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Layer formation in sedimentary fingering convection

Published online by Cambridge University Press:  07 March 2017

J. F. Reali ,
P. Garaud ,
A. Alsinan  and
E. Meiburg
J. F. Reali
Affiliation:
Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA
P. Garaud*
Affiliation:
Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA
A. Alsinan
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
E. Meiburg
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: pgaraud@ucsc.edu
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Abstract

When particles settle through a stable temperature or salinity gradient they can drive an instability known as sedimentary fingering convection. This phenomenon is thought to occur beneath sediment-rich river plumes in lakes and oceans, in the context of marine snow where decaying organic materials serve as the suspended particles or in the atmosphere in the presence of aerosols or volcanic ash. Laboratory experiments of Houk & Green (Deep-Sea Res., vol. 20, 1973, pp. 757–761) and Green (Sedimentology, vol. 34(2), 1987, pp. 319–331) have shown sedimentary fingering convection to be similar to the more commonly known thermohaline fingering convection in many ways. Here, we study the phenomenon using three-dimensional direct numerical simulations. We find evidence for layer formation in sedimentary fingering convection in regions of parameter space where it does not occur for non-sedimentary systems. This is due to two complementary effects. Sedimentation affects the turbulent fluxes and broadens the region of parameter space unstable to the $\unicode[STIX]{x1D6FE}$-instability (Radko, J. Fluid Mech., vol. 497, 2003, pp. 365–380) to include systems at larger density ratios. It also gives rise to a new layering instability that exists in $\unicode[STIX]{x1D6FE}$-stable regimes. The former is likely quite ubiquitous in geophysical systems for sufficiently large settling velocities, while the latter probably grows too slowly to be relevant, at least in the context of sediments in water.

JFM classification

Convection: Double diffusive convection Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 816 , 10 April 2017 , pp. 268 - 305
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© 2017 Cambridge University Press 

