Low‐degree mantle convection with strongly temperature‐ and depth‐dependent viscosity in a three‐dimensional spherical shell

Yoshida, Masaki; Kageyama, Akira

doi:10.1029/2005jb003905

Cited by 46 publications

(33 citation statements)

References 36 publications

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“…For instance, for a moderate viscosity contrast, i.e., the sluggish-lid 52 regime, the convection structure can become large-scale (e.g., McNamara and Zhong, 2005; 53 Tackley, 1996b; Yoshida and Kageyama, 2006) whereas convection under the stagnant lid is 54 typically characterized by small-scale convection (Reese et al, 2005;1999). 55…”

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confidence: 99%

Regime classification and planform scaling for internally heated mantle convection

Hüttig¹,

Breuer²

2011

Physics of the Earth and Planetary Interiors

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Abstract:8 Internally heated 3-D mantle convection models in a spherical shell with temperature and 9 pressure dependent viscosity have been performed to provide new insights into the various 10 convection regimes, the transition from steady state convection to time-dependent convection 11 and the associated convection pattern. The analysis of a total of 91 simulations reveals four 12 regime types, i.e., a mobile-lid regime, a sluggish regime, a low-degree regime, and a 13 stagnant-lid regime. The occurrence of these regimes depends on the viscosity contrast and 14 the internal Rayleigh number. The low-degree regime occurs close to the boundary of the 15 stagnant-lid regime in case of temperature dependent viscosity. In case of additional pressure 16 dependence, the range of the low-degree regime is smaller and a narrow range of the sluggish-17 lid regime exists in the weakly convecting part. Furthermore, the transition to the stagnant-lid 18 regime occurs at a lower viscosity contrast.

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confidence: 99%

Regime classification and planform scaling for internally heated mantle convection

Hüttig¹,

Breuer²

2011

Physics of the Earth and Planetary Interiors

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“…14b). In particular, the mode of convection denoted by the squares in the figure has been considered to be identical to the ST mode in most of the earlier studies [13,20,24,28], although it has been reported from two-dimensional convection models with a moderately wide box [3] that the changes from wide to narrow convection cells with increasing r η do not necessarily coincide with that in vertical flow structures.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…14a, the classification of convective regimes, inferred from the changes in the horizontal length scales of convection cells, obtained by earlier numerical experiments of thermal convection in three-dimensional spherical shells [2,13,18,28,31]. Among the symbols in the figure, the triangles indicate the conditions for a so-called "sluggish-lid" (SL) mode of convection which is characterized by convection cells of large horizontal scales (see Fig.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…We also note that, on the other hand, . Circles, triangles, and squares indicate that convective patterns with narrow, wide, and again narrow cells have been reported in earlier studies with increasing r η , respectively; black symbols from [28], blue symbols from [18], green symbols from [31], and red symbols from [2]. For γ = 0.55, in contrast, the values of Ra 2 * c0 moderately vary depending on E with a gradual increase for large E, since the aspect ratio γ 2c0 of the sublayer significantly increases with increasing E for a thick spherical shell.…”

Section: Analytical Estimates For the Condition For The Transition Inmentioning

confidence: 99%

“…Taken together with the two suites of changes in convective flow regimes, it has often been conjectured that the convection with strongly temperature-dependent viscosity is always characterized by narrow convection cells beneath stagnant lids of cold and highly viscous fluid. Moreover, in almost all of the recent numerical models of convection in three-dimensional spherical shells [18,27,28], the reduction in the horizontal length scales of convection cells has been used as the criterion of the transition into the ST regimes, even though in some of these studies [18,28], the relations between the two series of changes were slightly discussed. Implicit in the above conjecture is the assumption that the two series of changes in convective flow regimes are identical.…”

Section: Introductionmentioning

confidence: 99%

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A linear stability analysis on the onset of thermal convection of a fluid with strongly temperature-dependent viscosity in a spherical shell

Kameyama

Ichikawa

Miyauchi

2011

Theor. Comput. Fluid Dyn.

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A linear stability analysis was performed in order to study the onset of thermal convection in the presence of a strong viscosity variation, with a special emphasis on the condition for the stagnant-lid (ST) convection where a convection takes place only in a sublayer beneath a highly viscous lid of cold fluid. We consider the temporal evolution (growth or decay) of an infinitesimal perturbation superimposed to a Boussinesq fluid with an infinite Prandtl number which is in a static (motionless) and conductive state in a basally heated planar layer or spherical shell. The viscosity of the fluid is assumed to be exponentially dependent on temperature. The linearized equations for conservations of mass, momentum, and internal (thermal) energy are numerically solved for the critical Rayleigh number, Ra c , as well as the radial profiles of eigenfunctions for infinitesimal perturbations. The above calculations are repeatedly carried out by systematically varying (i) the magnitude of the temperature dependence of viscosity, E, and (ii) the ratio of the inner and outer radii of the spherical shell, γ . A careful analysis of the vertical structure of incipient flows demonstrated that the dominance of the ST convection can be quantitatively identified by the vertical profile of Δ h (a measure of conversion between horizontal and vertical flows), regardless of the model geometries. We also found that, in the spherical shell relevant to the Earth's mantle (γ = 0.55), the transition into ST convection takes place at the viscosity contrast across the layer r η 10 4 . Taken together with the fact that the threshold value of r η falls in the range of r η for a so-called sluggish-lid convection, our finding suggests that the ST-mode of convection with horizontally elongated convection cells is likely to arise in the Earth's mantle solely from the temperature-dependent viscosity.

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Self‐consistent generation of single‐plume state for Enceladus using non‐Newtonian rheology

et al. 2014

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The thermal dichotomy of Enceladus suggests an asymmetrical structure in its global heat transfer. So far, most of the models proposed that obtained such a distribution have prescribed an a priori asymmetry, i.e., some anomaly in or below the south polar ice shell. We present here the first set of numerical models of convection that yield a stable single-plume state for Enceladus without prescribed mechanical asymmetry. Using the convection code StagYY in a 2-D spherical annulus geometry, we show that a non-Newtonian ice rheology is sufficient to create a localized, single hot plume surrounded by a conductive ice mantle. We obtain a self-sustained state in which a region of small angular extent has a sufficiently low viscosity to allow subcritical to weak convection to occur due to the stress-dependent part of the rheological law. We find that the single-plume state is very unlikely to remain stable if the rheology is Newtonian, confirming what has been found by previous studies. In a second set of numerical simulations, we also investigate the first-order effect of tidal heating on the stability of the single-plume state. Tidal heating reinforces the stability of the single-plume state if it is generated in the plume itself. Lastly, we show that the likelihood of a stable single-plume state does not depend on the thickness of the ice shell.

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Low‐degree mantle convection with strongly temperature‐ and depth‐dependent viscosity in a three‐dimensional spherical shell

Cited by 46 publications

References 36 publications

Regime classification and planform scaling for internally heated mantle convection

Regime classification and planform scaling for internally heated mantle convection

A linear stability analysis on the onset of thermal convection of a fluid with strongly temperature-dependent viscosity in a spherical shell

Self‐consistent generation of single‐plume state for Enceladus using non‐Newtonian rheology

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