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Sedimentation and entrainment in dense layers of suspended particles stirred by an oscillating grid

Published online by Cambridge University Press:  26 April 2006

Herbert E. Huppert ,
J. Stewart Turner  and
Mark A. Hallworth
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20 Silver Street, Cambridge CB3 9EW, UK
J. Stewart Turner
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra ACT 0200, Australia
Mark A. Hallworth
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 20 Silver Street, Cambridge CB3 9EW, UK
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Abstract

Many flows, including those containing suspended particles, are kept turbulent by the action of the bottom stress, and this turbulence is also responsible for maintaining sedimenting particles in suspension and in some cases entraining more particles from the bed. A convenient one-dimensional analogue of these processes is provided by laboratory experiments conducted in a mixing box, where a characterizable turbulence is generated by the vertical oscillation of a horizontal grid. In the present paper we report the results of a series of experiments with a grid located close to the bottom boundary to simulate the action of stresses acting at a rough boundary, and compare the results with those obtained using the more extensively studied geometry in which a similar grid is located in the interior of a stirred fluid layer. Experiments have been conducted both with dense, particle-free fluid layers and with layers containing sufficiently high concentrations of dense particles to have a significant effect on the bulk density. In the fluid case, the interface at the top of the stirred dense layer continues to rise as lighter fluid is entrained across the interface. Sediment layers are distinctly different, because the particles responsible for the density difference between the layers can fall out of the suspension as it changes in thickness. The work done in keeping particles in suspension and the effect of this on the turbulence above the grid must be taken into account. The mechanism of resuspension of particles depends on the level of turbulence near the bottom boundary, below the grid. As the stirring rate, and thus the intensity of turbulence, are increased three possible equilibrium states can be attained sequentially: the particles eventually all precipitate; or some particles precipitate while the remainder are held indefinitely in suspension; or all the particles are suspended. In the last two cases a stable, self-limited suspension layer is produced, separated from the overlying fluid by a sharp density interface at a fixed height. Theoretical arguments are presented which provide a satisfactory scaling of the experimental data. These are compared with previous theories and numerical experiments aimed at modelling both the one-dimensional problem and the corresponding processes in turbulent gravity currents. Comparisons are also made with sediment-laden channel flows and convecting layers containing sedimenting particles. Similar results will hold for light, positively buoyant particles or non-coalescing bubbles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 289 , 25 April 1995 , pp. 263 - 293
Copyright
© 1995 Cambridge University Press

