Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

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

Computation of Wave Propagation by Scatter Method Associated with Variational Approximation

변분근사식과 연계된 산란체법에 의한 파랑변형 계산

  • Seo, Seung-Nam (Coastal Engineering & Ocean Energy Research Department, KORDI)
  • 서승남 (한국해양연구원 연안개발.에너지연구부)
  • Published : 2008.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

If an arbitrary topography is approximated to a number of vertical steps, both variational approximation and eigenfunction expansion method can be used to compute linear wave transformation over the bottom. In this study a scatterer method associated with variational approximation is proposed to calculate reflection and transmission coefficients. Present method may be shown to be more simple and direct than the successive-application-matrix method by O'Hare and Davies. And Several numerical examples are given which are in good agreement with existing results.

만일 임의의 지형을 다수의 계단으로 근사하면 이 지형 위를 지나는 선형 파랑의 변형을 계산하기 위해 변분근사법과 고유함수 전개법을 사용할 수 있다. 본 논문에서는 반사율과 투과율을 계산하기 위해 변분근사식과 연계된 산란체법을 제시하였다. 본 기법은 O'Hare and Davies의 변환행렬 축차법보다 간단하고 직접적인 방법임을 보였다. 또한 수 개의 수치실험을 실시하여 기존 결과와 거의 같은 결과를 얻었다.

Keywords

References

  1. 서승남 (2008a). 산란체법에 의한 다중 계단지형에서의 파랑변형 계산. 한국해안해양공학회논문집, 20(5), 439-451
  2. 서승남 (2008b). 단일계단 지형에서 변분근사법과 고유함수 전개법에 의한 파랑변형 해의 비교. 한국해안해양공학회 논문집, 심의중
  3. 조용식, 이창훈 (1998). 수심이 변하는 지형을 통과하는 파랑의 반사율과 통과율 산정. 대한토목학회논문집, 18(II-4), 351-358
  4. Bender, C.J. and Dean, R.G. (2003). Wave transformation by two-dimensional bathymetric anomalies with sloped transitions. Coastal Eng., 50, 61-84 https://doi.org/10.1016/j.coastaleng.2003.08.002
  5. 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
  6. Chamberlain, P.G. and Porter, D. (1995). The modified mildslope equation. J.Fluid Mech., 291, 393-407 https://doi.org/10.1017/S0022112095002758
  7. Davies, A.G. and Heathershaw, A.D. (1984). Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech., 144, 419-443 https://doi.org/10.1017/S0022112084001671
  8. Devillard, P., Dunlop, F. and Souillard B. (1988). Localization of gravity waves on a channel with a random bottom. J. Fluid Mech., 186, 521-538 https://doi.org/10.1017/S0022112088000254
  9. Guazzelli, E., Rey, V. and Belzons, M. (1992). Higher-order Bragg reflection of gravity surface waves by periodic beds. J. Fluid Mech., 245, 301-317 https://doi.org/10.1017/S0022112092000478
  10. Kirby, J.T. and Dalrymple, R.A. (1983). Propagation of obliquely incident water waves over a trench. J. Fluid Mech.,133, 47-63 https://doi.org/10.1017/S0022112083001780
  11. Kirby, J.T. (1986). A general wave equation for waves over rippled beds. J. Fluid Mech., 162, 171-186 https://doi.org/10.1017/S0022112086001994
  12. 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
  13. Miles, J.W. (1967). Surface-wave scattering matrix for a shelf. J. Fluid Mech., 28, 755-767 https://doi.org/10.1017/S0022112067002423
  14. O'Hare, T.J. and Davies, A.G (1992). A new model for surface-wave propagation over undulating topography. Coastal Eng., 18, 251-266 https://doi.org/10.1016/0378-3839(92)90022-M
  15. O'Hare, T.J. and Davies, A.G (1993). A comparison of two models for surface-wave propagation over rapidly varying topography. Applied Ocean Res., 15, 1-11 https://doi.org/10.1016/0141-1187(93)90028-V
  16. Porter, D. and Staziker, D.J. (1985). Extension of the mildslope equation. J. Fluid Mech., 300, 367-382
  17. Porter, D. (2003). The mild-slope equations. J. Fluid Mech.,494, 51-63 https://doi.org/10.1017/S0022112003005846
  18. 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
  19. Takano, K. (1960). Effets d'un obstacle paralllpipdique sur la propagation de la houle. La Houille Blanche, 15, 247-267