Heat transport in stagnant lid convection with temperature‐ and pressure‐dependent Newtonian or non‐Newtonian rheology

Dumoulin, Caroline; Doin, Marie‐Pierre; Fleitout, Luce

doi:10.1029/1999jb900110

Cited by 132 publications

(89 citation statements)

References 64 publications

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“…These numbers are in good agreement with the general scaling laws for convection with large viscosity contrasts which suggest qÁT u % 2.2 -2.6 and qÁT l % 1.1 -1.3 [Davaille and Jaupart, 1993;Manga et al, 2001;Grasset and Parmentier, 1998;Trompert and Hansen, 1998;Dumoulin et al, 1999;Solomatov and Moresi, 2000].…”

Section: Thermal Boundary Layerssupporting

confidence: 74%

“…Application of stagnant lid convection theory to small-scale convection in the asthenosphere gives similar estimates [Davaille and Jaupart, 1994;Doin et al, 1997;Dumoulin et al, 1999;Solomatov and Moresi, 2000]. This is consistent with the idea that the temperature in both regions is close to solidus provided the mantle viscosity is nearly constant along solidus.…”

Section: Viscositysupporting

confidence: 73%

“…However, a simple criterion based on this and other studies [Dumoulin et al, 1999] can be suggested: The transition occurs when the thickness of the convective layer is $4 times larger than the critical one for the onset of convection.…”

Section: Transition To Chaotic Regimementioning

confidence: 99%

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Small‐scale convection in the D″ layer

Solomatov

Moresi

2002

J. Geophys. Res.

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[1] Small-scale convection has been suggested as a possible explanation for seismic heterogeneities in the D 00 layer of the Earth's mantle. Recently developed scaling laws for convection with realistic viscosities allow quantitative assessment of this hypothesis. Large temperature and viscosity contrasts across the thermal boundary layer at the core-mantle boundary suggest that small-scale convection starts at the bottom of the thermal boundary layer and propagates upward before the thermal boundary layer as a whole becomes unstable. The convection boundary is likely to become a chemical boundary as a result of mixing within the convective layer. This implies that the D 00 discontinuity can represent both convective and chemical boundary and that the presence or absence of small-scale convection can be responsible for the observed intermittent nature of the D 00 discontinuity. Most lateral heterogeneities in the D 00 layer are concentrated near the convection boundary, consistent with seismic data. The length scale of lateral temperature variations, the topography of the core-mantle boundary, and the viscosity of the D 00 layer are in agreement with observational constraints. The thickness of the secondary thermal boundary layer formed at the bottom of the convective layer is similar to the thickness of the ultralow-velocity zone. The magnitude of lateral variations in temperature can only marginally be responsible for lateral variations in seismic velocities. Variations in the topography of the convection boundary and chemical heterogeneities are likely to be more important factors. A large seismic velocity drop in the ultralow-velocity zone cannot be explained by thermal effects alone and must be caused by other factors such as partial melting.

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Section: Thermal Boundary Layerssupporting

confidence: 74%

Section: Viscositysupporting

confidence: 73%

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Small‐scale convection in the D″ layer

Solomatov

Moresi

2002

J. Geophys. Res.

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“…(46). If the pseudolinear assumption holds, the heat flow is predicted to be in the region defined by straight lines for linear scaling results of (D&J) Jaupart [1993a, 1993b], (D) Dumoulin et al [1999], and (S&M) Solomatov and Moresi [2000]. Models assuming n = 3 and T h = 60 K (solid squares), n = 3 and T h = 40 K (crosses) define the same trend, which intersects the pseudolinear region at Å t = 0.06.…”

Section: Parameterized Convection With Strong Basal Dragmentioning

confidence: 99%

“…I include depth-dependent viscosity in equations (12) - (15) by letting h H be the viscosity at the base of the boundary layer and by replacing all T h (outside the exponential) with T A . I note that Dumoulin et al [1999] considered the geothermal gradient at the top of the boundary layer T H /Z H to obtain equation (16) without the factor of 2.…”

Section: Parameterized Convection With Weak Basal Dragmentioning

confidence: 99%

Survival of Archean cratonal lithosphere

2003

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[1] I use thermal convection models to search for combinations of physical parameters that are compatible with the results of xenolith studies on the history and present thermal structure of cratonal lithosphere. The cratonal lithosphere above $180 km depth formed in the Archean and remained stable until recently sampled. The mantle adiabat cooled $150 K over this time. The temperature change across the rheologically active boundary layer at the lithospheric base is <300 K over a depth range of several tens of kilometers. Modern cratonal lithospheric thicknesses are relatively uniform, $225 km, much thicker than old oceanic lithosphere. Cratonal lithosphere is now in quasi-steady state with conductive heat flow to the surface in balance with heat supplied to the base of the lithosphere by convection driven by local temperature contrasts within the rheologically active boundary layer. This heat flow and the lithosphere thickness changed little after the cratonal lithosphere stabilized. One possibility is that chemically buoyant lithosphere forms a conductive lid above the convecting normal mantle. To survive, the chemical lithosphere also needs to be more viscous than normal mantle. A reasonable situation has chemical lithosphere a factor of 20 more viscous than normal mantle with weakly temperature-dependent viscosity (a factor of e over 100 K) from 0.2 Â 10 20 Pa s along the modern mantle adiabat. However, a chemical lid is unnecessary for lithospheric thickness to change slowly over time. For example, the base of the lithosphere may be stable if the viscosity at its base (along an adiabat) decreases rapidly with depth.

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Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Yao¹,

Deschamps

Lowman

et al. 2014

J. Geophys. Res. Planets

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(2014), Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons, J. Geophys. Res. Planets, 119, 1895-1913, doi:10.1002 Abstract Because the viscosity of ice is strongly temperature dependent, convection in the ice layers of icy moons and dwarf planets likely operates in the stagnant lid regime, in which a rigid lid forms at the top of the fluid and reduces the heat transfer. A detailed modeling of the thermal history and radial structure of icy moons and dwarf planets thus requires an accurate description of stagnant lid convection. We performed numerical experiments of stagnant lid convection in 3-D spherical geometries for various ice shell curvatures f (measured as the ratio between the inner and outer radii), effective Rayleigh number Ra m , and viscosity contrast Δ . From our results, we derived scaling laws for the average temperature of the well-mixed interior, m , and the heat flux transported through the shell. The nondimensional temperature difference across the bottom thermal boundary layer is well described by (1 − m ) = 1.23 f 1.5 , where is a parameter that controls the magnitude of the viscosity contrast. The nondimensional heat flux at the bottom of the shell, F bot , scales as F bot = 1.46Ra 0.27 m 1.21 f 1.78 . Our models also show that the development of the stagnant lid regime depends on f . For given values of Ra m and Δ , the stagnant lid is less developed as the shell's curvature increases (i.e., as f decreases), leading to improved heat transfer. Therefore, as the outer ice shells of icy moons and dwarf planets grow, the effects of a stagnant lid are less pronounced.

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Heat transport in stagnant lid convection with temperature‐ and pressure‐dependent Newtonian or non‐Newtonian rheology

Cited by 132 publications

References 64 publications

Small‐scale convection in the D″ layer

Small‐scale convection in the D″ layer

Survival of Archean cratonal lithosphere

Stagnant lid convection in bottom-heated thin 3-D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

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