Parabolic Model for Water Waves
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 4
Abstract
A new parabolic equation is derived from the mild-slope equation. It is used as the governing equation for the propagation of periodic surface water waves without wave reflection. For the problem of forward wave propagation, the equation can be solved very efficiently by the parabolic equation method, without the angle limitation as for other parabolic models. Several cases involving incident wave angles up to 70° are adopted to test the model. The numerical results confirm that the new parabolic model is very stable, highly accurate, and economical to use. Finally, a parabolic equation for wave-current interaction based on the wave model developed in this paper is also presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Berkhoff, J. C. W. (1972). “Computation of combined refraction-diffraction.”Proc., 13th Coast. Engrs. Conf., ASCE, New York, N.Y., 471–490.
2.
Berkhoff, J. C. W. (1976). “Mathematical models for simple harmonic linear water waves.”Rep. on Math. Investigation No. W 154-IV, Delft Hydr. Lab., Delft, The Netherlands.
3.
Berkhoff, J. C. W. (1982). “Refraction and diffraction of water waves; wave deformation by a shoal, comparison between computations and measurements.”Rep. on Math. Investigation No. W 154-III, Delft Hydraulics Laboratory, Delft, The Netherlands.
4.
Berkhoff, J. C. W., Booij, N., and Radder, A. C.(1982). “Verification of numerical wave propagation models for simple harmonic water waves.”Coast. Engrg., 6, 255–279.
5.
Booij, N. (1981). “Gravity waves on water with non-uniform depth and current.”Rep. No. 81-1, Dept. Civil Engrg., Delft Univ. of Technol., Delft, The Netherlands.
6.
Dalrymple, R. A., and Kirby, J. T.(1988). “Models for very wide-angle water waves and wave diffraction.”J. Fluid Mech., Cambridge, U.K., 192, 33–50.
7.
Dalrymple, R. A., Suh, K. D., Kirby, J. T., and Chae, J. W.(1989). “Models for very wide-angle water waves and wave diffraction. 2: Irregular bathymetry.”J. Fluid Mech., Cambridge, U.K., 201, 299–322.
8.
Kirby, J. T. (1984). “A note on linear surface wave-current interaction over slowly varying topography.”J. Geophys. Res., 89(C1), 745–747.
9.
Kirby, J. T.(1986). “Rational approximations in the parabolic equation method for water waves.”Coast. Engrg., 10, 355–378.
10.
Li, B., and Anastasiou, K.(1992). “Efficient elliptic solvers for the mild-slope equation using the multigrid technique.”Coast. Engrg., 16, 245–266.
11.
Li, B. (1993). “Efficient water wave and current propagation modelling,” PhD thesis, Imperial Coll., London, U.K.
12.
Radder, A. C.(1979). “On the parabolic equation method for water wave propagation.”J. Fluid Mech., Cambridge, U.K., 95(1), 159–176.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123 • Issue 4 • July 1997
Pages: 192 - 199
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jul 1, 1997
Published in print: Jul 1997
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.