Oblique wave incidence on a plane beach: The classical problem revisited

Journal of Fluid Mechanics

Volumn 368, Issue , 1998, Pages 291-319

  Ehrenmark, Ulf Torsten ^a  

^a LONDON METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BEACHES; COMPUTATIONAL FLUID DYNAMICS; FLOW OF WATER; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; SPECTRUM ANALYSIS; WAVEFRONTS;

INVERSE KONTOROVICH-LEBEDEV INTEGRAL TRANSFORM; INVERSE MELLIN TRANSFORM; THREE-DIMENSIONAL WAVE INCIDENCE;

WATER WAVES;

EID: 0032137874     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098001888     Document Type: Article

References (38)

1. BLONDEAUX, P. & VITTORI, G. 1995 The nonlinear excitation of synchronous edge waves by a monochromatic wave normally approaching a plane beach. J. Fluid Mech. 301, 251-268.
2. BRUCE, J. 1998 PhD Dissertation, London Guildhall University (in preparation).
3. BOOIJ, N. 1983 A note on the accuracy of the mild-slope approximation. Coastal Engng 7, 191-203.
4. EHRENMARK, U. T. 1989 Overconvergence of the near-field expansion for linearised waves normally incident on a sloping beach. SIAM J. Appl. Maths 49, 799-815.
5. EHRENMARK, U. T. 1991 On viscous wave motion over a plane beach. SIAM J. Appl. Maths 51, 1-19.
6. EHRENMARK, U. T. 1994 Set-down computations over an arbitrarily inclined plane bed. J. Mar. Res. 52, 983-998.
7. EHRENMARK, U. T. 1995 The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature. J. Comput. Appl. Maths 61, (1995), 43-72.
8. EHRENMARK, U. T. 1996 Eulerian mean current and Stokes drift under non-breaking waves on a perfect fluid over a plane beach. Fluid Dyn. Res. 18, 117-150.
9. EHRENMARK, U. & WILLIAMS, P. 1996 Using the mild-slope equation on steep shoals. Proc. 2nd Intl Conf. Hydrodynamics, Hong-Kong (ed. Chwang, Lee & Leung), pp. 489-494. Balkema.
10. EVANS, D. V. 1988 Mechanisms for the generation of edge waves over a sloping beach. J. Fluid Mech. 186, 379-391.
11. EVANS, D. V. 1988 Edge waves over a sloping beach. Q. J. Mech. Appl. Maths 42, 131-142.
12. EVANS, D. V. & KUZNETSOV, N. 1997 Trapped modes. In Gravity Waves in Water of Finite Depth, (ed. J. N. Hunt) pp. 127-168. Computational Mechanics Publications, Southampton UK.
13. FRIEDRICHS, K. O. 1948 Water waves on a shallow sloping beach. Commun. Pure Appl. Maths 1, 109-134.
14. HANSON, E. T. 1926 The theory of ship waves. Proc. R. Soc. Lond. A 111, 491-529.
15. ISAACSSON, E. 1950 Water waves over a sloping bottom. Commun. Pure Appl. Maths 3, 11-31.
16. KELLER, J. 1961 Tsunamis - Water waves produced by earthquakes. Tsunami Hydrodynamics Conference, Honolulu, pp. 154-166.
17. KRAUSS, W. 1973 Methods and Results of Theoretical Oceanography, Vol. I. Gebrüder Borntraeger.
18. KUZNETSOV, N., PORTER, R., EVANS, D. V. & SIMON, M. J. 1998 Uniqueness and trapped modes for surface-piercing cylinders in oblique waves J. Fluid Mech. 365, 351-368.
19. LAUWERIER, H. A. 1959 A note on the problem of the sloping beach. Indag. Math. 21, 229-240.
20. LONGUET-HIGGINS, M. S. & STEWART, R. W. 1963 A note on wave set-up. J. Mar. Res. 21, 4-10.
21. MAGNUS, W., OBERHETTINGER, F. & SONI R. P. 1966 Special Functions of Mathematical Physics. Springer.
22. MILES, J. W. 1990a Parametrically excited standing edge waves. J. Fluid Mech. 214, 43-57.
23. MILES, J. W. 1990b Wave reflection from a gently sloping beach. J. Fluid Mech. 214, 59-66.
24. MINZONI, A. & WHITHAM, G. 1977 On the excitation of edge waves on beaches. J. Fluid Mech. 79 273-287.
25. OBERHETTINGER, F. 1972 Tables of Bessel Transforms. Springer.
26. PEREGRINE, D. H. 1983 Wave jumps and caustics in the propagation of finite-amplitude water waves. J. Fluid Mech. 136 435-452.
27. PEREGRINE, D. H. & RYRIE, S. C. 1983 Anomalous refraction and conjugate solutions of finite-amplitude water waves. J. Fluid Mech. 134, 91-101.
28. 2φ = 0 in a sector. Commun. Pure Appl. Math. 5, 87-108.
29. ROSEAU, M. 1951 Sur les mouvements ondulatoires de la mer sur une plage. C. R. Acad. Sci. Paris 232, 479-481.
30. ROSEAU, M. 1952 Contribution à la théorie des ondes liguides de gravité en profondeur variable. Publications Scientifiques et Techniques du Ministère de l'Air 275. Paris.
31. ROSEAU, M. 1958 Short waves parallel to the shore over a sloping beach. Commun. Pure Appl. Maths 9, 443-493,
32. RYRIE, S. & PEREGRINE, D. H. 1982 Refraction of finite-amplitude water waves obliquely incident on a uniform beach. J. Fluid Mech. 115, 91-104.
33. STOKER, J. J. 1947 Surface waves in water of variable depth. Q. Appl. Math 5, 1-54.
34. STOKER, J. J. 1958 Water Waves. J. Wiley.
35. URSELL, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 79-97.
36. WATSON, G. N. 1944 A Treatise on the theory of Bessel functions. Cambridge University Press.
37. WEINSTEIN, A. 1949 On surface waves. Can. J. Maths 1, 271-278.
38. WHITHAM G. B. 1979 Lectures on Wave Propagation. Tata Institute of Fundamental Research. Springer.