Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T07:28:29.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Further results for convection driven by the differential sedimentation of particles

Published online by Cambridge University Press:  26 April 2006

Ross C. Kerr  and
John R. Lister
Ross C. Kerr
Affiliation:
Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia
John R. Lister
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW. UK
Get access Rights & Permissions [Opens in a new window]

Abstract

When a well-mixed suspension of small particles is emplaced below a clear fluid whose density is greater than that of the interstitial fluid, but less than that of the bulk suspension, the subsequent settling of the dense particles releases buoyant interstitial fluid and drives convection in the overlying layer. Mixing of interstitial fluid and some entrained particles into the overlying fluid causes the density of the overlying fluid to evolve with time and changes the rate of descent of the interface between the sedimenting and convecting regions. These effects are investigated experimentally in a simple rectangular geometry using suspensions of spherical glass particles. It is found that the convecting region is well mixed in both composition and particle concentration and that the interfacial velocity may be predicted from the instantaneous (uniform) bulk density of the upper layer and the distribution of the particle settling velocities. In the case of an overlying density gradient, the convection does not extend through the depth of the overlying fluid but erodes the base of the gradient to form a well-mixed layer between the gradient and the sedimenting fluid. On completion of the first cycle of sedimentation-driven convection, sedimentation from this well-mixed layer produces further cycles of sedimentation-driven convection, which are of successively decreasing intensity and increasing duration. Whether the overlying fluid is uniform or stratified, both theory and experiment show that the particles that are lifted into the convection are smaller on average than those which settle at the base of the lower layer. Thus, when the lifted particles are eventually allowed to settle there is a discontinuity generated in the variation of the size distribution of particles with height in the final sedimented pile. This phenomenon may be an important mechanism for secondary layering in the deposits from turbidity currents and pyroclastic flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 227 - 245
Copyright
© 1992 Cambridge University Press

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.)

References

Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid Mech. 204, 1–30.Google Scholar
Davis, R. H. & Birdsell, K. H. 1988 Hindered settling of semi-dilute monodisperse and polydisperse suspensions. AIChE J. 34, 123–129.Google Scholar
Davis, R. H. & Hassen M, A. 1988 Spreading at the interface at the top of a slightly polydisperse sedimenting suspension. J. Fluid Mech. 196, 107–134.Google Scholar
Deardorff, J. W., Willis, G. E. & Lilly, D. K. 1969 Laboratory investigation of non-steady penetrative convection. J. Fluid Mech. 35, 7–31.Google Scholar
Deardorff, J. W., Willis, G. E. & Stockton, B. H. 1980 Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100, 41–64.Google Scholar
Fischer, H. B. List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Garon, A. M. & Goldstein, R. J. 1973 Velocity and heat transfer measurements in thermal convection. Phys. Fluids 16, 1818–1825.Google Scholar
Gilbert, R. 1975 Sedimentation in Lillooet Lake, British Columbia. Can. J. Earth Sci. 12, 1697–1711.Google Scholar
Gill, A. E. 1982 Atmosphere—Ocean Dynamics. Academic.
Gould, H. R. 1960 Turbidity currents In Comprehensive Survey of Sedimentation in Lake Mead, 1948–1949. Prof. Pap. US Geol. Surv., vol. 295, pp. 201–207.
Green, T. 1987 The importance of double diffusion to the settling of suspended material. Sedimentology 34, 319–331.Google Scholar
Gustavson, T. C. 1975 Bathymetry and sediment distribution in proglacial Malaspina Lake, Alaska. J. Sed. Petrol. 45, 450–461.Google Scholar
Houghton, J. T. 1977 The Physics of Atmospheres. Cambridge University Press.
Howard, L. N. 1966 Convection at high Rayleigh number In Proc. 11th Intl Congr. Appl. Mech., Munich, pp. 1109–1115. Springer.
Huppert, H. E., Kerr, R. C., Lister, J. R. & Turner, J. S. 1991 Convection and particle entrainment driven by differential sedimentation. J. Fluid Mech. 226, 349–369 (referred to herein as HKLT).Google Scholar
Jones, K. P. N., McCave, I. N. & Patel, P. D. 1988 A computer-interfaced sedigraph for modal size analysis of fine-grained sediment. Sedimentology 35, 163–172.Google Scholar
Kerr, R. C. 1991 Erosion of a stable density gradient by sedimentation-driven convection. Nature 353, 423–425.Google Scholar
Knauss, J. A. 1978 Introduction to Physical Oceanography. Prentice-Hall.
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 1374–1389.Google Scholar
Kynch, G. J. 1952 A theory for sedimentation. Trans. Faraday Soc. 48, 166–176.Google Scholar
Lick, W. 1965 The instability of a fluid layer with time dependent heating. J. Fluid Mech. 21, 565–576.Google Scholar
Lister, J. R. & Kerr, R. C. 1989 The effect of geometry on the gravitational instability of a buoyant region of viscous fluid. J. Fluid Mech. 202, 577–594.Google Scholar
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection.. Proc. R. Soc. Lond. A 225, 185–195.Google Scholar
Martin, D. 1988 Fractional crystallization in convecting magma chambers. Ph.D. thesis, Australian National University.
Oster, G. 1965 Density gradients. Sci. Am. 213, 70–76.Google Scholar
Oster, G. & Yamamoto, M. 1963 Density gradient techniques. Chem. Rev. 63, 257–268.Google Scholar
Quadfasel, D., Kudrass, H. & Frische, A. 1990 Deep-water renewal by turbidity currents in the Sulu Sea. Nature 348, 320–322.Google Scholar
Selig, F. 1965 A theoretical prediction of salt dome patterns. Geophysics 30, 633–643.Google Scholar
Smith, T. N. 1966 The sedimentation of particles having a dispersion of sizes. Trans. Instn Chem. Engrs 44, 153–157.Google Scholar
Sparks, R. S. J., Huppert, H. E. & Turner, J. S. 1984 The fluid dynamics of evolving magma chambers.. Phil. Trans. R. Soc. Lond. A 310, 511–534.Google Scholar
Stow, D. A. V. & Piper, D. J. W. 1984 Fine-grained Sediments: Deep Water Processes and Facies. Blackwell.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Wilson, C. J. N. 1986 Pyroclastic flows and ignimbrites. Sci. Prog., Oxf. 70, 171–207.Google Scholar