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

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

Transformation of Long Waves Propagating over Trench

트렌치 위를 통과하는 장파의 변형

  • Jung, Tae-Hwa (Department of Civil Engineering, Hanyang University) ;
  • Suh, Kyung-Duck (Department of Civil and Environmental Engineering & Engineering Research Institute, Seoul National University) ;
  • Cho, Yong-Sik (Department of Civil Engineering, Hanyang University) ;
  • Park, Sung-Hyun (Department of Civil Engineering, Hanyang University)
  • 정태화 (한양대학교 토목공학과) ;
  • 서경덕 (서울대학교 건설환경공학부 및 공학연구소) ;
  • 조용식 (한양대학교 토목공학과) ;
  • 박승현 (한양대학교 토목공학과)
  • Published : 2007.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

An analytical solution for long waves propagating over an asymmetric trench is derived. The water depth inside the trench varies in proportion to a power of distance from the center of the trench. The mild-slope equation, governing equation, is transformed into second order ordinary differential equation with variable coefficients by using the long wave assumption and then the analytical solution is obtained by using the power series technique. The analytical solution is confirmed by comparison with the numerical solution. After calculating the analytical solution under various conditions, the results are analyzed.

비대칭 트렌치 지형 위를 통과하는 장파의 해석 해를 유도하였다. 트렌치 내부의 수심은 트렌치 중심으로부터 거리의 멱에 비례하여 감소한다. 장파의 가정을 사용하여 지배 방정식인 완경사 방정식을 변수 계수를 갖는 이차 상미분 방정식으로 변환하였으며 멱급수를 이용하여 해석 해를 구하였다. 수치 모델과의 비교를 통하여 해석 해의 타당성을 확인하였다. 다양한 조건에서 해석 해를 계산하여 그 결과를 분석하였다.

Keywords

References

  1. 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
  2. Booij, N. (1983). A note on the accuracy of the mild-slope equation, Coastal. Eng., 191-203
  3. Chang, H.-K. and Liou, J.-C. (2007). Long wave reflection from submerged trapezoidal breakwaters. Ocean Eng., 34, 185-191 https://doi.org/10.1016/j.oceaneng.2005.11.017
  4. Cho, Y.-S. and Lee, C. (2000). Resonant reflection of waves over sinusoidally varying topographies, J. Coastal Res., 16, 870-879
  5. Dean, R.G. (1964). Long wave modification by linear transitions, Rev. Mat. Hisp.-Am., 90(1), 1-29
  6. Kirby, J. and Dalrymple, R.A. (1983). Propagation on oblique incident water waves over a trench, J. Fluid Mech., 133, 47-63 https://doi.org/10.1017/S0022112083001780
  7. Lamb, H. (1932). Hydrodynamics, 6th Ed., Dover, New York
  8. Lassiter, J.B. (1972). The propagation of water waves over sediment pockets, Ph. D. Thesis, Massachusetts Institute of Technology
  9. Lee, J.J. and Ayer, R.M. (1981). Wave propagation over a rectangular trench, J. Fluid Mech., 110, 335-347 https://doi.org/10.1017/S0022112081000773
  10. Lin, P. Liu, H.-W. (2005). Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape, J. of Eng. Mech., 131, 822-830 https://doi.org/10.1061/(ASCE)0733-9399(2005)131:8(822)
  11. Liu, P.L.-F. Cho, Y.-S. Kostense, J.K. and Dingemans, M.W. (1992). Propagation and trapping of obliquely incident wave groups over a trench with currents, Appl. Ocean. Res., 14, 201-212 https://doi.org/10.1016/0141-1187(92)90015-C
  12. Miles, J. (1981). Oblique surface-wave scattering matrix for a shelf, Dynamics of Atmosphere and Oceans, 6, 12-123
  13. Miles, J.W. (1982). On surface-wave diffraction by a trench, J. Fluid Mech., 115, 315-325 https://doi.org/10.1017/S0022112082000779
  14. Takano, K. (1960). Effects d'un obstacle parallelepipedique sur la propagation de la houle, Houille Blanche, 15, 247
  15. Zhang, Y. and Zhu, S. (1994). New solutions for the propagation of long water waves over variable depth, J. Fluid Mech., 278, 391-406 https://doi.org/10.1017/S0022112094003769