Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid | INSTITUT DE PHYSIQUE DU GLOBE DE PARIS

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

Type de publication:

Journal Article

Source:

Journal of Fluid Mechanics, Volume 572, p.433-469 (2007)

ISBN:

0022-1120

URL:

http://uk.cambridge.org/journals/flm

Mots-clés:

PLUMES

Résumé:

<p>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 &lt; similar to 0.1, the critical Rayleigh number, Ra-C, for oscillatory instability is small Ra-C &lt; similar to 50, and increases steeply for B similar to 0.25. For B &gt; similar to 0.5 and Ra-C &gt; similar to 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 &lt; 0.275, the entire lower layer is unstable, and wavelengths of perturbations that grow fastest are much larger than its thickness. For B &gt; 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 &lt; 0.275, and the maximum frequency of oscillatory instability is much larger than that for B &lt; 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.</p>

Notes:

J. Fluid Mech.ISI Document Delivery No.: 139MATimes Cited: 0Cited Reference Count: 59Cited References:CARLSON RW, 2000, GSA TODAY, V10, P1CHANDRASEKHAR S, 1961, HYDRODYNAMICS HYDROMCOTTRELL E, 2004, GEOPHYS RES LETT, V31CURRIE IG, 1967, J FLUID MECH, V29, P337DAVAILLE A, 1993, J FLUID MECH, V253, P141DAVAILLE A, 1994, J GEOPHYS RES-SOL EA, V99, P19853DAVAILLE A, 1999, J FLUID MECH, V379, P223DAVAILLE A, 1999, NATURE, V402, P756DAVAILLE A, 2002, EARTH PLANET SC LETT, V203, P621DEARDORFF JW, 1969, J FLUID MECH, V35, P7DJOMANI YHP, 2001, EARTH PLANET SC LETT, V184, P605DOIN MP, 1996, J GEOPHYS RES-SOL EA, V101, P16119DRAZIN PG, 1981, HYDRODYNAMIC STABILIEGLINGTON BM, 2004, S AFR J GEOL, V107, P13GONNERMANN HM, 2002, GEOPHYS RES LETT, V29GUNG YC, 2003, NATURE, V422, P707HIRTH G, 1996, EARTH PLANET SC LETT, V144, P93HOUSEMAN GA, 2006, UNPUB GEOPHYS J INTHOWARD LN, 1966, P 11 INT C APPL MECH, P1109HSUI AT, 2001, GEOCHEM GEOPHY GEOSY, V2JAUPART C, 1995, J GEOPHYS RES-SOL EA, V100, P17615JAUPART C, 1998, J GEOPHYS RES-SOL EA, V103, P15269JAUPART C, 1999, LITHOS, V48, P93JELLINEK AM, 2002, NATURE, V418, P760JELLINEK AM, 2004, REV GEOPHYS, V42JORDAN TH, 1975, REV GEOPHYS SPACE PH, V13, P1JORDAN TH, 1978, NATURE, V274, P544JORDAN TH, 1988, J PETROL, P11KOHLSTEDT DL, 1995, J GEOPHYS RES, V100, P587LAY T, 1997, J GEOPHYS RES-SOL EA, V102, P9887LEBARS M, 2002, J FLUID MECH, V471, P339LEBARS M, 2004, J FLUID MECH, V499, P75LISTER CRB, 1990, GEOPHYS J INT, V102, P603MCNAMARA AK, 2004, EARTH PLANET SC LETT, V222, P485MCNAMARA AK, 2004, J GEOPHYS RES-SOL EA, V109MCNAMARA AK, 2005, NATURE, V437, P1136NAMIKI A, 2003, GEOPHYS RES LETT, V30NAMIKI A, 2003, J GEOPHYS RES-SOL EA, V108OLSON P, 1991, J GEOPHYS RES-SOLID, V96, P4347PARSONS B, 1977, J GEOPHYS RES, V82, P803PARSONS B, 1978, J GEOPHYS RES, V83, P4485PEARSON DG, 1995, EARTH PLANET SC LETT, V134, P341PELLEW A, 1940, PROC R SOC LON SER-A, V176, P312PRENDERGAST MD, 2004, J GEOL SOC LONDON 3, V161, P431RICHARDSON SH, 1984, NATURE, V310, P198RICHARDSON SH, 2004, LITHOS, V77, P143RICHTER FM, 1974, J GEOPHYS RES, V79, P1635RUDNICK RL, 1998, CHEM GEOL, V145, P399SHIMIZU K, 2004, GEOLOGY, V32, P285SHIREY SB, 2002, SCIENCE, V297, P1683SHIREY SB, 2003, LITHOS, V71, P243TACKLEY PJ, 1998, CORE MANTLE BOUNDARY, P231TAIT S, 1989, NATURE, V338, P571TOWNSEND AA, 1964, QUARTERLY J ROYAL ME, V90, P248WENZEL MJ, 2004, GEOPHYS RES LETT, V31WHITE DB, 1988, J FLUID MECH, V191, P247WORSTER MG, 2004, J FLUID MECH, V505, P287ZARANEK SE, 2004, J GEOPHYS RES-SOL EA, V109ZHONG SJ, 2003, GEOPHYS J INT, V154, P666