Comparison between Variational Approximation and Eigenfunction Expansion Method for Wave Transformation over a Step Bottom

단일계단 지형에서 변분근사법과 고유함수 전개법에 의한 파랑변형 비교

  • Seo, Seung-Nam (Coastal Engineering & Ocean Energy Research Department, KORDI)
  • 서승남 (한국해양연구원 연안개발.에너지연구부)
  • Published : 2009.04.30

Abstract

In order to compute linear wave transformation over a single step bottom, both variational approximation and eigenfunction expansion method are used. Both numerical results are in good agreement for reflection and transmission coefficients, surface displacement respectively. However x velocity profiles at the boundary of step are seen to be different to each other even though x velocity matching condition is used.

단일 계단지형 위를 지나는 선형 파랑의 변형을 계산하기 위해 변분근사법과 고유함수 전개법을 사용하였다. 이들 수치해를 비교에서 반사율과 투과율 그리고 해면변위는 거의 일치한다. 그러나 계단 경계에서 유속 정합조건이 부여되었음에도 불구하고 계산된 x방향 유속의 수직구조는 차이를 보인다.

Keywords

References

  1. 서승남, 김상익 (1991). 혼합경계적분 요소법을 사용한 직교입사파랑의 반사율계산 모델. 한국해안해양공학회지, 3(3), 170-175
  2. 서승남, 전기천 (1992). 해저단애 지형 및 흐름에 의한 억류파랑. 한국해안해양공학회지, 4(1), 1-9
  3. 서승남 (2008). 산란체법에 의한 다중 계단지형에서의 파랑변형 계산. 한국해안해양공학회논문집, 20(5), 439-451
  4. 조용식, 이창훈 (1998). 수심이 변하는 지형을 통과하는 파랑의 반사율과 통과율 산정. 대한토목학회논문집, 18(11-4), 351-358
  5. Arfken, G. (1970). Mathematical Methods for Physicists. 2nd ed., Academic, New York
  6. Athanassoulis G.A. and Belibassakis K.A. (1999). A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions. J. Fluid Mech., 389, 275-301 https://doi.org/10.1017/S0022112099004978
  7. 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
  8. Greenberg, M.D. (1978). Foundations of Applied Mathematics, Prentice-Hall, Englewood Cliffs, New Jersey
  9. 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
  10. Kirby, J.T., Dalrymple, R.A. and Seo, S.N. (1987). Propagation of obliquely incident water waves over a trench. Part 2. Currents flowing along the trench. J. Fluid Mech., 176, 95-116 https://doi.org/10.1017/S0022112087000582
  11. Lamb, H. (1932). Hydrodynamics. Dover, New York
  12. Mei, C.C. (1989). The Applied Dynamics of Ocean Surface Waves. World Scientific, Singapore
  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. Miles, J.W. (1982). On surface-wave diffraction by a trench. J. Fluid Mech., 115, 315-325 https://doi.org/10.1017/S0022112082000779
  15. O'Hare, T.J. and Davies, A.G (1992). A new model for surfacewave propagation over undulating topography. Coastal Eng., 18, 251-266 https://doi.org/10.1016/0378-3839(92)90022-M
  16. Takano, K. (1960). Effets d'un obstacle paralllpipdique sur la propagation de la houle. La Houille Blanche, 15, 247-267