Journal of Korean Society of Coastal and Ocean Engineers (한국해안해양공학회지)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
권호 표지

A Parabolic Model to the Modified Mild Slope Equation

수정 완경사 파랑식에 대한 포물형 근사식 모형

  • 서승남 (한국해양연구원 연안개발연구본부) ;
  • 이종찬 (한국해양연구원 연안개발연구본부)
  • Published : 2006.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In order to calculate waves propagating into the shallow water region, a generalized parabolic approximate model is presented. The model is derived from the modified mild slope equation and includes all the existing parabolic models presented in the paper. Numerical results are presented in comparison to laboratory data of Berkhoff et al.(1982). The existing parabolic model shows almost same accuracy against the modified parabolic model and both results of models stand in closer agreement to the laboratory data. Therefore the existing parabolic model based on mild slope equation is a useful tool to compute shallow water waves which turns out to be more fast and stable in computational aspect.

천해역의 파랑을 추산하기 위한 포물형 근사식에 대해 기존 모형을 도출할 수 있는 일반화된 모형을 제시하고 이를 수정 완경사 파랑식에 대한 포물형 근사식으로 확장하였다. 제시한 수치모형을 Berkhoff et al.(1982)의 수리모형 실험과 비교하였으며 이 경우에는 기존 포물형 근사모형과 수정 포물형 근사모형의 결과가 거의 같으며 수리실험 결과와 아주 잘 일치하는 것으로 나타났다. 따라서 계산이 빠르고 안정성이 높은 기존 포물형 근사식은 천해역의 파랑 추산에 유용한 도구라 판단된다.

Keywords

References

  1. 서승남 (1990). 포물형 근사식에 의한 천해파 산정모델, 한국 해안.해양공학회지, 2(3), 134-142
  2. 해양수산부 (2005). 항만 및 어항 설계기준
  3. Berkhoff, J.C.W. (1972). Computation of combined refractiondiffraction. Proc. 13th Coastal Eng. Conf., 1, 471-490
  4. Berkhoff, J.C.W., Booij, N. and Radder, A.C. (1982). Verification of numerical wave propagation models for simple harmonic linear waves, Coastal Eng. 6, 255-279 https://doi.org/10.1016/0378-3839(82)90022-9
  5. Booij, N. (1981). Gravity waves on water with non-uniform depth and current. Rept. 81-1, Dept. of Civil Eng., Delft Univ. Technology
  6. Booij, N. (1983). A note on the accuracy of the mild-slope equation, Coastal Eng. 7, 191-203 https://doi.org/10.1016/0378-3839(83)90017-0
  7. Chamberlain, P.G. and Porter, D. (1995). 'The modified mildslope equation', J. Fluid Mech., 291, 393-407 https://doi.org/10.1017/S0022112095002758
  8. Dean, R.G. and Dalrymple, R.A. (1984). Water wave mechanics for engineers and scientists, Prentice-Hall, Englewood Cliffs, New Jersey
  9. Finlayson, B.A. (1972). Method of Weighted Residuals and Variational Principles, Academic Press, New York
  10. Goda, Y. (2000). Random seas and design of maritime structures, 2nd ed., World Scientific Pub., Singapore
  11. Hildebrant, F.B. (1965). Methods of Applied Mathematics, 2nd ed., Prentice-Hall, Englewood Cliffs, New Jersey
  12. Kirby, J.T. (1984). A note on linear surface wave-current interaction over slowly varying topography, J. Geophys. Res., 89(C1), 745-747 https://doi.org/10.1029/JC089iC01p00745
  13. Kirby, J.T. (1986a). Higher order approximations in the parabolic equation method for water waves, J. Geophys. Res., 91, 933-952 https://doi.org/10.1029/JC091iC01p00933
  14. Kirby, J.T. (1986b). Rational approximations in the parabolic equation method for water waves, Coastal Eng., 10, 355-378 https://doi.org/10.1016/0378-3839(86)90021-9
  15. Kirby, J.T. (1997). Nonlinear, dispersive long waves in water of variable depth, In Hunt, J. N.(Editor), Gravity waves in water of finite depth, Advances in fluid mechanics, Vol. 10, 55-125, Computational Mechanics Publications
  16. Kirby, J.T. and Dalrymple, R. A. (1984). Verification of a parabolic equation for propagation of weakly-nonlinear waves, Coastal Eng. 8, 212-232
  17. Kirby, J.T. and Dalrymple, R.A. (1986). Approximate model for nonlinear dispersion in monochromatic wave propagation, Coastal Eng., 9, 545-561 https://doi.org/10.1016/0378-3839(86)90003-7
  18. Luke, J.C. (1967). 'A variational principle for a fluid with a free surface', J. Fluid Mech., 27, 395-397 https://doi.org/10.1017/S0022112067000412
  19. Liu, P.L.-F. (1990). Wave transformation, In: B. LeMehaute, and D.M. Hanes(Editors), The Sea, Ocean Engineering Science Vol. 9, 27-63, Wiley, New York
  20. Liu, P.L.-F. (1994). Model equations for wave propagations from deep to shallow water, In: Liu, P.L.-F. (Editor), Advances in Coastal and Ocean Engineering, Vol. 1, 125-157, World Scientific Pub., Singapore
  21. Lozano, C.J. and P.L.-F. Liu, (1980). Refraction-diffraction model for linear surface water waves, J. Fluid Mech., 101, 705-720 https://doi.org/10.1017/S0022112080001887
  22. Massel, S.R. (1993). Extended refraction-diffraction equation for surface waves. Coastal Eng. 19, 97-126 https://doi.org/10.1016/0378-3839(93)90020-9
  23. Mei, C.C. (1989). The Applied Dynamics of Ocean Surface Waves. World Scientific, Singapore
  24. Mikhlin, S.G. (1964). Variational Methods in Mathematical Physics, Macmillan, New York
  25. Miles, J.W. (1977). On Hamilton's principle for surface waves, J. Fluid Mech., 83, 153-158 https://doi.org/10.1017/S0022112077001104
  26. Miles, J.W. and Chamberlain, P.G. (1998). 'Topographical scattering of gravity waves', J. Fluid Mech., 361, 175-188 https://doi.org/10.1017/S002211209800857X
  27. Radder, A.C. (1979). On the parabolic equation method for waterwave propagation, J. Fluid Mech., 95, 159-176 https://doi.org/10.1017/S0022112079001397
  28. Smith, R. and Sprinks, T. (1975). 'Scattering of surface waves by a conical island', J. Fluid Mech., 72, 373-384 https://doi.org/10.1017/S0022112075003424
  29. Suh, K.D., Lee, C. and Park, W.S. (1997). Time-dependent equations for wave propagation on rapidly varying topography, Coastal Eng. 32, 91-117 https://doi.org/10.1016/S0378-3839(97)81745-0