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References

Alldredge, A. L. & Cohen, Y. 1987 Can microscale chemical patches persist in the sea? Microelectrode study of marine snow, fecal pellets. Science 235 (4789), 689–691.CrossRefGoogle ScholarPubMed
Alsinan, A., Meiburg, E. & Garaud, P. 2017 A settling-driven instability in two-component, stably stratified fluids. J. Fluid Mech. 816, 243–267.CrossRefGoogle Scholar
Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306.CrossRefGoogle Scholar
Brown, J. M., Garaud, P. & Stellmach, S. 2013 Chemical transport and spontaneous layer formation in fingering convection in astrophysics. Astrophys. J. 768, 34.CrossRefGoogle Scholar
Burns, P. & Meiburg, E. 2012 Sediment-laden fresh water above salt water: linear stability analysis. J. Fluid Mech. 691, 279–314.CrossRefGoogle Scholar
Burns, P. & Meiburg, E. 2015 Sediment-laden fresh water above salt water: nonlinear simulations. J. Fluid Mech. 762, 156–195.CrossRefGoogle Scholar
Carazzo, G. & Jellinek, A. M. 2013 Particle sedimentation and diffusive convection in volcanic ash-clouds. J. Geophys. Res. 118 (4), 1420–1437.CrossRefGoogle Scholar
Garaud, P. 2013 Double-diffusive convection. In EAS Publications Series (ed. Alecian, G., Lebreton, Y., Richard, O. & Vauclair, G.), EAS Publications Series, vol. 63, pp. 285–295.Google Scholar
Garaud, P. & Brummell, N. 2015 2D or Not 2D: the effect of dimensionality on the dynamics of fingering convection at low Prandtl number. Astrophys. J. 815, 42.CrossRefGoogle Scholar
Green, T. 1987 The importance of double diffusion to the settling of suspended material. Sedimentology 34 (2), 319–331.CrossRefGoogle Scholar
Ham, J. M. & Homsy, G. M. 1988 Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions. Intl J. Multiphase Flow 14 (5), 533–546.CrossRefGoogle Scholar
Holyer, J. Y. 1981 On the collective instability of salt fingers. J. Fluid Mech. 110, 195–207.CrossRefGoogle Scholar
Houk, D. & Green, T. 1973 Descent rates of suspension fingers. Deep Sea Res. 20, 757–761.Google Scholar
Hoyal, D. C. J. D., Bursik, M. I. & Atkinson, J. F. 1999a Settling-driven convection: a mechanism of sedimentation from stratified fluids. J. Geophys. Res. 104, 7953–7966.CrossRefGoogle Scholar
Hoyal, D. C. J. D., Bursik, M. I. & Atkinson, J. F. 1999b The influence of diffusive convection on sedimentation from buoyant plumes. Mar. Geol. 159 (14), 205–220.CrossRefGoogle Scholar
Krishnamurti, R. 2003 Double-diffusive transport in laboratory thermohaline staircases. J. Fluid Mech. 483, 287–314.CrossRefGoogle Scholar
Krishnamurti, R. 2009 Heat, salt and momentum transport in a laboratory thermohaline staircase. J. Fluid Mech. 638, 491–506.CrossRefGoogle Scholar
Kunze, E. 2003 A review of oceanic salt-fingering theory. Prog. Oceanogr. 56 (3–4), 399–417.CrossRefGoogle Scholar
Lambert, R. B. & Demenkow, J. W. 1972 On the vertical transport due to fingers in double diffusive convection. J. Fluid Mech. 54, 627–640.CrossRefGoogle Scholar
Linden, P. F. 1973 On the structure of salt fingers. Deep Sea Res. 20, 325–340.Google Scholar
Maxworthy, T. 1999 The dynamics of sedimenting surface gravity currents. J. Fluid Mech. 392, 27–44.CrossRefGoogle Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2002 High-resolution simulations of particle-driven gravity currents. Intl J. Multiphase Flow 28 (2), 279–300.CrossRefGoogle Scholar
Nicolai, H., Herzhaft, B., Hinch, E. J., Oger, L. & Guazzelli, E. 1995 Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-brownian spheres. Phys. Fluids 7 (1), 12–23.CrossRefGoogle Scholar
Parsons, J. D., Bush, J. W. M. & Syvitski, J. P. M. 2001 Hyperpycnal plume formation from riverine outflows with small sediment concentrations. Sedimentology 48, 465–478.CrossRefGoogle Scholar
Radko, T. 2003 A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech. 497, 365–380.CrossRefGoogle Scholar
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.CrossRefGoogle Scholar
Radko, T. & Smith, D. P. 2012 Equilibrium transport in double-diffusive convection. J. Fluid Mech. 692, 5–27.CrossRefGoogle Scholar
