Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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A numerical simulation of propagating turbidity currents using the ULTIMATE scheme

ULTIMATE 기법을 이용한 부유사 밀도류 전파 수치모의

  • Choi, Seongwook (Department of Civil & Environmental Engineering, Yonsei University) ;
  • Choi, Sung-Uk (Department of Civil & Environmental Engineering, Yonsei University)
  • 최성욱 (연세대학교 공과대학 토목환경공학과) ;
  • 최성욱 (연세대학교 공과대학 토목환경공학과)
  • Received : 2016.10.11
  • Accepted : 2016.12.07
  • Published : 2017.01.31
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Abstract

This study presents a numerical model for simulating turbidity currents using the ULTIMATE scheme. For this, the layer-averaged model is used. The model is applied to laboratory experiments, where the flume is composed of sloping and flat parts, and the characteristics of propagating turbidity currents are investigated. Due to the universal limiter of the ULTIMATE scheme, the frontal part of the turbidity currents at a sharp gradient without numerical oscillations is computed. Simulated turbidity currents propagate super-critically to the end of the flume, and internal hydraulic jumps occur at the break-in-slope after being affected by the downstream boundary. It is found that the hydraulic jumps are computed without numerical oscillations if Courant number is less than 1. In addition, factors that affect propagation velocity of turbidity currents is studied. The particle size less than $9{\mu}m$ does not affect propagation velocity but the buoyancy flux affects clearly. Finally, it is found that the numerical model computes the bed elevation change due to turbidity currents properly. Specifically, a discontinuity in the bed elevation, arisen from the hydraulic jumps and resulting difference in sediment entrainment, is observed.

본 연구에서는 ULTIMATE 기법을 이용하여 밀도류 층적분 모형의 해석을 위한 수치모형을 제시하였다. 개발된 모형을 경사부와 평탄부로 이루어진 실내 실험에 적용하여 경사부에 유입된 부유사 밀도류의 전파 특성에 대해 분석하였다. ULTIMATE 기법의 범용제한자로 인하여 밀도류의 선단부가 수치진동 없이 비교적 급한 형태로 전파되는 것을 모의하였다. 그리고 사류로 전파되고 수로 끝에서부터 상류로 변화되는 밀도류의 내부 도수 발생 과정을 재현하였다. 이러한 내부 도수는 ULTIMATE 제한자를 사용하면 Courant 수가 1 미만일 때 안정적으로 모의되는 것을 확인하였다. 또한 밀도류의 전파 속도에 영향을 주는 인자에 대하여 분석하였다. 입자의 크기는 $9{\mu}m$ 이하일 때 밀도류의 전파 속도에 큰 영향을 주지 않는 반면, 부력 흐름률은 확연한 영향을 주는 것을 확인하였다. 마지막으로 부유사 밀도류에 의한 하상변동에 대해 검토하였다. 수치모형으로 부유사 밀도류의 전파에 의한 하상변동을 정량적으로 적절히 모의하였으며, 도수로 인한 부유사 연행의 차이와 이로 인한 하상의 불연속적인 형태를 관찰할 수 있었다.

