Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-mzfmx Total loading time: 0.382 Render date: 2022-08-07T22:44:52.300Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid

Published online by Cambridge University Press:  23 January 2007

CLAUDE JAUPART
Affiliation:
Institut de Physique du Globe de Paris, Paris, 75252 Cedex 05, France
PETER MOLNAR
Affiliation:
Department of Geological Sciences, Cooperative Institute for Research in Environmental Science (CIRES), University of Colorado at Boulder, Boulder, CO 80309-0399, USA
ELIZABETH COTTRELL
Affiliation:
Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA

Abstract

Near the threshold of stability, an intrinsically denser fluid heated from below and underlying an isothermal fluid can undergo oscillatory instability, whereby perturbations to the interface between the fluids rise and fall periodically, or it can be mechanically stable and in thermal equilibrium with heat flux extracted by small-scale convection at the interface. Both the analysis of marginal stability and laboratory experiments in large-Prandtl-number fluids show that the critical Rayleigh number, scaled to parameters of the lower fluid, depends strongly on the buoyancy number, B, the ratio of the intrinsic density difference between the fluids and the maximum density difference due to thermal expansion. For small buoyancy number, B < ∼ 0.1, the critical Rayleigh number, RaC, for oscillatory instability is small RaC < ∼50, and increases steeply for B ∼ 0.25. For B > ∼ 0.5 and RaC > ∼1100, a second form of instability develops, in which convection is confined to the lower layer. The analysis of marginal stability for layers with very different viscosities shows further that two modes of oscillatory instability exist, depending on the value of B. For B < 0.275, the entire lower layer is unstable, and wavelengths of perturbations that grow fastest are much larger than its thickness. For B > 0.275, only the bottom of the lower layer is buoyant, and instability occurs by its penetrating the upper part of the lower layer; the wavelengths of the perturbations that grow fastest are much smaller than those for B < 0.275, and the maximum frequency of oscillatory instability is much larger than that for B < 0.275. Oscillations in the laboratory experiments show that the heights to which plumes of the lower fluid rise into the upper one increase with the Rayleigh number. Moreover, in the finite-amplitude regime, the oscillation is not symmetrical. Plumes that reach maximum heights fall quickly, folding on themselves and entraining some of the upper fluid. Hence oscillatory convection provides a mechanism for mixing the fluids. Applied to the Earth, these results bear on the development of continental lithosphere, whose mantle part is chemically different from the underlying asthenosphere. As shown by the laboratory experiments and stability analysis, the lithosphere can be mechanically stable and in thermal equilibrium such that heat supplied by small-scale convection at the top of the asthenosphere is conducted through it. The lithosphere seems to have developed in a state near that of instability with different thicknesses depending on its intrinsic buoyancy. It may have grown not only by chemical differentiation during melting, but also by oscillatory convection entraining chemically denser material from the asthenosphere.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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

