DOI QR코드

DOI QR Code

LES와 Dynamic Smagorinsky 난류모형을 이용한 쇄파역에서의 경계층 Streaming 수치해석

Numerical Analysis of the Hydraulic Characteristics of a Boundary Layer Streaming over Surf-Zone Using LES and Dynamic Smagorinsky Turbulence Model

  • 조용준 (서울시립대학교 토목공학과)
  • Cho, Yong Jun (Department of Civil Engineering, University of Seoul)
  • 투고 : 2020.01.07
  • 심사 : 2020.02.25
  • 발행 : 2020.02.28

초록

자연 해빈은 해양환경에 따라 침·퇴적을 반복하며 고 파랑에 의해 해빈이 대규모로 침식되더라도 폭풍이 잦아들고 다시 너울이 우세한 해양환경이 회복되는 경우 점진적으로 복원되며, 이러한 해빈 복원은 경계층 streaming을 통해 이루어진다. 이처럼 경계층 streaming은 그 공학적 가치에도 불구하고 해안에서 가용한 표사의 대부분이 공급되는 쇄파 역에서의 경계층 streaming에 대한 우리의 이해는 아직 상당히 부족하다. 이러한 인식에 기초하여 본 연구에서는 쇄파역 경계층 streaming 수리특성을 살펴보기 위해 단조 해안과 사주를 포함한 해안에서의 천수 과정을 수치모의하였다. 수치 모의는 Spatially filtered Navier-Stokes Eq., LES(Large Eddy Simulation), Dynamic Smagorinsky 난류모형으로 구성된 정교한 수치모형에 기초하여 수행되었으며, 이 과정에서 k-ε 난류모형과 LES Turbulence Closure가 모의결과에 미치는 영향도 함께 살펴보았다. 모의결과 해안공학계에 잘 알려진 k-ε 난류모형의 한계로 인해 wall function에 기반한 k-ε 난류모형의 경우 LES와 비교하면 저면 인근 유속이 다소 과다하게 모의 되었다. 또한, 바닥과 가까운 해역에서의 유속이 바닥의 영향으로부터 비교적 자유로운 상층부에서의 유속보다 우월한 Longuet-Higgins(1957)가 이야기하는 전형적인 경계층 streaming이 천수 초입부에서부터 쇄파 역 깊숙이까지 존재하는 것을 확인하였다. 또한, 주기가 상대적으로 긴 경우 경계층 streaming의 세기와 생성범위는 해안 방향으로 확대되며 이러한 경향은 경계층 streaming이 바닥 인근에서 진행되는 마찰로 인한 파랑에너지손실로 결과되며 주기가 긴 경우 천수 과정이 일찍 시작된다는 사실을 상기하면 충분히 수용 가능해 보이며, Longuet-Higgins(1957)의 해석 해에서도 같은 경향을 확인할 수 있다.

Natural shoreline repeats its re-treatment and advance in response to the endlessly varying sea-conditions, and once severely eroded under stormy weather conditions, natural beaches are gradually recovered via a boundary layer streaming when swells are prevailing after storms cease. Our understanding of the boundary layer streaming over surf-zone often falls short despite its great engineering value, and here it should be noted that the most sediments available along the shore are supplied over the surf-zone. In this rationale, numerical simulation was implemented to investigate the hydraulic characteristics of boundary layer streaming over the surf zone in this study. In doing so, comprehensive numerical models made of Spatially filtered Navier-Stokes Eq., LES (Large Eddy Simulation), Dynamic Smagorinsky turbulence closure were used, and the effects of turbulence closure such as Dynamic Smagorinsky in LES and k-ε on the numerically simulated flow field were also investigated. Numerical results show that due to the intrinsic limits of k-ε turbulence model, numerically simulated flow velocity near the bottom based on k-ε model and wall function are over-predicted than the one using Dynamic Smagorinsky in LES. It is also shown that flow velocities near the bottom are faster than the one above the bottom which are relatively free from the presence of the bottom, complying the typical boundary layer streaming by Longuet-Higgins (1957), the spatial scope where boundary layer streaming are occurring is extended well into the surf zone as incoming waves are getting longer. These tendencies are plausible considering that it is the bottom friction that triggers a boundary layer streaming, and longer waves start to feel the bottom much faster than shorter waves.