Keywords

References

  1. Altinakar, S., Graf, W. H., and Hopfinger, E. J. (1990). "Weakly depositing turbidity current on a small slope." Journal of Hydraulic Research, Vol. 28, No. 1, pp. 55-80. https://doi.org/10.1080/00221689009499147
  2. An, S., and Julien, P. Y. (2014). "Three-dimensional modeling of turbid density currents in Imha Reservoir, South Korea." Journal of Hydraulic Engineering, Vol. 140, No. 5, p. 05014004. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000851
  3. Bonnecaze, R. T., Hallworth, M. A., Huppert, H. E., and Lister, J. R. (1995). "Axisymmetric particle-driven gravity currents." Journal of Fluid Mechanics, Vol. 294, pp. 93-121. https://doi.org/10.1017/S0022112095002825
  4. Britter, R. E., and Linden, P. F. (1980). "The motion of the front of gravity current travelling down an incline." Journal of Fluid Mechanics, Vol. 99, pp. 531-543. https://doi.org/10.1017/S0022112080000754
  5. Cao, Z., Li, J., Pender, G., and Liu, Q. (2015). "Whole-process modeling of reservoir turbidity currents by a double layer-averaged model." Journal of Hydraulic Engineering, Vol. 141, No. 2, p. 04014069. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000951
  6. Choi, S.-U., and Garcia, M. H. (1995). "Modeling of one-dimensional turbidity currents with a dissipative-Galerkin finite element method." Journal of Hydraulic Research, Vol. 33, No. 5, pp. 623-648. https://doi.org/10.1080/00221689509498561
  7. Choi, S.-U., and Garcia, M. H. (2002). "Turbulence modeling of density currents developing two-dimensionally on a slope." Journal of Hydraulic Engineering, Vol. 128, No. 1, pp. 55-63. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(55)
  8. Chung, S. W., Hipsey, M. R., and Imberger, J. (2009). "Modelling the propagation of turbid density inflows into a stratified lake: Daecheong Reservoir, Korea." Environmental Modelling and Software, Vol. 24, No. 12, pp. 1467-1482. https://doi.org/10.1016/j.envsoft.2009.05.016
  9. Crank, J. (1984). Free and moving boundary problems. Clarendon Press, Oxford, p. 425.
  10. Fukushima, Y., Parker, G., and Pantin, H. M. (1985). "Prediction of ignitive turbidity currents in Scripps Submarine Canyon." Marine Geology, Vol. 67, No. 1-2, pp. 55-81. https://doi.org/10.1016/0025-3227(85)90148-3
  11. Garcia, M. H. (1990). Depositing and eroding sediment-driven flows: turbidity currents, University of Minnesota, Minneapolis, Minnesota, USA.
  12. Garcia, M. H. (1993). "Hydraulic jumps in sediment-driven bottom currents." Journal of Hydraulic Engineering, Vol. 119, No. 10, pp. 1094-1117. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:10(1094)
  13. Garcia, M., and Parker, G. (1989). "Experiments on hydraulic jumps in turbidity currents near a canyon-fan transition." Science, Vol. 245, No. 4916, pp. 393-396. https://doi.org/10.1126/science.245.4916.393
  14. Garcia, M., and Parker, G. (1993). "Experiments on the entrainment of sediment into suspension by a dense bottom current." Journal of Geophysical Research, Vol. 98, pp. 4793-4793. https://doi.org/10.1029/92JC02404
  15. Kostic, S., and Parker, G. (2003). "Progradational sand-mud deltas in lakes and reservoirs. part 1. theory and numerical modeling." Journal of Hydraulic Research, Vol. 41, No. 2, pp. 127-140. https://doi.org/10.1080/00221680309499956
  16. Lai, Y. G., Huang, J., and Wu, K. (2015). "Reservoir turbidity current modeling with a two-dimensional layer-averaged model." Journal of Hydraulic Engineering, Vol. 141, No. 12, p. 04015029. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001041
  17. Leonard, B. P. (1979). "A stable and accurate convective modelling procedure based on quadratic upstream interpolation." Computer Methods in Applied Mechanics and Engineering, Vol. 19, No. 1, pp. 59-98. https://doi.org/10.1016/0045-7825(79)90034-3
  18. Leonard, B. P. (1991). "The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection." Computer Methods in Applied Mechanics and Engineering, Vol. 88, No. 1, pp. 17-74. https://doi.org/10.1016/0045-7825(91)90232-U
  19. Oehy, C. D., and Schleiss, A. J. (2007). "Control of turbidity currents in reservoirs by solid and permeable obstacles." Journal of Hydraulic Engineering, Vol. 133, No. 6, pp. 637-648. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:6(637)
  20. Parker, G., Garcia, M., Fukushima, Y., and Yu, W. (1987). "Experiments on turbidity currents over an erodible bed." Journal of Hydraulic Research, Vol. 25, No. 1, pp. 123-147. https://doi.org/10.1080/00221688709499292
  21. Ryu, I. G., Chung, S. W., and Yoon, S. W. (2011). "Modelling a turbidity current in Soyang reservoir (Korea) and its control using a selective withdrawal facility." Water Science and Technology, Vol. 63, No. 9, pp. 1864-1872. https://doi.org/10.2166/wst.2011.397
  22. Toniolo, H., Parker, G., and Voller, V. (2007). "Role of ponded turbidity currents in reservoir trap efficiency." Journal of Hydraulic Engineering, Vol. 133, No. 6, pp. 579-595. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:6(579)