Carlson, R. W., Boyd, F. R., Shirey, S. B., Janney, P. E., Grove, T. L., Bowring, S. A., Schmitz, M. D., Dann, J. C., Pearson, D. G., Bell, D. R., Gurney, J. J., Richardson, S. H., Tredoux, M., Menzies, A. H., Hart, R. J., Wilson, A. H. & Moser, D. 2000 Continental growth, preservation and modification in southern Africa, GSA Today 10, 16.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.Google Scholar
Cottrell, E., Jaupart, C. & Molnar, P. 2004 Marginal stability of thick continental lithosphere, Geophys. Res. Lett. 31, L18612, doi:10.1029/2004GL020332.CrossRefGoogle Scholar
Currie, I. G. 1967 The effect of heating rate on the stability of stationary fluids. J. Fluid Mech. 29, 337347.CrossRefGoogle Scholar
Davaille, A. 1999a Two-layer thermal convection in miscible viscous fluids. J. Fluid Mech. 379, 223253.CrossRefGoogle Scholar
Davaille, A. 1999b Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle. Nature 402, 756760.CrossRefGoogle Scholar
Davaille, A. & Jaupart, C. 1993 Transient high-Rayleigh-number thermal convection with large viscosity variations. J. Fluid Mech. 250, 141166.CrossRefGoogle Scholar
Davaille, A. & Jaupart, C. 1994 Onset of thermal convection in fluids with temperature-dependent viscosity: application to the upper mantle. J. Geophys. Res. 99, 19 85319 866.CrossRefGoogle Scholar
Davaille, A., Girard, F. & Le Bars, M. 2002 How to anchor hotspots in a convecting mantle? Earth Planet. Sci. Lett. 203, 621634.CrossRefGoogle Scholar
Deardorff, J. W., Willis, G. E. & Lilly, D. K. 1969 Laboratory experiments of non-steady penetrative convection. J. Fluid Mech. 35, 731.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Doin, M.-P., Fleitout, L. & McKenzie, D. 1996 Geoid anomalies and the structure of continental and oceanic lithospheres. J. Geophys. Res. 101, 16 11916 135.CrossRefGoogle Scholar
Eglington, B. M. & Armstrong, R. A. 2004 The Kaapvaal Craton and adjacent orogens, southern Africa: a geochronological database and overview of the geological development of the craton. South African J. Geol. 107, 1332.CrossRefGoogle Scholar
Gonnermann, H. M., Manga, M. & Jellinek, A. M. 2002 Dynamics and longevity of an initially stratified mantle. Geophys. Res. Lett. 29 (10), 1399, doi:10.1029/2002GL01485.CrossRefGoogle Scholar
Gung, Y., Panning, M. & Romanowicz, B. 2003 Global anisotropy and the thickness of continents. Nature, 422, 707711.CrossRefGoogle ScholarPubMed
Hirth, G. & Kohlstedt, D. L. 1996 Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere. Earth Planet. Sci. Lett. 144, 93108.CrossRefGoogle Scholar
Houseman, G. A. & Houseman, D. K. 2006 Stability and periodicity in the thermal and mechanical evolution of continental tectonics. Geophys. J. Intl (submitted).Google Scholar
Howard, L. N. 1966 Convection at high Rayleigh numbers. In Proc. 11th Intl Congress of Applied Maths, (ed. Görtler, H.). pp. 11091115. Springer.Google Scholar
Hsui, A. T. & Riahi, D. N. 2001 Onset of thermal chemical convection with crystallization and its geological implications. Geochem. Geophys. Geosyst. 2 (4), doi: 10.1029/2000GC000075.CrossRefGoogle Scholar
Jaupart, C. & Mareschal, J. C. 1999 The thermal structure and thickness of continental roots. Lithos 48, 93114.CrossRefGoogle Scholar
Jaupart, C. & Tait, S. 1995 The dynamics of differentiation in magma chambers. J. Geophys. Res. 100, 17 61517 636.CrossRefGoogle Scholar
Jaupart, C., Mareschal, J. C., Guillou-Frottier, L. & Davaille, A. 1998 Heat flow and thickness of the lithosphere in the Canadian Shield. J. Geophys. Res. 103, 15 26915 286.CrossRefGoogle Scholar
Jellinek, A. M. & Manga, M. 2002 The influence of a chemical boundary layer on the fixity, spacing and lifetime of mantle plumes. Nature 418, 760763.CrossRefGoogle ScholarPubMed
Jellinek, A. M. & Manga, M. 2004 Links between long-lived hot spots, mantle plumes, D'', and plate tectonics. Rev. Geophys. 42, RG3002, doi:10.1029/2003RG000144.CrossRefGoogle Scholar
Jordan, T. H. 1975 The continental tectosphere. Rev. Geophys. Space Phys. 13, 112.CrossRefGoogle Scholar
Jordan, T. H. 1978 Composition and development of the continental tectosphere. Nature 274, 544548.CrossRefGoogle Scholar
Jordan, T. H. 1988 Structure and formation of the continental tectosphere. J. Petrol. Special Lithosphere Issue, pp. 11–37.Google Scholar
Kohlstedt, D. L., Evans, B. & Mackwell, S. J. 1995 Strength of the lithosphere: constraints imposed by laboratory experiments. J. Geophys. Res. 100, 17 58717 602.CrossRefGoogle Scholar
Lay, T., Garnero, E. J., Young, C. J. & Gaherty, J. B. 1997 Scale length of shear velocity heterogeneity at the base of the mantle from S wave differential travel times. J. Geophys. Res. 102, 98879909.CrossRefGoogle Scholar
Le Bars, M. & Davaille, A. 2002 Stability of thermal convection in two superimposed miscible viscous fluids. J. Fluid Mech. 471, 339363.CrossRefGoogle Scholar
Le Bars, M. & Davaille, A. 2004 Large interface deformation in two-layer thermal convection of miscible viscous fluids. J. Fluid Mech. 499, 75110.CrossRefGoogle Scholar