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References

Bagnold, R. A. 1962 Auto-suspension of transported sediment; turbidity currents. Proc. R. Soc. Lond. A 265, 315–319.Google Scholar
Dade, W. B., Lister, J. R. & Huppert, H. E. 1994 Fine-sediment deposition from gravity surges on uniform slopes. J. Sed. Res. A 64, 423–432.Google Scholar
E, X. & Hopfinger, E. J. 1986 On mixing across an interface in a stably stratified fluid. J. Fluid Mech. 166, 227–244.Google Scholar
E, X. & Hopfinger, E. J. 1987 Stratification by solid particle suspensions. 3rd Intl. Symp. on Stratified Flows, Caltech, Pasadena, pp. 1–8.
Einstein, H. A. 1968 Deposition of suspended particles in a gravel bed. J. Hydraul. Div., ASCE 94, 1197–1205.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.Google Scholar
Fernando, H. J. S. 1988 Growth of a turbulent patch in a stratified fluid. J. Fluid Mech. 190, 55–70.Google Scholar
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 23, 455–493.Google Scholar
Hopfinger, E. J. & Linden, P. F. 1982 Formation of a thermocline in zero-mean-shear turbulence subject to a stabilizing buoyancy flux. J. Fluid Mech. 114, 157–173.Google Scholar
Hopfinger, E. J. & Toly, J.-A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.Google Scholar
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.Google Scholar
Huppert, H. E., Turner, J. S. & Hallworth, M. A. 1993 Sedimentation and mixing of a turbulent fluid suspension: a laboratory study. Earth Planet. Sci. Lett. 114, 259–267.Google Scholar
Kitaigorodskii, S. A. 1960 On the computation of the thickness of the wind-mixing layer in the ocean. Bull. Acad. Sci. USSR Geophys. Ser. 3, 284–287.Google Scholar
Koyaguchi, T., Hallworth, M. A. & Huppert, H. E. 1993 An experimental study on the effects of phenocrysts on convection in magmas. J. Volcan. Geotherm. Res. 55, 15–32.Google Scholar
Koyaguchi, T., Hallworth, M. A., Huppert, H. E. & Sparks, R. S. J. 1990 Sedimentation of particles from a convecting fluid. Nature 343, 447–450.Google Scholar
Long, R. R. 1978 A theory of mixing in a stably stratified fluid. J. Fluid Mech. 84, 113–124.Google Scholar
Martin, D. & Nokes, R. 1988 Crystal settling in a vigorously convecting magma. Nature 332, 534–536.Google Scholar
Martin, D. & Nokes, R. 1989 A fluid-dynamical study of crystal settling in convecting magmas. J. Petrol. 30, 1471–1500.Google Scholar
McCave, I. N. 1970 Deposition of fine grained suspended sediment from tidal currents. J. Geophys. Res. 75, 4151–4159.Google Scholar
Noh, Y. & Fernando, J. H. S. 1991a A numerical study on the formation of a thermocline in shear-free turbulence. Phys. Fluids A 3, 422–426.Google Scholar
Noh, Y. & Fernando, J. H. S. 1991b Dispersion of suspended particles in turbulent flow. Phys. Fluids A 3, 1730–1740.Google Scholar
Nokes, R. I. 1988 On the entrainment rate across a density interface. J. Fluid Mech. 188, 185–204.Google Scholar
Pantin, H. M. 1979 Interaction between velocity and effective density in turbidity flow: phase-plane analysis, with criteria for autosuspension. Mar. Geol. 31, 59–99.Google Scholar
Parker, G. 1982 Conditions for the ignition of catastrophically erosive turbidity currents. Mar. Geol. 46, 307–327.Google Scholar
Parker, G., Fukushima, Y. & Pantin, H. M. 1986 Self-accelerating turbidity currents. J. Fluid Mech. 171, 145–181.Google Scholar
Phillips, O. M. 1972 Turbulence in a strongly stratified fluid – is it unstable? Deep-Sea Res. 19, 79–81.Google Scholar
Ruddick, B. R., Mcdougall, T. J. & Turner, J. S. 1989 The formation of layers in a uniformly stirred density gradient. Deep-Sea Res. 36, 597–609.Google Scholar
Seymour, R. J. 1990 Autosuspending turbidity flows. In The Sea (Ocean Engineering Science) 9B, 919–940.
Solomatov, V. S., Olson, P. & Stevenson, D. J. 1993 Entrainment from a bed of particles by thermal convection. Earth Planet. Sci. Lett. 120, 387–393.Google Scholar
Sparks, R. S. J., Bonnecaze, R. T., Huppert, H. E., Lister, J. R., Hallworth, M. A., Mader, H. & Phillips, J. 1993 Sediment-laden gravity currents with reversing buoyancy. Earth Planet. Sci. Lett. 114, 243–257.Google Scholar
Stacey, M. W. & Bowen, A. J. 1988a The vertical structure of turbidity currents and a necessary condition for self-maintenance. J. Geophys. Res. 93, 3543–3553.Google Scholar
Stacey, M. W. & Bowen, A. J. 1988b A comparison of an autosuspension criterion to field observations of five turbidity currents. Sedimentology 37, 1–5.Google Scholar
Thompson, S. M. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, 349–368.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656.Google Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption and its application to geophysical flows. J. Fluid Mech. 173, 431–471.Google Scholar
Wolanski, E., Chappell, J., Ridd, P. & Verlessy, R. 1988 Fluidization of mud in estuaries. J. Geophys. Res. 93, 2351–2361.Google Scholar
Wolanski, E., Chappell, J., Ridd, P. & Verlessy, R. 1989 Reply to comments on ‘Fluidization of mud in estuaries’. J. Geophys. Res. 94, 6295–6296.Google Scholar
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