Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T06:09:30.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivation of a Multilayer Approach to Model Suspended Sediment Transport: Application to Hyperpycnal and Hypopycnal Plumes

Part of: Hyperbolic equations and systems Equilibrium (steady-state) problems Numerical methods

Published online by Cambridge University Press:  31 October 2017

T. Morales de Luna ,
E.D. Fernández Nieto  and
M. J. Castro Díaz
T. Morales de Luna*
Affiliation:
Dpto. de Matemáticas. Universidad de Córdoba. Campus de Rabanales. 14071 Córdoba, Spain
E.D. Fernández Nieto*
Affiliation:
Dpto. Matemática Aplicada I. E.T.S. Arquitectura. Universidad de Sevilla. Avda. Reina Mercedes N.2. 41012 Sevilla, Spain
M. J. Castro Díaz*
Affiliation:
Dpto. de Análisis Matemático. Facultad de Ciencias. Universidad de Málga. Campus de Teatinos, s/n. 29071 Málaga, Spain
*
*Corresponding author. Email addresses:[email protected](T. Morales), [email protected](E. D. Fernández), [email protected](M. J. Castro)
*Corresponding author. Email addresses:[email protected](T. Morales), [email protected](E. D. Fernández), [email protected](M. J. Castro)
*Corresponding author. Email addresses:[email protected](T. Morales), [email protected](E. D. Fernández), [email protected](M. J. Castro)
Get access

Abstract

We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow. The model can describe as well the vertical profile of the sediment concentration and the velocity components of each one of the sediment species that form the turbidity current. To do so, it takes into account the settling velocity of the particles and their interaction with the fluid. This allows to better describe the phenomena than a single layer approach. It is in better agreement with the physics of the problem and gives promising results. The numerical simulation is carried out by rewriting the multilayer approach in a compact formulation, which corresponds to a system with nonconservative products, and using path-conservative numerical scheme. Numerical results are presented in order to show the potential of the model.

Keywords

Sediment transport modellingmultilayer approachturbidity currentsshallow water models

MSC classification

Secondary: 74S10: Finite volume methods 35L60: Nonlinear first-order hyperbolic equations 35L65: Conservation laws 74G15: Numerical approximation of solutions
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 5 , November 2017 , pp. 1439 - 1485
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Communicated by Boo-Cheong Khoo

