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

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid,10.1017/S0022112006003521,Journal of Fluid Mechani

Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid   (Citations: 6)
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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, Ra_C , for oscillatory instability is small Ra_C {} {˜}0.5 and Ra_C {>} {˜}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, 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.
Journal: Journal of Fluid Mechanics - J FLUID MECH , vol. 572, pp. 433-469, 2007
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    • ...The two important compositional parameters are the buoyancy ratio B (i.e., the chemical density contrast between dense and regular material relatively to the total thermal density contrast), and the volume fraction of dense material, X. The buoyancy ratio controls the amplitude of the deformation of the dense layer (e.g., Davaille, 1999; McNamara and Zhong, 2004; Jaupart et al., 2007)...
    • ...Linear stability analysis and analogical experiments (Jaupart et al., 2007) and numerical experiments with spherical geometry (McNamara and Zhong, 2004) suggest that the effects of the volume fraction are of second order compared to those of the buoyancy ratio...
    • ...good agreement with the analogue experiments of Jaupart et al. (2007)...

    Frédéric Deschampset al. Searching for models of thermo-chemical convection that explain probab...

    • ...Recent analogue experiments and stability analysis (Jaupart et al., 2007) suggest that continental lithosphere is close to the instability of thermochemical convection, and may have grown by successive episodes of oscillatory convection...

    Frédéric Deschampset al. Stratified seismic anisotropy reveals past and present deformation ben...

    • ...To put this issue into context, we note that the gravitationally unstable thermal boundary at the base of the lithosphere drives convection in the form of drips beneath both cratons and platforms (Figure 2) [Jaupart et al., 2007]...
    • ...Jaupart et al. [2007] address the effect of stabilizing chemical buoyancy due to a deformable chemical layer on transient isoviscous thermal convection from a heated boundary...

    Norman H. Sleepet al. Scaling relationships for chemical lid convection with applications to...

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