Skip to main content
×
×
Home

Numerical study of convective sedimentation through a sharp density interface

  • Yun-Chuan Shao (a1), Chen-Yen Hung (a1) and Yi-Ju Chou (a1) (a2) (a3)
Abstract

We conduct numerical simulations using the Eulerian–Lagrangian approach to investigate the formation of the leaking, finger, and stable-settling modes in convective sedimentation when a sediment-laden fluid layer descends through a sharply stratified ambient flow. We show that the temporal evolution of the sedimentation process for the leaking mode can be divided into three stages, including (in temporal order) Rayleigh–Taylor instability, convection, and leaking stages. The presence of sheet-like descending plumes of suspended particles is an important characteristic of the leaking mode, which marks the existence of the leaking stage. For larger particles, the motion is more dominated by gravitational settling and less affected by buoyancy-induced flow motion. The resulting lack of the leaking stage for the larger-particle case leads to persistent finger-like plumes of suspended particles, known as the finger mode. The stable-settling mode occurs when the particles are large and the concentration is dilute such that flow motion due to Rayleigh–Taylor instability has no effect on the particle motion, and the convective motion of suspended particles is insignificant. For the third stage of the leaking mode, which is also the final stationary state, we derive the criterion for the occurrence of the leaking pattern from a scaling argument of the viscous boundary layer. The criterion is further confirmed by the present simulation results and previous laboratory experiments. Through analysis of the energy budget and the vertical flux, we show that although the settling of individual particles is accelerated, the presence of the sheet-like descending plumes in the leaking mode does not contribute to an efficient settling enhancement compared with the finger mode and the Rayleigh–Taylor instability, i.e., the cases with no background stratification. This implies a negative effect on the settling enhancement for small suspended particles when a stable background density stratification exists. In addition, simulations using the equilibrium Eulerian description for the suspended particles are also conducted to examine the difference between the present Lagrangian particle approach and the conventional Eulerian model.