References

[1] Alexander, J. and Morris, S.. Observations on experimental, nonchannelized, highconcentration turbidity currents and variations in deposits around obstacles. Journal of Sedimentary Research, 64:899–909, Oct. 1994.Google Scholar
[2] Audusse, E., Bristeau, M., Perthame, B., and Sainte-Marie, J.. Amultilayer Saint-Venant system with mass exchanges for shallow water flows. derivation and numerical validation. ESAIM: Mathematical Modelling and Numerical Analysis, 45(1):169–200, 2010.Google Scholar
[3] Audusse, E., Bristeau, M.-O., Pelanti, M., and Sainte-Marie, J.. Approximation of the hydrostatic Navier–Stokes system for density stratified flows by a multilayer model: Kinetic interpretation and numerical solution. Journal of Computational Physics, 230(9):3453–3478, May 2011.Google Scholar
[4] Baldock, T. E., Tomkins, M. R., Nielsen, P., and Hughes, M. G.. Settling velocity of sediments at high concentrations. Coastal Engineering, 51(1):91–100, Mar. 2004.CrossRefGoogle Scholar
[5] Bradford, S. F. and Katopodes, N. D.. Hydrodynamics of turbid underflows. i: Formulation and numerical analysis. Journal of Hydraulic Engineering, 125(10):1006–1015, 1999.Google Scholar
[6] Castro Díaz, M. J. and Fernández-Nieto, E.. A class of computationally fast first order finite volume solvers: PVM methods. SIAM Journal on Scientific Computing, 34(4):A2173–A2196, Jan. 2012.Google Scholar
[7] Casulli, V. and Cheng, R. T.. Semi-implicit finite difference methods for three-dimensional shallow water flow. International Journal for Numerical Methods in Fluids, 15(6):629–648, Sept. 1992.Google Scholar
[8] Chu, F. H., Pilkey, W. D., and Pilkey, O. H.. An analytical study of turbidity current steady flow. Marine Geology, 33(3-4):205–220, 1979. Cited By (since 1996): 11.Google Scholar
[9] Cuthbertson, A., Dong, P., King, S., and Davies, P.. Hindered settling velocity of cohesive/noncohesive sediment mixtures. Coastal Engineering, 55(12):1197–1208, Dec. 2008.Google Scholar
[10] Dal Maso, G., Lefloch, P. G., and Murat, F.. Definition and weak stability of nonconservative products. J. Math. Pures Appl. (9), 74(6):483–548, 1995.Google Scholar
[11] Fernández-Nieto, E. D., Koné, E. H., and Rebollo, T. C.. A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution. Journal of Scientific Computing, 60(2):408–437, Nov. 2013.Google Scholar
[12] Fernández-Nieto, E. D., Koné, E. H., Morales de Luna, T., and Bürger, R.. A multilayer shallow water system for polydisperse sedimentation. Journal of Computational Physics, 238:281–314, Apr. 2013.Google Scholar
[13] Garcia, M. and Parker, G.. Experiments on the entrainment of sediment into suspension by a dense bottom current. Journal of Geophysical Research, 98(C3):4793–4808, 1993.Google Scholar
[14] Haney, R. L.. On the pressure gradient force over steep topography in sigma coordinate ocean models. Journal of Physical Oceanography,, 21:610–619, Apr. 1991.2.0.CO;2>CrossRefGoogle Scholar
[15] Khan, S. M., Imran, J., Bradford, S., and Syvitski, J.. Numerical modeling of hyperpycnal plume. Marine Geology, 222-223:193–211, November 2005.CrossRefGoogle Scholar
[16] Kubo, Y.. Experimental and numerical study of topographic effects on deposition from twodimensional, particle-driven density currents. Sedimentary Geology, 164(3-4):311–326, February 2004.CrossRefGoogle Scholar
[17] Kubo, Y. and Nakajima, T.. Laboratory experiments and numerical simulation of sedimentwave formation by turbidity currents. Marine Geology, 192(1-3):105–121, December 2002.Google Scholar
[18] Middleton, G. V.. Experiments on density and turbidity currents: Iii. deposition of sediment. Canadian Journal of Earth Sciences, 4:297–307, 1967.Google Scholar
[19] Morales de Luna, T., Castro Díaz, M. J., Parés Madroñal, C., and Fernández Nieto, E. D.. On a shallow water model for the simulation of turbidity currents. Communications in Computational Physics, 6(4):848–882, 2009.Google Scholar
[20] Mulder, T. and Syvitski, J. P. M.. Turbidity Currents Generated at River Mouths during Exceptional Discharges to the World Oceans. The Journal of Geology, 103(3):285–299, May 1995.Google Scholar
[21] Parés, C.. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal., 44(1):300–321 (electronic), 2006.Google Scholar
[22] Parés, C. and Castro, M.. On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. M2AN Math. Model. Numer. Anal., 38(5):821–852, 2004.Google Scholar
[23] Parker, G., Fukushima, Y., and Pantin, H. M.. Self-accelerating turbidity currents. Journal of Fluid Mechanics, 171:145–181, 1986.Google Scholar
[24] Parsons, J. D., Bush, J. W. M., and Syvitski, J. P. M.. Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology, 48(2):465–478, Apr. 2001.CrossRefGoogle Scholar
[25] Paul, J. F.. Observations related to the use of the sigma coordinate transformation for estuarine and coastal modeling studies. In Estuarine and Coastal Modeling, pages 336–350. ASCE, 1993.Google Scholar
[26] Richardson, J. F. and Zaki, W. N.. Sedimentation and fluidisation: Part I. Chemical Engineering Research and Design, 75, Supplement:S82–S100, Dec. 1954.Google Scholar
[27] Snow, K. and Sutherland, B.. Particle-laden flow down a slope in uniform stratification. Journal of Fluid Mechanics, 755:251–273, 2014.Google Scholar
[28] Toumi, I.. A weak formulation of Roe's approximate Riemann solver. J. Comput. Phys., 102(2):360–373, 1992.Google Scholar