키워드

참고문헌

  1. Bailard, J.A. and Inman D.L. (1981). An energetics bedload model for a plane sloping beach: local transport. J. Geophys. Res., 86(C3), 2035-2043. https://doi.org/10.1029/JC086iC03p02035
  2. Cho, Y.J. and Kim, G.S. (2008). Development of 3-D nonlinear wave driver using SPH. Journal of the Korean Society of Civil Engineers B 28(5B), 559-573 (in Korean).
  3. Cho, Y.J., Kim, G.S. and Ryu, H.S. (2008). Suspension of sediment over swash zone. Journal of the Korean Society of Civil Engineers B 28(1B), 95-109 (in Korean).
  4. Cho, Y.J. (2019a). Numerical analysis of the beach stabilization effect of an asymmetric ripple mat. Journal of Korean Society of Coastal and Ocean Engineers 31(4), 209-220 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.4.209
  5. Cho, Y.J. (2019b). Grand circulation process of beach cusp and its seasonal variation at the Mang-Bang beach from the perspective of trapped mode Edge waves as the driving mechanism of beach cusp formation. Journal of Korean Society of Coastal and Ocean Engineers, 31(5), 265-277 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.5.265
  6. Cho, Y.J. (2019c). Preliminary study on the development of a platform for the optimization of beach stabilization measures against beach erosion II - centering on the development of physics-based morphology model for the estimation of an erosion rate of nourished beach. Journal of Korean Society of Coastal and Ocean Engineers, 31(5), 320-333 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.5.320
  7. Cho, Y.J. and Bae, J.H. (2019). On the feasibility of freak waves formation within the harbor due to the presence of Infra-gravity waves of bound mode underlying the ever-present swells. Journal of Korean Society of Coastal and Ocean Engineers. 31(1), 17-27 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.1.17
  8. Cho, Y.J. and Kim, I.H. (2019). Preliminary study on the development of platform for the selection of an optimal beach stabilization measures against the beach erosion-centering on the yearly sediment budget of the Mang-Bang beach. Journal of Korean Society of Coastal and Ocean Engineers, 31(1), 28-39 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.1.28
  9. Cho, Y.J. and Lee, H. (2007). Numerical analysis of nonlinear shoaling characteristics over surf zone using SPH and lagrangian dynamic smagorinsky model. Journal of Korean Society of Coastal and Ocean Engineers, 19(1), 81-96 (in Korean).
  10. Chang, P.S. and Cho, Y.J. (2019). Preliminary study on the development of a platform for the optimization of beach stabilization measures against beach erosion III - centering on the effects of random Waves occurring during the unit observation period, and infra-gravity waves of bound mode, and boundary layer streaming on the sediment transport. Journal of Korean Society of Coastal and Ocean Engineers, 31(6), 434-449 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.6.434
  11. Deigaard, R., Jacobsen, J.B. and Fredsoe, J. (1999). Net sediment transport under wave groups and bound long waves. Journal of Geophysical Research, 104(C6), 13559-13575. https://doi.org/10.1029/1999JC900072
  12. Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. (1991). A dynamic sub-grid scale eddy viscosity model. Physical Fluids, A3, 1760-1765.
  13. Holmedal, L.E. and Myrhaug, D. (2009). Wave-induced steady streaming, mass transport and net sediment transport in rough turbulent ocean bottom boundary layers. Continental Shelf Research, 29, 911-926. https://doi.org/10.1016/j.csr.2009.01.012
  14. Holmedal, L.E., Myrhaug, D. and Rue, H. (2003). The sea bed boundary layer under random waves plus current. Continental Shelf Research, 23, 717-750. https://doi.org/10.1016/S0278-4343(03)00020-7
  15. Jensen, B.L., Sumer, B.M. and Fredsoe, J. (1989). Turbulent oscillatory boundary layers at high Reynolds numbers. Journal of Fluid Mechanics, 206, 265-297. https://doi.org/10.1017/S0022112089002302
  16. Justesen, P. (1991), A note on turbulence calculations in the wave boundary layer. Journal of Hydraulic Research, 29, 699-711. https://doi.org/10.1080/00221689109498985
  17. Lee, H.J. and Cho, Y.J. (2019). Numerical analysis of synchronous Edge wave known as the driving mechanism of beach cusp. Journal of Korean Society of Coastal and Ocean Engineers, 31(6), 409-422 (in Korean). https://doi.org/10.9765/KSCOE.2019.31.6.409
  18. Longuet-Higgins, M.S. (1957). The mechanics of the boundary layer near the bottom in a progressive wave. Proc. 6th International Conference on Coastal Engineering, Gainesville, Palm Beach and Miami Beach, Florida, December 1957, 184-193.
  19. Losada, I.J., Gonzalez-Ondina, J.M., Diaz, G. and Gonzalez, E.M. (2008). Numerical simulation of transient nonlinear response of semi-enclosed water bodies: model description and experimental validation. Coastal Engineering, 55(1), 21-34. https://doi.org/10.1016/j.coastaleng.2007.06.002
  20. Meneveau, C., Lund, T.S. and Cabot, W.H. (1996). A Lagrangian dynamic sub-gird scale model of turbulence. Journal of Fluid Mechanics, 319, 353-385. https://doi.org/10.1017/S0022112096007379
  21. Pope, S.B. (2004). Ten equations concerning the large-eddy simulation of turbulent flows. New Journal of Physics, 6(35), 1-24. https://doi.org/10.1088/1367-2630/6/1/001
  22. Rodi, W. (1993). Turbulence models and their application in hydraulics - a state of art review, International Association for Hydraulic Research, Delft, 3rd edition 1993, Balkema.
  23. Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly Weather Rev NWB, 91(3), 99-164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  24. Trowbridge, J. and Madsen, O.S. (1984). Turbulent wave boundary layers 2. Second order theory and mass transport. Journal of Geophysical Research, 89(C5), 7999-8007. https://doi.org/10.1029/JC089iC05p07999
  25. Yoshizawa, A. and Horiuti, K. (1985). A Statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. Journal of the Physical Society of Japan, 54(8), 2834-2839. https://doi.org/10.1143/JPSJ.54.2834