, D. R. (1994). “Seasonal variation of the three-dimensional residual circulation on Georges Bank.”J. Geophys. Res., 99, 15,967–15,989.
95.
Nøst, E.(1994a). “Calculating tidal current profiles from vertically integrated models near the critical latitude in the Barents Sea.”J. Geophys. Res., 99, 7885–7901.
96.
Nøst, E. (1994b). “Tidal currents near the critical latitude in the Barents Sea,” Doctor Scientiarum thesis, Dept. of Mathematics, University of Oslo, Norway.
97.
Owen, A.(1980). “A three-dimensional model of the Bristol Channel.”J. Phys. Oceanography, 10, 1290–1302.
98.
Panchang, V. G., and O'Brien, J. J. (1989). “On the determination of hydraulic model parameters using the adjoint state formulation.”Modeling marine systems, Vol. 1, A. M. Davies, ed., CRC Press, Boca Raton, Fla., 5–18.
99.
Parker, B. B. (1991). “The relative importance of the various nonlinear mechanisms in a wide range of tidal interactions (review).”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, New York, N.Y., 237–268.
100.
Pingree, R. D. (1983). “Spring tides and quadratic friction.”Deep Sea Res., 30(9A), 929–944.
101.
Provis, D. G., and Lennon, G. W. (1983). “Eddy viscosity and tidal cycles in a shallow sea. Estuarine Coast. Shelf Sci., 16, 351.
102.
Pugh, D. T., and Vassie, J. M.(1976). “Tide and surge propagation offshore in the Dowsing region of the North Sea.”Deutsche Hydrographische Zeitschrift, Hamburg, Germany, 29, 163–213.
103.
Ridderinkhof, H. (1995). “Lagrangian flows in complex Eulerian fields.”Quantitative skill assessment for coastal ocean models, D. R. Lynch and A. M. Davies, eds., Am. Geophys. Union, Washington, D.C., 31–48.
104.
Ridderinkhof, H., and Zimmerman, J. T. F.(1992). “Chaotic stirring in a tidal system.”Sci., 258, 1107–1110.
105.
Ridderinkhof, H., Zimmerman, J. T. F., and Phillippart, M. E.(1990). “Tidal exchange between the North Sea and Dutch Wadden Sea and mixing time scales of the tidal basins.”Netherlands J. Sea Res., 25, 331–350.
106.
Roed, L. P., and Cooper, C. K. (1987). “A study of various open boundary conditions for wind-forced barotropic numerical ocean models.” J. C. J. Nihoul and B. N. Jamart, eds., Elsevier Science Publishers BV (North Holland), Amsterdam, The Netherlands.
107.
Signell, R. P., Beardsley, R. C., Graber, H. C., and Capotondi, A.(1990). “Effect of wave-current interaction on wind-driven circulation in narrow, shallow embayments.”J. Geophys. Res., 95, 9671–9678.
108.
Smagorinsky, J.(1963). “General circulation experiments with the primitive equations, I. The basic experiment.”Monthly Weather Rev., 91, 99–164.
109.
Spaulding, M. L.(1984). “A vertically averaged circulation model using boundary fitted coordinates.”J. Phys. Oceanography, 14, 973–982.
110.
Stelling, G. S., and Leendertse, J. J. (1992). “Approximation of convective processes by cyclic AOI methods.”Estuarine and Coast. Modeling; Proc., 2nd ASCE Int. Conf., M. L. Spaulding, K. Bedford, A. Blumberg, R. Cheng, and C. Swanson, eds., ASCE, New York, N.Y.
111.
Stelling, G. S., and Van-Kester, J. A. T. M.(1994). “On the approximation of horizontal gradients in sigma coordinates for bathymetry with steep bottom slopes.”Int. J. Numer. Methods in Fluids, 10, 915–937.
112.
Stelling, G. S., Wiersma, A. K., and Willemse, J. B. T. M.(1986). “Practical aspects of accurate tidal computations.”J. Hydr. Engrg., ASCE, 112(9), 802–817.
113.
Tang, Y., and Tee, K.-T.(1987). “Effects of mean and tidal current interaction on the tidally induced residual current.”J. Phys. Oceanography, 17, 215–230.
114.
Tee, K.-T. (1987). “Simple models to simulate three-dimensional tidal and residual currents.”Three-dimensional coastal ocean models, N. S. Heaps, ed., Am. Geophys. Union, Washington, D.C., 125–147.
115.
Ten-Brummelhuis, P. G. J., Heemink, A. W., and Van Den Boogaard, H. F. P.(1993). “Identification of shallow sea models.”Int. J. Numer. Methods in Fluids, 17, 637–665.
116.
Walters, R. A., and Werner, F. E.(1989). “A comparison of two finite element models of tidal hydrodynamics using a North Sea data set.”Adv. in Water Resour., 12, 184–193.
117.
Walters, R. A., and Werner, F. E. (1991). “Nonlinear generation of overtides, compound tides, and residuals.”Tidal hydrodynamics, B. B. Parker, ed., John Wiley and Sons, New York, N.Y., 297–320.
118.
Werner, F. E., and Lynch, D. R.(1989). “Harmonic structure of English Channel-Southern Bight tides from a wave equation simulation.”Adv. in Water Resour., 12, 121–142.
119.
Westerink, J. J., Connor, J. J., and Stolzenbach, K. D.(1988). “A frequency-time domain finite element model for tidal circulation based on the least squares harmonic analysis method.”Int. J. Numer. Methods in Fluids, 8, 813–843.
120.
Westerink, J. J., Luettich, R. A., Baptista, A. M., Scheffner, N. W., and Farrar, P.(1992). “Tide and storm surge predictions using finite element model.”J. Hydr. Engrg., ASCE, 118, 1373–1390.
121.
Westerink, J. J., Luettich, R. A., and Muccino, J. C. (1994). “Modeling tides in the western North Atlantic using unstructured graded grids.”Tellus, 46A, 178–199.
122.
Westerink, J. J., Stolzenback, K. D., and Connor, J. J.(1989). “General spectral computation of the nonlinear shallow water tidal interactions within the Bight of Abaco.”J. Phys. Oceanography, 19, 1348–1371.
123.
Wilders, P., van Stijn, T. L., Stelling, G. S., and Fokkema, G. A.(1988). “A fully implicit splitting method for accurate tidal computations.”Int. J. Numer. Methods in Engrg., 26, 2707–2721.
124.
Wolf, J.(1983). “A comparison of a semi-implicit with an explicit scheme in a three-dimensional hydrodynamic model.”Continental Shelf Res., 2, 215–229.
125.
Wright, D. G., and Loder, J. W.(1988). “On the influences of nonlinear bottom friction on the topographic rectification of tidal currents.”Geophys. Astrophys. Fluid Dyn., 42, 227–245.
126.
Xing, J., and Davies, A. M.(1995a). “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.
127.
Xing, J., and Davies, A. M.(1995b). “Application of a range of turbulence energy models to the determination of M4 tidal current profiles.”Continental Shelf Res., 16, 517–547.
128.
Zimmerman, J. T. F.(1986). “The tidal whirlpool: A review of horizontal dispersion by tidal and residual currents.”Netherlands J. Sea Res., 20, 133–154.
129.
Zitman, T. J.(1992). “Quasi three-dimensional current modelling based on a modified version of Davies' shape function approach.”Continental Shelf Res., 12, 143–158.

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Journal of Hydraulic Engineering
Volume 123Issue 4April 1997
Pages: 278 - 292

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Published online: Apr 1, 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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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
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Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

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