Lister, C. R. B., Sclater, J. G., Davis, E. E., Villinger, H. & Nagihara, S. 1990 Heat flow maintained in ocean basins of great age: investigations in the north-equatorial Pacific. Geophys. J. Intl 102, 603630.CrossRefGoogle Scholar
McNamara, A. K. & Zhong, S. 2004a Thermochemical structures within a spherical mantle: Superplumes or piles? J. Geophys. Res. 109, B07402, doi:10.1029/2003JB002847.CrossRefGoogle Scholar
McNamara, A. K & Zhong, S. 2004b The influence of thermochemical convection on the fixity of mantle plumes. Earth Planet. Sci. Lett. 222, 485500.CrossRefGoogle Scholar
McNamara, A. K. & Zhong, S. 2005 Thermochemical structures beneath Africa and the Pacific Ocean. Nature 437, 11361139.CrossRefGoogle ScholarPubMed
Namiki, A. 2003 Can the mantle entrain D”? J. Geophys. Res. 108 (B10), 2487, doi:10.1029/2002JB002315.CrossRefGoogle Scholar
Namiki, A. & Kurita, K. 2003 Heat transfer and interfacial temperature of two-layered convection: Implications for the D''-mantle coupling. Geophys. Res. Lett. 30 (1), 1023, doi:10.1029/2002GL015809.CrossRefGoogle Scholar
Olson, P. & Kincaid, C. 1991 Experiments on the interaction of thermal convection and compositional layering at the base of the mantle. J. Geophys. Res. 96, 43474354.CrossRefGoogle Scholar
Parsons, B. & McKenzie, D. 1978 Mantle convection and the thermal structure of the plates. J. Geophys. Res. 83, 44854496.CrossRefGoogle Scholar
Parsons, B. & Sclater, J. G. 1977 An analysis of the variation of ocean floor bathymetry and heat flow with age. J. Geophys. Res. 82, 803827.CrossRefGoogle Scholar
Pearson, D. G., Carlson, R. W., Shirey, S. B., Boyd, F. R. & Nixon, P. H. 1995 The stabilisation of Archaean lithospheric mantle: a Re–Os isotope study of peridotite xenoliths from the Kaapvaal craton. Earth Planet. Sci. Lett. 134, 341357.CrossRefGoogle Scholar
Pellew, A. & Southwell, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. Roy. Soc. A 176, 312343.CrossRefGoogle Scholar
Poudjom Djomani, Y. H., O'Reilly, S. Y., Griffin, W. L. & Morgan, P. 2001 The density structure of subcontinental lithosphere through time. Earth Planet. Sci. Lett. 184, 605621.CrossRefGoogle Scholar
Prendergast, M. D. 2004 The Bulawayan Supergroup: a late Archaean passive margin-related large igneous province in the Zimbabwe craton. J. geol. Soc., Lond. 161, 431445.CrossRefGoogle Scholar
Richardson, S. H., Gurney, J. J., Erlank, E. J. & Harris, J. W. 1984 Origin of diamonds in old enriched mantle. Nature 310, 198202.CrossRefGoogle Scholar
Richardson, S. H., Shirey, S. B. & Harris, J. W. 2004 Episodic diamond genesis at Jwaneng, Botswana, and implications for Kaapvaal craton evolution. Lithos 77, 143154.CrossRefGoogle Scholar
Richter, F. M. & Johnson, C. E. 1974 Stability of a chemically layered mantle. J. Geophys. Res. 79, 16351639.CrossRefGoogle Scholar
Rudnick, R. L., McDonough, W. F. & O'Connell, R. J. 1998 Thermal structure, thickness and composition of continental lithosphere. Chem. Geol. 145, 399416.CrossRefGoogle Scholar
Shimizu, K., Nakamura, E., Kobayashi, K. & Maruyama, S. 2004 Discovery of Archean continental and mantle fragments inferred from xenocrysts in komatiites, the Belingwe greenstone belt, Zimbabwe. Geology 32, 285288.CrossRefGoogle Scholar
Shirey, S. B., Harris, J. W., Richardson, S. H., Fouch, M. J., James, D. E., Cartigny, P., Deines, P. & Viljoen, F. 2002 Diamond genesis, seismic structure & evolution of the Kaapvaal-Zimbabwe craton. Science 297, 16831686.CrossRefGoogle ScholarPubMed
Shirey, S. B., Harris, J. W., Richardson, S. H., Fouch, M. J., James, D. E., Cartigny, P., Deines, P. & Viljoen, F. 2003 Regional patterns in the paragenesis and age of inclusions in diamond, diamond composition & the lithospheric seismic structure of Southern Africa. Lithos 71, 243258.CrossRefGoogle Scholar
Tackley, P. J. 1998 Three-dimensional simulations of mantle convection with a thermochemical CMB boundary layer: D"? In The Core–Mantle Boundary Region (ed. Gurnis, M., Wysession, M. E., Knittle, E. & Buffett, B. A.), pp. 231253, American Geophysical Union.CrossRefGoogle Scholar
Tait, S. & Jaupart, C. 1989 Compositional convection in viscous melts. Nature 338, 571574.CrossRefGoogle Scholar
Townsend, A. A. 1964 Natural convection in water over an ice surface. Q. J. R. Met. Soc. 90, 248259.CrossRefGoogle Scholar
Wenzel, M. J., Manga, M. & Jellinek, A. M. 2004 Tharsis as a consequence of Mars' dichotomy and layered mantle. Geophys. Res. Lett. 31, L04702, doi:10.1029/2003GL019306.CrossRefGoogle Scholar
White, D. B. 1988 The planforms and onset of convection with a temperature-dependent viscosity. J. Fluid Mech 191, 247286.CrossRefGoogle Scholar
Worster, M. G. 2004 Time-dependent fluxes across double-diffusive interfaces. J. Fluid Mech. 505, 287307.CrossRefGoogle Scholar
Zaranek, S. E. & Parmentier, E. M. 2004 Convective cooling of an initially stably stratified fluid with temperature-dependent viscosity: implications for the role of solid-state convection in planetary evolution. J. Geophys. Res. 109, B03409, doi:10.1029/2003JB002462.CrossRefGoogle Scholar
Zhong, S. & Hager, B. H. 2003 Entrainment of a dense layer by thermal plumes. Geophys. J. Int. 154, 666676.CrossRefGoogle Scholar
32
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *