Time-dependent equations for wave propagation on rapidly varying topography

Coastal Engineering

Volumn 32, Issue 2-3, 1997, Pages 91-117

  Suh, Kyung Doug ^a   Lee, Changhoon ^b   Park, Woo Sun ^b  

^a Seoul National University   (South Korea)

^b Korea Research Institute of Ships and Ocean Engineering   (South Korea)

Author keywords

Numerical model; Surface waves; Wave equation; Wave scattering

Indexed keywords

MATHEMATICAL MODELS; SCATTERING; SURFACE WAVES; WAVE PROPAGATION;

RANDOM WAVES; TIME DEPENDENT EQUATIONS; TOPOGRAPHY;

WAVEFORM ANALYSIS;

EQUATION; MATHEMATICAL MODELING; TOPOGRAPHY; WAVE PROPAGATION;

RAPIDLY VARYING; TOPOGRAPHY; WAVE MODELLING; WAVE PROPAGATION;

EID: 0031279878     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3839(97)81745-0     Document Type: Article

References (35)

1. Benjamin, T.B., Boczar-Karakiewicz, B., Pritchard, W.G., 1987. Reflection of water waves in a channel with corrugated bed. J. Fluid Mech. 185, 249-274.
2. Berkhoff, J.C.W., 1972. Computation of combined refraction-diffraction. In: Proc. 13th Coastal Eng. Conf., Vancouver, Vol. 1, pp. 471-490.
3. Booij, N., 1983. A note on the accuracy of the mild-slope equation. Coastal Eng. 7, 191-203.
4. Bouws, E., Günther, H., Rosenthal, W., Vincent, C.L., 1985. Similarity of the wind wave spectrum in finite depth water 1. Spectral form. J. Geophys. Res. 90 (C1), 975-986.
5. Chamberlain, P.G., Porter, D., 1995. The modified mild-slope equation. J. Fluid Mech. 291, 393-407.
6. Copeland, G.J.M., 1985. A practical alternative to the mild-slope wave equation. Coastal Eng. 9, 125-149.
7. Dalrymple, R.A., Kirby, J.T., 1986. Water waves over ripples. J. Waterw. Port Coastal Ocean Eng. 112, 309-319.
8. Davies, A.G., Heathershaw, A.D., 1984. Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419-443.
9. Guazzelli, E., Rey, V., Belzons, M., 1992. Higher-order Bragg reflection of gravity surface waves by periodic beds. J. Fluid Mech. 245, 301-317.
10. Hara, T., Mei, C.C., 1987. Bragg scattering of surface waves by periodic bars: theory and experiment. J. Fluid Mech. 178, 221-241.
11. Kirby, J.T., 1984. A note on linear surface wave-current interaction over slowly varying topography. J. Geophys. Res. 89 (C1), 745-747.
12. Kirby, J.T., 1986. A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171-186.
13. Kirby, J.T., Anton, J.P., 1990. Bragg reflection of waves by artificial bars. In: Proc. 22nd Coastal Eng. Conf., New York, Vol. 1, pp. 757-768.
14. Kirby, J.T., Lee, C., Rasmussen, C., 1992. Time-dependent solutions of the mild-slope wave equation. In: Proc. 23rd Coastal Eng. Conf., Venice, Vol. 1. pp. 391-404.
15. Kubo, Y., Kotake, Y., Isobe, M., Watanabe, A., 1992. Time-dependent mild slope equation for random waves. In: Proc. 23rd Coastal Eng. Conf., Venice, Vol. 1, pp. 419-431.
16. Larsen, J., Dancy, H., 1983. Open boundaries in short wave simulations: A new approach. Coastal Eng. 7, 285-297.
17. Lee, C., Suh, K.D. 1997. Internal generation of waves for time-dependent mild-slope equations. Coastal Eng. (submitted).
18. Luke, J.C., 1967. A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395-397.
19. Madsen, P.A., Larsen, J., 1987. An efficient finite-difference approach to the mild-slope equation. Coastal Eng. 11, 329-351.
20. Mansard, E.P.D., Funke, E.R., 1980. The measurement of incident and reflected spectra using a least squares method. In: Proc. 17th Coastal Eng. Conf., Sydney, Vol. 1, pp. 154-172.
21. Massel, S.R., 1993. Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126.
22. Massel, S.R., 1994. Measurement and modelling of waves incident on steep islands and shoals. In: Proc. Int. Symp. Waves, Physical and Numerical Modelling, Vancouver, Vol. 2, pp. 982-991.
23. Mei, C.C., 1985. Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech. 152, 315-335.
24. Miles, J.W., 1981. Oblique surface-wave diffraction by a cylindrical obstacle. Dyn. Atmos. Oceans 6, 121-123.
25. Nadaoka, K., Beji, S., Nakagawa, Y., 1994. A fully-dispersive nonlinear wave model and its numerical solutions. In: Proc. 24th Coastal Eng. Conf., Kobe, Vol. 1, pp. 427-441.
26. O'Hare, T.J., Davies, A.G., 1992. A new model for surface-wave propagation over undulating topography. Coastal Eng. 18, 251-266.
27. O'Hare, T.J., Davies, A.G., 1993. A comparison of two models for surface-wave propagation over rapidly varying topography. Appl. Ocean Res. 15, 1-11.
28. Otnes, R.K., Enochson, L., 1978. Applied Time Series Analysis, Vol. 1, Basic Techniques. John Wiley & Sons, New York.
29. Park, W.S., Lee, D.S., Oh, Y.M., Jeong, W.M., 1991. Infinite elements for analysis of diffraction and radiation problems in the vertical plane. J. Korean Soc. Coastal Ocean Engrs. 3 (4), 235-243, (in Korean, with English abstract).
30. Porter, D., Staziker, D.J., 1995. Extensions of the mild-slope equation. J. Fluid Mech. 300, 367-382.
31. Radder, A.C., 1979. On the parabolic equation method for water-wave propagation. J. Fluid Mech. 95, 159-176.
32. Radder, A.C., Dingemans, M.W., 1985. Canonical equations for almost periodic, weakly nonlinear gravity waves. Wave Motion 7, 473-485.
33. Smith, R., Sprinks, T., 1975. Scattering of surface waves by a conical island. J. Fluid Mech. 72, 373-384.
34. Suh, K.D., Park, W.S., 1995. Wave reflection from perforated-wall caisson breakwaters. Coastal Eng. 26, 177-193.
35. Takano, K., 1960. Effects d'un obstacle parallélépipédique sur la propagation de la houle. Houille Blanche 15, 247-267.