An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal

Coastal Engineering

Volumn 51, Issue 5-6, 2004, Pages 421-437

  Liu, Huan Wen ^a,b   Lin, Pengzhi ^b   Shankar, N Jothi ^b  

^a GUANGXI UNIVERSITY FOR NATIONALITIES   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Analytical solution; Homma's island; The mild slope equation; Wave diffraction; Wave dispersion; Wave refraction

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFRACTION; FOURIER TRANSFORMS; SURFACE TOPOGRAPHY;

CYLINDRICAL ISLAND; MILD-SLOPE EQUATION; MONOCHROMATIC WAVES; TAYLOR SERIES;

WATER WAVE EFFECTS;

SHALLOW-WATER EQUATION; WAVE BEHAVIOR; WAVE DIFFRACTION; WAVE REFRACTION;

REFRACTION; SHALLOW-WATER EQUATION; WAVE DIFFRACTION; WAVE DISPERSION;

EID: 12144252053     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2004.04.005     Document Type: Article

References (42)

1. Agnon Y. Pelinovsky E. Accurate refraction-diffraction equations for water waves on a variable-depth rough bottom J. Fluid Mech. 449 2001 301-31
2. Berkhoff J.C.W. Computation of combined refraction-diffraction Proc. 13th Int. Conf. Coastal Eng. 1972 471-490 ASCE Vancouver
3. Berkhoff J.C.W. 1976 Mathematical Models for Simple Harmonic Linear Water Waves Wave Diffraction and Refraction. Doctoral Thesis Delft Technical University Netherlands
4. Bettess P. Zienkiewicz O.C. Diffraction and refraction of surface waves using finite and infinite elements Int. J. Numer. Methods Eng. 2 1977 127
5. Chamberlain P.G. Porter D. The modified mild-slope equation J. Fluid Mech. 291 1995 393-407
6. Chamberlain P.G. Porter D. On the solutions of the dispersion relation for water waves Appl. Ocean Res. 21 1999 161-166
7. Chamberlain P.G. Porter D. Scattering and near-trapping of water waves by axisymmetric topography J. Fluid Mech. 388 1999 335-354
8. Chandrasekera C.N. Cheung K.F. Extended linear refraction-diffraction model J. Waterw. Port Coast. Ocean Eng. 123 1997 280-28
9. Chen H.S. Mei C.C. Oscillations and Wave Forces in a Man-Made Harbor in the Open Sea. TR No. 190 1974 Ralph M. Parsons Laboratory Dept. Civil Engrg. MIT Cambridge MA
10. Ehrenmark U.T. Williams P.S. Wave parameter tuning for the application of the mild-slope equation on steep beaches and in shallow water Coast. Eng. 42 2001 17-34
11. Fenton J.D. Mckee W.D. On calculating the lengths of water waves Coast. Eng. 14 1990 499-51
12. Guo J.K. Simple and explicit solutionof wave dispersion equation Coast. Eng. 45 2002 71-7
13. Homma S. On the behaviour of seismic sea waves around circular island Geophys. Mag. 21 1950 199-208
14. Houston J.R. Combined refraction and diffraction of short waves using the finite element method Appl. Ocean Res. 3 1981 163-170
15. Hunt J.N. Direct solution of wave dispersion equation J. Waterw. Port Coast. Ocean Div. Proc. ASCE 105 1979 457-459
16. Jonsson I.G. Skovgaard O. Brink-Kjaer O. Diffraction and refraction calculations for waves incident on an island J. Mar. Res. 34 1976 469-496
17. Kânoǧlu U. Synolakis C.E. Long wave runup on piecewise linear topographies J. Fluid Mech. 374 1998 1-28
18. Lambert J.D. Numerical Methods for Ordinary Differential Systems 1992 Wiley New Yor
19. Li B. A generalized conjugate-gradient model for the mild slope equation Coast. Eng. 23 1994 215-225
20. Li B. An evolution equation for water-waves Coast. Eng. 23 1994 227-242
21. Li B. Fleming C.A. Modified mild-slope equations for wave propagation Proc. Inst. Civ. Eng., Water Marit. Eng. 136 1999 43-60
22. Lin P.Z. A compact numerical algorithm for solving the time-dependent mild slope equation Int. J. Numer. Methods Fluids 45 2004 625-642
23. Liu H.-W. 2001 Numerical Modeling of the Propagation of Ocean Waves Doctoral thesis University of Wollongong Australia
24. Liu P.L.-F. Yoon S.B. Stem waves along a depth discontinuity J. Geophys. Res. 91 1986 3979-3982
25. MacCamy R.C. Fuchs R.A. Wave forces on piles: A diffraction theorys Tech. Mem. vol. 69 1954 US Army Corps of Engineering Beach Erosion Board Washington DC
26. Miles J.W. Chamberlain P.G. Topographical scattering of gravity waves J. Fluid Mech. 361 1998 175-188
27. Nardini D. Brebbia C.A. A new approach to free vibration analysis using boundary elements Appl. Math. Modeling 7 1983 157-162
28. Newman J.N. Numerical solutions of the water-wave dispersion relation Appl. Ocean Res. 12 1990 14-18
29. Nielsen P. Explicit formulae for practical wave calculations Coast. Eng. 6 1982 389-398
30. Porter D. Staziker D.J. Extensions of the mild-slope equation J. Fluid Mech. 300 1995 367-382
31. Spiegel M.R. Applied Differential Equations 1981 Prentice-Hall Englewood Cliffs NJ
32. Suh K.D. Lee C. Park W.S. Time-dependent equations for wave propagation on rapidly varying topography Coast. Eng. 32 1997 91-117
33. Tsay T.-K. Liu P.L.-F. A finite element model for wave refraction and diffraction Appl. Ocean Res. 5 1983 30-37
34. Vastano A.C. Reid R.O. Tsunami response for islands: Verification of a numerical procedure J. Mar. Res. 25 1967 129-139
35. Venezian G. Discussion of "Direct solution of wave dispersion equation", by J.N. Hunt J. Waterw. Port Coast. Ocean Eng. Div. ASCE 106 1980 501-502
36. Xu B. Panchang V. Outgoing boundary conditions for finite-difference elliptic water-wave models Proc. R. Soc. Lond. A 441 1993 575-588
37. You Z.J. Discussion of "Simple and explicit solution to the wave dispersion equation" Coast. Eng. 48 2003 133-135
38. Yu X.P. Zhang B.Y. An extended analytic solution for combined refraction and diffraction of long waves over circular shoals Ocean Eng. 30 2003 1253-1267
39. Zhang Y.L. Zhu S.-P. New solutions for the propagation of long water waves over variable depth J. Fluid Mech. 278 1994 391-406
40. Zhu S.-P. A new DRBEM model for wave refraction and diffraction Eng. Anal. Bound. Elem. 12 1993 261-274
41. Zhu S.-P. Zhang Y.L. Scattering of long waves around a circular island mounted on a conical shoal Wave Motion 23 1996 353-362
42. Zhu S.-P. Liu H.-W. Chen K. A general DRBEM model for wave refraction and diffraction Eng. Anal. Bound. Elem. 24 2000 377-390