Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box

Kameyama, Masanori; Ogawa, Masaki

doi:10.1016/s0012-821x(00)00171-0

Cited by 44 publications

(45 citation statements)

References 25 publications

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“…The vertical profiles of Δ h (z) for E 3 have maxima at z = 1. This is consistent with the feature of so-called whole-layer (WH) mode of convection [3,15] occurring with a weakly temperature-dependent viscosity, where the coldest fluid along the top surface is involved in an overall convective motion. For E = 5, in contrast, the profile of Δ h has a local maximum in the mid-depth at around z = 0.6.…”

Section: Control Experiments: Onset Of Convection In a Planar Layersupporting

confidence: 85%

“…Implicit in the above conjecture is the assumption that the two series of changes in convective flow regimes are identical. However, as has been demonstrated from a systematic numerical study for thermal convection with strongly temperature-dependent viscosity in a two-dimensional rectangular box [3], the changes in horizontal and vertical flow structures belong to different series of transitions for convection. In addition, recent numerical studies by using two-dimensional cylindrical [5,7] and three-dimensional spherical shell geometries [17] suggested the existence of convection patterns with large horizontal length scales beneath thick cold thermal boundary layers.…”

Section: Introductionmentioning

confidence: 88%

“…Note again that the Rayleigh number is defined with the viscosity for non-dimensional temperature T = 0.5, which is of little significance to the dominance of the ST convection in a spherical shell geometry (see Sect. 3…”

Section: Empirical Estimates For the Condition For The St-mode For Spmentioning

confidence: 99%

“…The influence of the temperature-dependent viscosity on the pattern of the thermal convection has been investigated mainly by theoretical [19] and numerical [3,9,10,15,16] studies in Cartesian domains. From the changes in vertical flow structures, three convective regimes have been identified depending on the magnitude of temperature dependence of viscosity; the small-viscosity-contrast or whole-layer (WH) regime where convection involves all of the fluid in the vessel, the stagnant-lid (ST) regime where convection occurs only beneath a cold stagnant lid that develops along the surface boundary, and the transitional (TR) regime between the WH and ST regimes.…”

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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Section: Control Experiments: Onset Of Convection In a Planar Layersupporting

confidence: 85%

Section: Introductionmentioning

confidence: 88%

Section: Empirical Estimates For the Condition For The St-mode For Spmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…He discussed the influence of different values for the negative Clausius -Clapeyron slope on the results. Kameyama and Ogawa [2000] then applied that model to a wide box. In the Ogawa [2003b] models, chemical stratification develops regardless of the strength of the olivine barrier and lithospheric plates move if the mass exchange through the 660-km discontinuity is not strongly impeded by the olivine barrier.…”

Section: Chemical Differentiationmentioning

confidence: 99%

Mantle convection and evolution with growing continents

Walzer

Hendel

2008

J. Geophys. Res.

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[1] We present a three-dimensional spherical shell numerical model for chemical differentiation and redistribution of incompatible elements in a convective Earth's mantle heated mostly from within by U, Th, and K and slightly from below. The evolution-model equations guarantee conservation of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs 238 U-206 Pb, 235 U-207 Pb, 232 Th-208 Pb, and 40 K-40 Ar. The pressure-and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, s y . The lithospheric viscosity is partly imposed to mimic its increase by dehydration of oceanic lithosphere and other effects. Also, the asthenosphere is generated not only by the distribution of temperature and melting temperature, but essentially by the profiles of water solubility and water abundance. Therefore we introduced a radial viscosity profile factor describing that behavior. However, the focus of this paper is the episodic growth of continents and oceanic plateaus. As a complement, the differentiation generates the depleted MORB mantle (DMM) which predominates immediately beneath the lithosphere. Our continents are not artificially imposed on the surface of the spherical shell, but instead they evolve by the interplay between chemical differentiation and convection/mixing. No restrictions are imposed regarding number, size, form, and distribution of continents. However, oceanic plateaus that impinge upon a continent have to be united with it. This mimics the accretion of terranes. The numerical results show an episodic growth of the total mass of the continents and display a plausible time history for the laterally averaged surface heat flow, qob, and the Rayleigh number, Ra. We use our model to explore a moderate region of Ra-s y parameter space. We find Earth-like continent distributions in a central part of the Ra-s y space we explored. We identified a Ra-s y region where the calculated total continental volume is very close to the observed value; another Ra-s y region where the Urey number, Ur, is close to the accepted value; a third Ra-s y area where surface heat flow is very close to the present-day observed mean global heat flow using typical abundances of the heat-producing elements. It is remarkable that these different acceptable Ra-s y regions share a common overlap area, where Earth-like behavior is simultaneously fulfilled.Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Ra t , is relatively well predictable and the stochastic parts of the Ra t (t) curves are small. Regarding the time distribution of juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution, presumed that the initial conditions are given. Later on, the distribution of the continental growth episodes is increasingly stochastic. Independent of the varying individual runs, our model shows that the total mass of the presen...

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Mantle evolution in Venus due to magmatism and phase transitions: From punctuated layered convection to whole‐mantle convection

Ogawa

Yanagisawa

2014

JGR Planets

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A series of numerical models of magmatism and mantle convection with a stagnant lithosphere are developed to understand the mantle evolution in Venus. Magmatism is modeled as a permeable flow of basaltic magma generated by decompression melting, and the solid-state convection of mantle materials with temperature-dependent Newtonian rheology is affected by the garnet-perovskite transition and the postspinel transition. In our preferred models, the mantle evolves in two stages: The earlier stage is characterized by layered mantle convection punctuated by repeated bursts of hot material from the deep mantle to the surface. Mantle bursts induce vigorous magmatism and also cause the basaltic crust, enriched in heat-producing elements (HPEs), to recycle into the mantle. A part of the recycled basaltic crusts accumulates along the postspinel boundary to form a barrier, and this basalt barrier causes mantle convection to become layered. At a later stage, when the HPEs have already decayed, in contrast, the basalt barrier disappears and whole-mantle convection occurs more steadily. Mild magmatism is induced by small-scale partial melting at the base of the crust and hot plumes from the deep mantle. The internal heating by the HPEs that recycled into the mantle in the earlier stage allows the magmatism of the later stage to continue throughout the calculated history of mantle evolution. The two stages arise when the barrier effect of the postspinel transition is weak and the lithosphere is mechanically strong enough. The two-stage evolution model meshes with the observed history of magmatism and the lithosphere on Venus.

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Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box

Cited by 44 publications

References 25 publications

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

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

Mantle convection and evolution with growing continents

Mantle evolution in Venus due to magmatism and phase transitions: From punctuated layered convection to whole‐mantle convection

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