Hydrodynamics of Turbid Underflows. I: Formulation and Numerical Analysis
Publication: Journal of Hydraulic Engineering
Volume 125, Issue 10
Abstract
A mathematical model is developed for unsteady, two-dimensional, single-layer, depth-averaged turbid underflows driven by nonuniform, noncohesive sediment. The numerical solution is obtained by a high-resolution, total variation diminishing, finite-volume numerical model, which is known to capture sharp fronts accurately. The monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to prevent the development of spurious oscillations near discontinuities. The model also possesses the capability to track the evolution and development of an erodible bed, due to sediment entrainment and deposition. This is accomplished by solving a bed-sediment conservation equation at each time step, independent of the hydrodynamic equations, with a predictor-corrector method. The model is verified by comparison to experimental data for currents driven by uniform and nonuniform sediment.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bonnecaze, R. T., Hallworth, M. A., Huppert, H. E., and Lister, J. R. (1995). “Axisymmetric particle-driven gravity currents.” J. Fluid Mech., 294, 93–121.
2.
Bonnecaze, R. T., Huppert, H. E., and Lister, J. R. (1993). “Particle-driven gravity currents.” J. Fluid Mech., 250, 339–369.
3.
Bradford, S. F. ( 1996). “Numerical simulation of a turbidity current hydrodynamics and sedimentation,” PhD dissertation, University of Michigan, Ann Arbor, Mich.
4.
Bradford, S. F., Katopodes, N. D., and Parker, G. (1997). “Characteristic analysis of turbid underflows.”J. Hydr. Engrg., ASCE, 123(5), 420–431.
5.
Dengler A. T., and Wilde, P. (1987). “Turbidity currents on steep slopes: Application of an avalanche-type numeric model for ocean thermal energy conversion design.” Ocean Engrg., 14, 409–433.
6.
Dietrich, W. E. (1982). “Settling velocity of natural particles.” Water Resour. Res., 18, 1615–1626.
7.
Flood, R. D., and Damuth, J. E. (1987). “Quantitative characteristics of sinuous distributary channels of the Amazon deep-sea fan.” Geolog. Soc. of Am. Bull., 98, 728–738.
8.
Fraccarollo, L., and Toro, E. F. (1995). “Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.”J. Hydr. Res., ASCE, 33, 843–864.
9.
Garcia, M. H. (1994). “Depositional turbidity currents laden with poorly sorted sediment.”J. Hydr. Engrg., ASCE, 120(11), 1240–1263.
10.
Garcia, M., and Parker, G. (1991). “Entrainment of bed sediment into suspension.”J. Hydr. Engrg., ASCE, 117(4), 414–435.
11.
Garcia, M., and Parker, G. (1993). “Experiments on the entrainment of sediment into suspension by a dense bottom current.” J. Geophys. Res., 98(C3), 4793–4807.
12.
Hay, A. E. (1987). “Turbidity currents and submarine channel formation in Rupert Inlet, British Columbia 1. Surge observations.” J. Geophys. Res., 92, 2875–2881.
13.
Heezen, B. C., and Ewing, M. C. (1952). “Turbidity currents and submarine slumps, and the 1929 Grand Banks earthquake.” Am. J. Sci., 250, 849–873.
14.
Hirsch, C. (1990). Numerical computation of internal and external flows. Wiley, New York.
15.
Hiscott, R. N. (1984). “Loss capacity, not competence, as the fundamental process governing deposition from turbidity currents.” J. Sedimentary Res., A64, 209–214.
16.
Huppert, H. E., and Simpson, J. E. (1980). “The slumping of gravity currents.” J. Fluid Mech., 99, 785–799.
17.
Imran, J., Parker, G., and Katopodes, N. (1998). “A numerical model of channel inception on submarine fans.” J. Geophys. Res., 103(C1), 1219–1238.
18.
Inman, D. L., Nordstrom, C. E., and Flick, R. E. (1976). “Currents in submarine canyons: An air-sea-land interaction.” Annu. Rev. of Fluid Mech., 8, 275–310.
19.
Komar, P. D. ( 1977). “Computer simulation of turbidity current flow and the study of deep-sea channels and fan sedimentation.” The sea, Wiley, New York.
20.
Middleton, G. V. (1966). “Experiments on density and turbidity currents I. Motion of the head.” Can. J. Earth Sci., 3, 523–546.
21.
Middleton, G. V., and Neal, W. J. (1989). “Experiments on the thickness of beds deposited by turbidity currents.” J. Sedimentary Petrology, 59, 297–307.
22.
Normark, W. R. (1989). “Observed parameters for turbidity-current flows in channels, Reserve Fan, Lake Superior.” J. Sedimentary Petrology, 59, 423–431.
23.
Parker, G. (1982). “Conditions for the ignition of catastrophically erosive turbidity currents.” Marine Geol., 46, 307–327.
24.
Parker, G., Fukushima, Y., and Pantin, H. M. (1986). “Self-accelerating turbidity currents.” J. Fluid Mech., 171, 145–181.
25.
Parker, G., Garcia, M., Fukushima, Y., and Yu, W. (1987). “Experiments on turbidity currents over an erodible bed.”J. Hydr. Res., 25(1), 123–147.
26.
Reynolds, S. (1987). “A recent turbidity current event, Hueneme Fan, California: Reconstruction of flow properties.” Sedimentology, 34, 129–137.
27.
Roe, P. L. (1981). “Approximate Riemann solvers, parameter vectors, and difference schemes.” J. Computat. Phys., 43, 357–372.
28.
Sloff, C. J. ( 1997). “Sedimentation in Reservoirs,” PhD thesis, Delft University of Technology, Delft, The Netherlands.
29.
Stow, D. A. V., Howell, D. G., and Nelson, C. H. ( 1985). “Sedimentary, tectonic, and sea-level controls.” Submarine fans and related turbidite systems, Springer, New York.
30.
Sweby, P. K. (1984). “High resolution schemes using flux limiters for hyperbolic conservation laws.” SIAM J., 21, 995–1011.
31.
Van Leer, B. (1979). “Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method.” J. Computat. Phys., 32, 101–136.
32.
Van Leer, B., Lee, W. T., and Powell, K. G. (1989). “Sonic point capturing.” Proc., AIAA 9th Computat. Fluid Dyn. Conf., Buffalo, N.Y., American Institute of Aeronautics and Astronautics, Reston, Va.
33.
Wilde, P., Normark, W. R., Chase, T. E., and Gutmacher, C. E. ( 1985). “Potential petroleum reservoirs on deep-sea fans off central California.” Submarine fans and related turbidite systems, Springer, New York.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 125 • Issue 10 • October 1999
Pages: 1006 - 1015
History
Received: May 19, 1997
Published online: Oct 1, 1999
Published in print: Oct 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.