확장형 Boussinesq 방정식에서 비선형파의 내부 조파: 선 조파기법과 원천함수기법

Internal Generation of Nonlinear Waves for Extended Boussinesq Equations: Line Source Method and Source Function Method

  • 김건우 (서울대학교 지구환경시스템공학부) ;
  • 이창훈 (세종대학교 토목환경공학과) ;
  • 서경덕 (서울대학교 지구환경시스템공학부)
  • Kim Gunwoo (School of Civil, Urban and Geosystem Engineering, Seoul National University) ;
  • Lee Changhoon (Department of Civil and Environmental Engineering, Sejong University) ;
  • Suh Kyung-Duck (School of Civil, Urban and Geosystem Engineering, Seoul National University)
  • 발행 : 2005.03.01

초록

본 연구에서 Nwogu(1993)의 확장형 Boussinesq 방정식에 대하여 한 격자의 조파 띠에 균일하게 분포하는 원천함수를 유도하였다. 원천함수를 포함하는 확장형 Boussinesq 방정식에 부분단계분리법을 적용하여, 에너지 전송속도를 사용하는 선 조파기법의 타당성을 해석적으로 증명하였다. 수평공간 1차원의 경우 선형파 뿐만 아니라 비선형파를 조파하여 원천함수기법에 의한 내부조파기법의 정확성을 검증하였다. 또한 원천함수기법에 의한 수치 결과가 선 내부조파기법에 의한 수치 결과와 동일함을 확인하였다.

In this study, derivation is made of a one-grid source function for the extended Boussinesq equations of Nwogu (1993) in order to generate nonlinear waves internally. The energy velocity approach used in the line source method is verified analytically by the fractional step splitting method. The source function method is verified by generating accurately nonlinear waves as well as linear waves for horizontally one-dimensional cases. It is found that numerical solutions by the source function method are the same as those by the line source method.

키워드

참고문헌

  1. 김건우, 이창훈, 서경덕 (2004), 시간의존 파랑변형식에서의 내부조파: 선 조파기법과 원천함수기법. 대한토목학회논문집, 24(6B), 585-594
  2. 이종인, 윤성범, 이정규 (1999), 다성분 파동방정식의 내부조파와 유속성분의 특성. 대한토목학회논문집, 19(2-5), 635-644
  3. Kim, G, Lee, C. and Suh, K.-D. (2004). Generation of incident random waves in numerical mild-slope equation models using a source function method. Proc. of 2nd lnt. Conf. on Asian and Pacific Coasts, Makuhari
  4. Larsen, J. and Dancy, H. (1983). Open boundaries in short wave simulations a new approach. Coastal Engineering, 7, 285-297 https://doi.org/10.1016/0378-3839(83)90022-4
  5. Lee, C, Cho, Y.-S. and Yum, K (2001). Internal generation of waves for extended Boussinesq equations. Coastal Engineering,42,155-162 https://doi.org/10.1016/S0378-3839(00)00056-9
  6. Lee, C, Kim, G and Suh, K-D. (2003). Extended mild-slope equation for random waves. Coastal Engineering, 48, 277-287 https://doi.org/10.1016/S0378-3839(03)00033-4
  7. Lee, C., Park,WS., Cho, Y.-S. and Suh, K.D. (1998). Hyperbolic mild-slope equations extended to account for rapidly varying topography. Coastal Engineering, 34, 243-257 https://doi.org/10.1016/S0378-3839(98)00028-3
  8. Lee, C. and Suh, K.D. (1998). Internal generation of waves for time-dependent mild-slope equations. Coastal Engineering, 34, 35-57 https://doi.org/10.1016/S0378-3839(98)00012-X
  9. Madsen, P.A. and Larsen, J. (1987). An efficient finite-difference approach to the mild-slope equation. Coastal Engineering, 11, 329-351 https://doi.org/10.1016/0378-3839(87)90032-9
  10. Madsen, P.A. and Schaffer, H.A. (1998). Higher order Boussinesq-type equations for surface gravity waves derivation and analysis. Phil. Trans. R. Soc. Lond. A, 356, 3123-3184 https://doi.org/10.1098/rsta.1998.0309
  11. Madsen, P.A. and Sorensen, O.R. (1992). A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly varying bathymetry. Coastal Engineering, 18, 183-204 https://doi.org/10.1016/0378-3839(92)90019-Q
  12. Nadaoka, K Beji, S., and Nakagawa, Y. (1994). A fully-dispersive nonlinear wave model and its numerical solutions. Proc. of 24th Int. Conf. Coastal Eng., 427-442
  13. Nwogu, O. (1993). Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal Ocean Engineering, ASCE, 119, 618-638 https://doi.org/10.1061/(ASCE)0733-950X(1993)119:6(618)
  14. Peregrine, D.H. (1967). Long waves on a beach. J. Fluid Mech., 27, 815-827 https://doi.org/10.1017/S0022112067002605
  15. Radder, A.C. and Dingemans, M.W. (1985). Canonical equations for almost periodic, weakly nonlinear gravity waves. Wave Motion, 7, 473-485 https://doi.org/10.1016/0165-2125(85)90021-6
  16. Suh, KD., Lee, C. and Park, WS. (1997). Time-dependent equations for wave propagation on rapidly varying topography. Coastal Engineering, 32, 91-117 https://doi.org/10.1016/S0378-3839(97)81745-0
  17. Wei, G and Kirby, J.T. (1995). Time-dependent numerical code for extended Boussinesq equations. J. Waterway, Port, Coastal Ocean Engineering, 121(5),251-261 https://doi.org/10.1061/(ASCE)0733-950X(1995)121:5(251)
  18. Wei, G, Kirby, J.T., Grilli, S.T. and Subramanya, R. (1995). A fully nonlinear Boussinesq model for surface waves. Part I. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71-92 https://doi.org/10.1017/S0022112095002813
  19. Wei, G, Kirby, J.T. and Sinha, A. (1999). Generation of waves in Boussinesq models using a source function method. Coastal Engineering, 36, 271-299 https://doi.org/10.1016/S0378-3839(99)00009-5
  20. Woo, S.-B. and Liu, P. L.-F. (2004). Finite-element model for modified Boussinesq equations. II: applications to nonlinear harbor oscillations. J. Waterway, Port, Coastal Ocean Engineering, 130(1), 17-28 https://doi.org/10.1061/(ASCE)0733-950X(2004)130:1(17)