Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure

Hansen, Ulrich; Yuen, David A.; Kroening, Sherri E.; Larsen, Tine B.

doi:10.1016/0031-9201(93)90099-u

Cited by 126 publications

(57 citation statements)

References 52 publications

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“…Instead, they are swept horizontally to feed into the only coherent lower mantle plume, which thus gathers enough buoyancy to penetrate the phase transition region occasionally. This effect of plume concentration would even be stronger with a pressure-dependent viscosity [26,27]. The tendency towards fewer, deeper-seated plumes at high T 0 is in accordance with data from the Magellan mission, which suggest that there are a few large volcanic swells on Venus [28].…”

Section: Discussionsupporting

confidence: 86%

The influences of surface temperature on upwellings in planetary convection with phase transitions

Steinbach

Yuen

1998

Earth and Planetary Science Letters

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The importance of surface temperature for mantle convection appears with the presence of adiabatic heating and cooling and the release and consumption of latent heat in the presence of phase transitions. For some planetary bodies these effects cannot be neglected. The dimensionless surface temperature T 0 , which is the ratio between the temperature at the top of the convective region and the temperature drop across the mantle, is close to one for Mars and Venus. For the Earth, T 0 lies between 0.2 and 0.5. The dynamical influence of T 0 is especially poignant for internally heated convection with temperature-dependent viscosity. There is a tight coupling between the magnitude of the temperature field and the viscosity itself. We have studied temperature-dependent viscosity convection for both low-T 0 (0.2) and high-T 0 (1.2) situations and with internal heating in mantle convection with two upper-mantle phase transitions. Our results show that within this range of T 0 there exist two regimes for the evolution of upwellings in the mantle. In transient situations plume-plume collisions lead to the formation of megaplumes for high-T 0 regimes but are less likely to do so for low T 0 . In the long-term regime, plumes with low T 0 are prone to develop from the transition zone with a supply of hot material coming from the shallow lower mantle. In systems with high T 0 , however, long-lived plumes tend to have deeper mantle origins. In quasi-layered situations high T 0 may act as a positive feed-back mechanism in inducing powerful hot upwellings into the upper mantle.

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Section: Discussionsupporting

confidence: 86%

The influences of surface temperature on upwellings in planetary convection with phase transitions

Steinbach

Yuen

1998

Earth and Planetary Science Letters

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“…Hansen et al, 1993) and increased thermal conductivity (e.g. van den Berg et al, 2001van den Berg et al, , 2002Dubuffet et al, 2002;Matyska and Yuen, 2006;Naliboff and Kellogg, 2006), which should be present due to the radiative heat transfer.…”

Section: Discussionmentioning

confidence: 99%

Lower-mantle material properties and convection models of multiscale plumes

Matyska

Yuen²

2007

Special Paper 430: Plates, Plumes and Planetary Processes

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We present the results of numerical mantle convection models demonstrating that dynamical effects induced by variable mantle viscosity, depth-dependent thermal expansivity, radiative thermal conductivity at the base of the mantle, the spinel to perovskite phase change and the perovskite to post-perovskite phase transition in the deep mantle can result in multiscale mantle plumes: stable lower-mantle superplumes are followed by groups of small upper-mantle plumes. Both radiative thermal conductivity at the base of the lower-mantle and a strongly decreasing thermal expansivity of perovskite in the lower-mantle can help to induce partially layered convection with intense shear heating under the transition zone, which creates a low viscosity zone and allow for the production of secondary mantle plumes emanating from this zone. Large-scale upwellings in the lower-mantle, which are induced mainly by both the style of lower-mantle viscosity stratification and decrease of thermal expansivity, control position of central upper-mantle plumes of each group as well as the upper-mantle plume-plume interactions.

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“…We have also lent support to this idea of the ability of radiative conductivity to suppress time-dependent flows in the lower mantle by carrying out two separate numerical experiments in which the nonlinear temperature dependent components of the conductivity are switched off in a systematic manner, leaving finally a linear thermal conductivity with only depth-dependence. Therefore, the radiative component of thermal conductivity now joins the ranks of other mantle properties, such as depth-dependent thermal expansivity (Hansen et al, 1993), depth-dependent viscosity (Hansen et al, 1993;Zhang and Yuen 1995;Bunge et al, 1996;Dubuffet et al, 2000c;Forte and Mitrovica, 2001), and endothermic phase transition (Tackley, 1996b), which are all mechanisms responsible for inducing mantle flow to a less chaotic environment with fewer plumes and longer horizontal wavelengths . This tendency is caused by the formation of strong thermal attractors in the solution space, whose physical manifestations are the recurrent plume-plume merging events (Vincent and Yuen, 1988) occurring at nearly the same place in the bottom boundary layer.…”

Section: Discussionmentioning

confidence: 99%

Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity

Dubuffet

Yuen

Rainey

2002

Nonlin. Processes Geophys.

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Abstract. The thermal conductivity of mantle materials has two components, the lattice component k lat from phonons and the radiative component k rad due to photons. These two contributions of variable thermal conductivity have a nonlinear dependence in the temperature, thus endowing the temperature equation in mantle convection with a strongly nonlinear character. The temperature derivatives of these two mechanisms have different signs, with ∂k lat /∂T negative and dk rad /dT positive. This offers the possibility for the radiative conductivity to control the chaotic boundary layer instabilities developed in the deep mantle. We have parameterized the weight factor between k rad and k lat with a dimensionless parameter f , where f = 1 corresponds to the reference conductivity model. We have carried out two-dimensional, time-dependent calculations for variable thermal conductivity but constant viscosity in an aspect-ratio 6 box for surface Rayleigh numbers between 10 6 and 5 × 10 6 . The averaged Péclet P e numbers of these flows lie between 200 and 2000. Along the boundary in f separating the chaotic and steady-state solutions, the P e number decreases and the Nusselt number increases with internal heating, illustrating the feedback between internal heating and radiative thermal conductivity. For purely basal heating situation, the timedependent chaotic flows become stabilized for values of f of between 1.5 and 2. The bottom thermal boundary layer thickens and the surface heat flow increases with larger amounts of radiative conductivity. For magnitudes of internal heating characteristic of a chondritic mantle, much larger values of f , exceeding 10, are required to quench the bottom boundary layer instabilities. By isolating the individual conductive mechanisms, we have ascertained that the lattice conductivity is partly responsible for inducing boundary layer instabilities, while the radiative conductivity and purely depthdependent conductivity exert a stabilizing influence and help to control thermal chaos developed in the deep mantle. These results have been verified to exist also in three-dimensional geometry and would argue for the need to consider the poCorrespondence to: F. Dubuffet (fabien@msi.umn.edu) tentially important role played by radiative thermal conductivity in controlling chaotic flows in time-dependent mantle convection, the mantle heat transfer, the number of hotspots and the attendant mixing of geochemical anomalies.

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Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure

Cited by 126 publications

References 52 publications

The influences of surface temperature on upwellings in planetary convection with phase transitions

The influences of surface temperature on upwellings in planetary convection with phase transitions

Lower-mantle material properties and convection models of multiscale plumes

Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity

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