Rosenblum, E., Garaud, P., Traxler, A. & Stellmach, S. 2011 Turbulent mixing and layer formation in double-diffusive convection: three-dimensional numerical simulations and theory. Astrophys. J. 731, 66.CrossRefGoogle Scholar
Sánchez, X. & Roget, E. 2007 Microstructure measurements and heat flux calculations of a triple-diffusive process in a lake within the diffusive layer convection regime. J. Geophys. Res. 112 (C2), C02012.Google Scholar
Scheu, K. R., Fong, D. A., Monismith, S. G. & Fringer, O. B. 2015 Sediment transport dynamics near a river inflow in a large alpine lake. Limnol. Oceanogr. 60 (4), 1195–1211.CrossRefGoogle Scholar
Schmitt, R. W. 1979a The growth rate of super-critical salt fingers. Deep Sea Res. 26A, 23–40.CrossRefGoogle Scholar
Schmitt, R. W. 1979b Flux measurements on salt fingers at an interface. J. Mar. Res. 37 (3), 419–436.Google Scholar
Schmitt, R. W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26 (1), 255–285.CrossRefGoogle Scholar
Schmitt, R. W. 1995 The salt finger experiments of Jevons (1857) and Rayleigh (1880). J. Phys. Oceanogr. 25 (1), 8–17.2.0.CO;2>CrossRefGoogle Scholar
Schmitt, R. W. 2003 Observational and laboratory insights into salt finger convection. Prog. Oceanogr. 56, 419–433.CrossRefGoogle Scholar
Schmitt, R. W., Ledwell, J. R., Montgomery, E. T., Polzin, K. L. & Toole, J. M. 2005 Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical atlantic. Science 308 (5722), 685–688.CrossRefGoogle ScholarPubMed
Schmitt, R. W., Perkins, H., Boyd, J. D. & Stalcup, M. C. 1987 C-salt: an investigation of the thermohaline staircase in the western tropical north atlantic. Deep Sea Res. 34 (10), 1655–1665.CrossRefGoogle Scholar
Segre, P. N., Liu, F., Umbanhowar, P. & Weitz, D. A. 2001 An effective gravitational temperature for sedimentation. Nature 409 (6820), 594–597.CrossRefGoogle ScholarPubMed
Stellmach, S., Traxler, A., Garaud, P., Brummell, N. & Radko, T. 2011 Dynamics of fingering convection. Part 2. The formation of thermohaline staircases. J. Fluid Mech. 677, 554–571.CrossRefGoogle Scholar
Stern, M. E. 1960 The salt fountain and thermohaline convection. Tellus 12 (2), 172–175.CrossRefGoogle Scholar
Stern, M. E. 1969 Collective instability of salt fingers. J. Fluid Mech. 35, 209–218.CrossRefGoogle Scholar
Stern, M. E., Radko, T. & Simeonov, J. 2001 Salt fingers in an unbounded thermocline. J. Mar. Res. 59 (3), 355–390.CrossRefGoogle Scholar
Stern, M. E. & Simeonov, J. A. 2002 Internal wave overturns produced by salt fingers. J. Phys. Oceanogr. 32, 3638–3656.2.0.CO;2>CrossRefGoogle Scholar
Stern, M. E. & Turner, J. S. 1969 Salt fingers and convecting layers. Deep Sea Res. 16 (1), 97–511.Google Scholar
Tait, R. I. & Howe, M. R. 1968 Some observations of thermohaline stratification in the deep ocean. Deep Sea Res. 15, 275–280.Google Scholar
Tait, R. I. & Howe, M. R. 1971 Thermohaline staircase. Nature 231 (5299), 178–179.CrossRefGoogle ScholarPubMed
Traxler, A., Stellmach, S., Garaud, P., Radko, T. & Brummell, N. 2011 Dynamics of fingering convection. Part 1. Small-scale fluxes and large-scale instabilities. J. Fluid Mech. 677, 530–553.CrossRefGoogle Scholar
Turner, J. S. 1967 Salt fingers across a density interface. Deep Sea Res. 14 (5), 599.Google Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6 (1), 37–54.CrossRefGoogle Scholar
Turner, J. S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17 (1), 11–44.CrossRefGoogle Scholar
Vauclair, S. 2004 Metallic fingers and metallicity excess in exoplanets’ host stars: the accretion hypothesis revisited. Astrophys. J. 605 (2), 874–879.CrossRefGoogle Scholar
Yoshida, J. & Nagashima, H. 2003 Numerical experiments on salt-finger convection. Prog. Oceanogr. 56 (3), 435–459.CrossRefGoogle Scholar
You, Y. 2002 A global ocean climatological atlas of the Turner angle: implications for double-diffusion and water-mass structure. Deep Sea Res. 49 (11), 2075–2093.CrossRefGoogle Scholar
Yu, X., Hsu, T.-J. & Balachandar, S. 2013 Convective instability in sedimentation: linear stability analysis. J. Geophys. Res. 118, 256–272.CrossRefGoogle Scholar
Yu, X., Hsu, T.-J. & Balachandar, S. 2014 Convective instability in sedimentation: 3-D numerical study. J. Geophys. Res. 119, 8141–8161.CrossRefGoogle Scholar