Solution Comparisons of Modified Mild Slope Equation and EFEM Plane-wave Approximation

수정 완경사파랑식과 EFEM 평면파 근사식의 해 비교

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

Abstract

In order to test the accuracy between the modified mild slope equation (MMSE) without evanescent modes and the plane-wave approximation (PA) of eigenfunction expansion method, various numerical results from both models are presented. In this study, analytical solutions of two models are employed, one based on the MMSE derived by Porter (2003) and the other on the scatterer method of PA by Seo (2008a). Judging from direct comparisons against existing results of rapidly varying topography, the PA model gives better predictions of the wave propagation than the MMSE model.

억류파를 제외한 수정 완경사파랑식과 고유함수 전개법의 평면파 근사식에 대한 정밀도를 검토하기 위해 다수의 수치실험 결과를 제시하였다. 본 연구에서 두 해석해가 사용되었으며 하나는 수정 완경사파랑식에 대한 Porter(2003)의 해이고 다른 하나는 평면파 근사식에 산란체법을 적용한 서(2008a)의 해이다. 급변 지형에서의 파랑변형에 대한 기존 결과와의 직접 비교를 통해 평면파 근사식 모형이 수정 완경사파랑식 보다 잘 기술하는 것으로 나타났다.

Keywords

References

  1. 서승남 (2008a). 산란체법에 의한 다중 계단지형에서의 파랑변형 계산. 한국해안해양공학회논문집, 20(5), 439-451
  2. 서승남 (2008b). 변분근사식과 연계된 산란체법에 의한 파랑변형 계산. 한국해안해양공학회논문집, 20(6), 553-563
  3. 조용식, 이창훈 (1998). 수심이 변하는 지형을 통과하는 파랑의 반사율과 통과율 산정. 대한토목학회논문집, 18(11-4), 351-358
  4. Athanassoulis, G.A. and Belibassakis, K.A. (1999). A consistent coupled-mode theory for the propagation of smallamplitude water waves over variable bathymetry regions. J. Fluid Mech., 389, 275-301 https://doi.org/10.1017/S0022112099004978
  5. Berkhoff, J.C.W. (1972). Computation of combined refractiondiffraction. Proc. 13th Coastal Eng. Conf., 1, 471-490
  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 mild-slope equation. J. Fluid Mech., 291, 393-407 https://doi.org/10.1017/S0022112095002758
  8. 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
  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. Kim, J.W and Bai, K.J. (2004). A new complementary mildslope equation. J. Fluid Mech., 5111, 24-40
  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. 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
  13. 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
  14. 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
  15. Porter, D. (2003). The mild-slope equations. J. Fluid Mech., 494, 51-63 https://doi.org/10.1017/S0022112003005846
  16. Porter, D. and Staziker, D.J. (1985). Extension of the mildslope equation. J. Fluid Mech., 300, 367-382
  17. 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
  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