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(6)
Heat Flux
Laboratory Experiment
Oscillations
Stability Analysis
Thermal Expansion
Viscous Fluid
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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
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Instability of a chemically dense layer heated from below and overlain by a deep less viscous fluid
(
Citations: 6
)
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Claude Jaupart
,
Peter Molnar
,
Elizabeth Cottrell
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 smallscale convection at the interface. Both the analysis of marginal stability and laboratory experiments in largePrandtlnumber 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 finiteamplitude 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 smallscale 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. 433469, 2007
DOI:
10.1017/S0022112006003521
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Citation Context
(3)
...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 Deschamps
,
et al.
Searching for models of thermochemical 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 Deschamps
,
et 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. Sleep
,
et al.
Scaling relationships for chemical lid convection with applications to...
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Citations
(6)
Thermal evolution of cratonic roots
(
Citations: 9
)
Chloe Michaut
,
Claude Jaupart
,
JeanClaude Mareschal
Journal:
Lithos
, vol. 109, no. 1, pp. 4760, 2009
Searching for models of thermochemical convection that explain probabilistic tomography. II—Influence of physical and compositional parameters
(
Citations: 8
)
Frédéric Deschamps
,
Paul J. Tackley
Journal:
Physics of The Earth and Planetary Interiors  PHYS EARTH PLANET INTERIORS
, vol. 176, no. 1, pp. 118, 2009
Stratified seismic anisotropy reveals past and present deformation beneath the Eastcentral United States
(
Citations: 10
)
Frédéric Deschamps
,
Sergei Lebedev
,
Thomas Meier
,
Jeannot Trampert
Journal:
Earth and Planetary Science Letters  EARTH PLANET SCI LETT
, vol. 274, no. 3, pp. 489498, 2008
Scaling relationships for chemical lid convection with applications to cratonal lithosphere
(
Citations: 9
)
Norman H. Sleep
,
A. Mark Jellinek
Journal:
Geochemistry Geophysics Geosystems  GEOCHEM GEOPHYS GEOSYST
, vol. 9, no. 12, 2008
Searching for models of thermochemical convection that explain probabilistic tomography
(
Citations: 2
)
Frédéric Deschamps
,
Paul J. Tackley
Journal:
Physics of The Earth and Planetary Interiors  PHYS EARTH PLANET INTERIORS
, vol. 171, no. 1, pp. 357373, 2008