3D Analytic Model for Testing Numerical Tidal Models
Publication: Journal of Hydraulic Engineering
Volume 127, Issue 9
Abstract
A 3D analytic solution is presented for tides in channels with arbitrary lateral depth variation. The solution is valid for narrow channels in which the lateral variation of the amplitude of tidal elevation is small. The error introduced by the solution is on the order of a few percent in a tidal channel of a few kilometers in width. The solution allows an arbitrary lateral depth variation and thus provides a wide choice of depth functions, especially those with large bottom slopes. The largest amplitude of the along-estuary velocity appears on the surface in the deepest water. The depth-averaged velocity is the largest in the deepest water. The time of flood (ebb) in deep water lags that in shallow water. The time of flood (ebb) on the surface lags that at the bottom. Since this solution is simple and allows arbitrary lateral depth variations, it can be used to demonstrate the first-order tidal flow in narrow tidal channels of variable depth, and to test high-resolution numerical models with large depth gradients.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Carrier, G. F. ( 1996). “Gravity waves on water of variable depth.” J. Fluid Mech. 24(4), 641–659.
2.
Chen, C. L. (1989). “Analytic solutions for tidal model testing.”J. Hydr. Engrg., ASCE, 115(12), 1707–1714.
3.
Clarke, A. J. ( 1990). “Application of a frictional channel flow theory to flow in the Prince of Wales Channel, Torres Strait.” J. Phys. Oceanography, 20(6), 890–899.
4.
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(8), 15,187–15,196.
5.
Defant, A. ( 1961). Physical oceanography, Vol. 2, Pergamon, Tarrytown, N.Y.
6.
Ippen, T., and Harleman, D. R. F. ( 1961). “One-dimensional analysis of salinity intrusion in estuaries.” Tech. Bull. No. 5, U.S. Army Corps of Engineers, Vicksburg, Miss.
7.
Keller, J. B. ( 1958). “Surface waves on water of non-uniform depth.” J. Fluid Mech., 4(4), 607–614.
8.
Lamb, H. ( 1932). Hydrodynamics, Cambridge University Press, London.
9.
LeBlond, P. H. ( 1978). “On tidal propagation in shallow rivers.” J. Geophys. Res., 83(C9), 4717–4721.
10.
Li, C. ( 1996). “Tidally induced residual circulation in estuaries with cross channel bathymetry.” PhD dissertation, University of Connecticut, Storrs, Conn.
11.
Li, C., and O'Donnell, J. ( 1997). “Tidally driven residual circulation in shallow estuaries with lateral depth variation.” J. Geophys. Res., 102(C13), 27,915–27,929.
12.
Li, C., O'Donnell, J., Valle-Levinson, A., Li, H.-Y., Wong, K.-C., and Lwiza, K. M. M. ( 1998). “Tide induced mass-flux in shallow estuaries.” Ocean wave measurement and analysis, B. L. Edge and J. M. Hemsley, eds., Vol. 2, ASCE, Reston, Va., 1510–1524.
13.
Li, C., and Valle-Levinson, A. ( 1999). “A two-dimensional analytic tidal model for a narrow estuary of arbitrary lateral depth variation: The intratidal motion.” J. Geophys. Res., 104(C10), 23,525–23,543.
14.
Luyten, P. J., Jones, J. E., Proctor, R., Tabor, A., Tett, P., and Wild-Allen, K. ( 1999). “COHERENS—A coupled hydrodynamical-ecological model for regional and shelf seas: User documentation.” Management Unit of the Mathematical Models of the North Sea (MUMM), Brussels.
15.
Lynch, D. R., and Gray, W. G. (1978). “Analytic solutions for computer flow model testing.”J. Hydr. Div., ASCE, 104(10), 1409–1428.
16.
Nachbin, A., and Papanicolaou, G. C. ( 1992). “Water waves in shallow channels of rapidly varying depth.” J. Fluid Mech., 241(2), 311–332.
17.
Officer, C. B. ( 1976). Physical oceanography of estuaries (and associated coastal waters), Wiley, New York.
18.
Parker, B. B. ( 1984). “Frictional effects on the tidal dynamics of shallow estuary.” PhD dissertation, Johns Hopkins University, Baltimore.
19.
Proudman, J. ( 1953). Dynamical oceanography, Methuen, London.
20.
Taylor, G. I. ( 1921). “Tidal oscillations in gulfs and rectangular basins.” Proc., London Math. Soc., Vol. 20, 148–181.
21.
Thacker, W. C. ( 1981). “Some exact solutions to the nonlinear shallow-water wave equations.” J. Fluid Mech., 107(3), 499–508.
22.
Wang, X. H., and Craig, P. D. ( 1993). “An analytic model of tidal circulation in a narrow estuary.” J. Marine Res., 51(3), 447–465.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 127 • Issue 9 • September 2001
Pages: 709 - 717
History
Received: Apr 19, 2000
Published online: Sep 1, 2001
Published in print: Sep 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.