Copyright
Corresponding author
Email address for correspondence: yjchou@iam.ntu.edu.tw
References
Hide All
Arthur, R. S. & Fringer, O. B. 2014 The dynamics of breaking internal solitary waves on slopes. J. Fluid Mech. 761, 360398.
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.
Bradley, W. H. 1965 Vertical density currents. Science 150, 14231428.
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279314.
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156195.
Carey, S. 1997 Influence of convective sedimentation on the formation of widespread tephra fall layers in the deep sea. Geology 25 (9), 839842.
Carpenter, J. R., Sommer, T. & Wuest, A. 2012 Simulations of a double-diffusive interface in the diffusive convection regime. J. Fluid Mech. 711, 411436.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 133147.
Chou, Y. J. & Fringer, O. B. 2008 Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model. Phys. Fluids 20, 11503.
Chou, Y. J. & Fringer, O. B. 2010 A model for the simulation of coupled flow-bedform evolution in turbulent flows. J. Geophys. Res. 115, C10041.
Chou, Y.-J., Gu, S.-H. & Shao, Y.-C. 2015 An Euler–Lagrange model for simulating fine particle suspension in liquid flows. J. Comput. Phys. 299, 955973.
Chou, Y.-J. & Shao, Y.-C. 2016 Numerical study of particle-induced Rayleigh–Taylor instabilityeffects of particle settling and entrainment. Phys. Fluids 28, 043302.
Chou, Y.-J., Wu, F.-C. & Shih, W.-R. 2014a Toward numerical modeling of fine particle suspension using a two-way coupled Euler–Euler model. Part 1: theoretical formualtion and comparison to single-phase approximation. Intl J. Multiphase Flow 64, 3543.
Chou, Y.-J., Wu, F.-C. & Shih, W.-R. 2014b Toward numerical modeling of fine particle suspension using a two-way coupled Euler–Euler model. Part 2: simulation of particle-induced Rayleigh–Taylor instability. Intl J. Multiphase Flow 64, 4454.
Cui, A.1999 On the parallel computing of turbulent rotating stratified flows. PhD dissertation, Stanford Univ., Stanford, CA.
Cui, A. & Street, R. L. 2004 Large-eddy simulation of coastal upwelling flow. Environ. Fluid Mech. 4, 197223.
Davarpanah Jazi, S. & Wells, M. G. 2016 Enhanced sedimentation beneath particle-laden flows in lakes and the ocean due to double-diffusive convection. Geophys. Res. Lett. 43 (20), 1088310890.
Ferry, J. & Balachandar, S. 2001 A fast Eulerian method for disperse two-phase flow. Intl J. Multiphase Flow 27, 11991226.
Fringer, O. B. & Street, R. L. 2003 The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494, 319.
Green, T. 1987 The importance of double diffusion to the settling of suspended material. Sedimentology 34, 319331.
Green, T. & Diez, T. 1995 Vertical plankton transport due to self-induced convection. J. Plankton Res. 17 (9), 17231730.
Hoyal, D. C., Bursik, M. I. & Atkinson, J. F. 1999a The influence of diffusive convection on sedimentation from buoyant plumes. Mar. Geol. 159, 205220.
Hoyal, D. C., Bursik, M. I. & Atkinson, J. F. 1999b Settling-driven convection: a mechanism of sedimentation from stratified fluids. J. Geophys. Res. 104, 79537966.
Huppert, H. E. & Manins, P. C. 1973 Limiting conditions for salt-fingering at an interface. Deep-Sea Res. 20, 315323.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19, 59.
Manville, V. & Wilson, C. J. N. 2004 Vertical density currents: a review of their potential role in the deposition and interpretation of deep-sea ash layers. J. Geol. Soc. Lond. 161, 947958.
Maxey, M. R. & Riley, J. J. 1983 Equation of motion of a small sphere in linear shear flows. Phys. Fluids 26, 883889.
Mulder, T & Syvitski, J. P. M 1995 Turbidity currents generated at river mouths during exceptional discharge to the world oceans. J. Geol. 103, 285299.
Parsons, J. D., Bush, J. W. M. & Syvitski, J. P. M. 2001 Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology 48, 465478.
Perng, C. Y. & Street, R. L. 1989 3-d unsteady flow simulation: alternative strategies for a volume-average calculation. Intl J. Numer. Fluids 9 (3), 341362.
Schiller, L. & Nauman, A. 1935 A drag coefficient correlation. VDI Zeitung 77, 318320.
Segre, P. N., Herbolzheimer, E. & Chaikin, P. M. 1997 Long-range correlations in sedimentation. Phys. Rev. Lett. 13, 25742577.
Soria, J. & Cantwell, B. J. 1993 Identification and classification of topological structures in free shear flows. In Eddy Structure Idenfication in Free Turbulent Shear Flow (ed. Bonnet, J. P. & Glauser, M. N.). Springer.
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. Natl Acad. Sci. USA 52 (1), 4953.
Venayagamoorthy, S. K. & Fringer, O. B. 2007 On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577, 137159.
Warrick, J. A., Xu, J., Nobel, M. A. & Lee, J. H. 2008 Rapid formation of hyperpycnal sediment gravity currents offshore of a semi-arid California river. Cont. Shelf Res. 28, 9911009.
Yamamoto, Y., Hisatake, F. & Harada, S. 2015 Numerical simulation of concentration interface in stratified suspension: continuum–particle transition. Intl J. Multiphase Flow 73, 7179.
Yu, X., Hsu, T.-J. & Balachandar, S. 2013 Convective instability in sedimentation: linear stability analysis. J. Geophys. Res. 118, 256272.
Yu, X., Hsu, T.-J. & Balachandar, S. 2014 Convective instability in sedimentation: 3-d numerical study. J. Geophys. Res. 119, 81418161.
Zang, Y. & Street, R. L. 1995 Numerical simulation of coastal upwelling and interfacial instability of a rotational and stratified fluid. J. Fluid Mech. 305, 47.
Zang, Y., Street, R. L. & Koseff, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible navier-stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18.
Zedler, E. A. & Street, R. L. 2001 Large-eddy simulation of sediment transport: current over ripples. J. Hydraul. Engng ASCE 127 (6), 444.
Zedler, E. A. & Street, R. L. 2006 Sediment transport over ripples in oscillatory flow. J. Hydraul. Engng ASCE 132 (2), 1.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed