Special Effects in Mantle Convection

Here we summarize special physical effects that give mantle convection its unique character. The often subtle interplay between these effects may hold the key to the further understanding of mantle convection.

15.7.1 Solid-state Phase Transformations

From depths of 220-660 km there are increases in density and density discontinuities that require deviations from the adiabatic behavior of an iso-mineralic mantle; this is the transition zone. The behavior of the transition zone can be attributed to either phase changes or changes in composition [Question 9.5]. The shallowest density change at a depth of 220km is known as the Lehmann seismic discontinuity. Both its existence and its origin are controversial [Question 3.3].

The stronger density and seismic discontinuity at a depth of 410 km is attributed to the transformation of olivine to the spinel phase. In equilibrium, the phase boundary would be elevated in the descending slab and would provide additional slab pull. However, if the phase transformation is slow (out of equilibrium), a metastable wedge of olivine could develop in the slab below 410km depth [Questions 4.10, 4.11]. In any case, there is no evidence that this phase boundary significantly influences mantle convection.

The density and seismic discontinuity at a depth of 660 km is another matter. It has long been debated whether this is simply a transformation from spinel to perovskite or if it also includes a change in composition [Questions 3.4, 3.5]. This question is directly related to the question of whether this discontinuity is a barrier to convection [Questions 7.1, 9.6, 9.9, 13.6]. It is certainly a partial barrier and it definitely has an important influence on mantle convection [Questions 4.13, 10.5]. Seismic tomographic data appear to indicate that some, but not all, descending slabs penetrate through this boundary into the lower mantle. If there is a substantial interchange of material between the upper and lower mantle, the mantle will be homogenized and any compositional difference between the upper and lower mantle would be reduced. In this case, the morphological diversity of slab behavior at this boundary must be attributed to the phase change [Question 10.2]. Related questions are whether the partial blockage of convection at this depth (1) requires a thermal boundary layer [Question 4.16], (2) has an influence on the penetration of plumes [Question 9.10], (3) explains the long-wavelength variations in seismic velocity [Question 10.3] and the long-wavelength geoid anomalies [Question 10.6]. Deep earthquakes are also associated with the phase changes, but questions remain about the details of this association [Question 4.12].

Numerical studies of mantle convection indicate that the 660 km phase change may trigger avalanches of material transport between the upper mantle and the lower mantle [Question 10.4]. If these avalanches occur they could explain the episodicity associated with the geological record on the continents [Question 13.10]. Whether or not mantle avalanches are real, models of mantle convection emphasize that the endothermic phase change at 660km depth has a profound influence on the style of mantle convection. The spinel-perovskite phase change tends to oppose the downwelling of cold material and provides an explanation for the seismic tomographic observations of bent and thickened slabs in the transition zone [Question 10.2]. A viscosity increase from the upper mantle to the lower mantle could also account for slab distortion around 660 km depth so it is not certain that the endothermic nature of the spinel-perovskite phase change is the entire explanation of the seismic observations.

The temporary ponding of cold downwelling material above the 660 km phase change imposes a long-wavelength signature on models of mantle convection that can explain the dominance of long wavelengths in spectra of mantle seismic heterogeneity and the geoid [Questions 10.3, 10.6]. Again, it is not certain that the observational data are fully explained by the action of the endothermic phase change alone since other things such as an increase in mantle viscosity with depth, the size of plates, and the ocean-continent dichotomy also impose a long-wavelength pattern on mantle convection.

15.7.2 Variable Viscosity: Temperature, Pressure, Depth

Variations of mantle viscosity with temperature, pressure, mineralogy, and volatile content combine to produce lateral and radial changes in mantle viscosity. Together with the phase changes in the transition zone, viscosity variations with temperature and depth provide the most important control on the nature of mantle convection [Questions 9.7, 9.12]. We have already noted in the previous section how an increase of viscosity from the upper mantle to the lower mantle could deform and broaden slabs and impose a long-wavelength structure on mantle convection. An important question is whether the 660 km phase change results directly in an increase in viscosity [Question 5.8]. A high viscosity in the lower mantle could also reduce the amount of convective mixing by the mantle and preserve geochemical reservoirs over long periods of time; a high lower mantle viscosity could also help to explain the relative fixity of mantle plumes. The present consensus about mantle viscosity is that the lower mantle is more viscous than the upper mantle, but the amount of the increase and other details about the variation of mantle viscosity with depth are uncertain [Questions 5.4, 13.5]. Studies using postglacial rebound data tend to indicate some viscosity increase with depth in the mantle, whereas inversions of geoid data favor a larger increase [Question 10.8].

Models of mantle convection with strongly temperature dependent viscosity reveal three regimes of convection - constant viscosity, sluggish lid, and stagnant lid. The different convection regimes feature different convective planforms and efficiencies of heat transfer. The Earth is in the constant viscosity convection regime, because nonviscous crustal and litho-spheric deformation facilitates plate subduction. The sluggish-lid or stagnant-lid convection regimes may pertain to other planets such as Venus.

15.7.3 Nonlinear Viscosity

An important question is whether the mantle viscosity is Newtonian (linear) or non-Newtonian (nonlinear) [Question 5.7]. This is directly related to the question of whether the dominant mechanism for solid-state creep in the mantle is diffusion creep or dislocation creep [Question 5.6]. Diffusion creep gives a Newtonian behavior and dislocation creep gives a nonlinear, non-Newtonian behavior. Studies of postglacial rebound strongly favor a linear rheology, whereas laboratory studies suggest the applicability of the nonlinear dislocation creep mechanism. If the governing mechanism is diffusion creep there may be a significant dependence on grain size [Question 5.5]. In order to do detailed and realistic numerical calculations of mantle convection, it is also necessary to specify the rheology of the crust and mantle lithosphere [Question 9.1].

Two-dimensional Cartesian models of convection with non-Newtonian viscosity emphasize the importance of simultaneously accounting for the dependence of viscosity on temperature and pressure when assessing effects of the stress dependence of viscosity on convection [Question 9.11]. When viscosity depends on temperature, pressure, and stress, the effect of the stress dependence is to moderate the influence of temperature and pressure. Stated another way, a convective flow with temperature-, pressure-, and stress-dependent viscosity has a Newtonian viscous counterpart with a viscosity that depends more weakly on temperature and pressure. Convection with non-Newtonian viscosity has smaller internal viscosity variation than would be predicted on the basis of temperature and pressure variations alone. If the dependence of viscosity on temperature and pressure is of the Arrhenius type with an activation enthalpy, then the Newtonian analogue of the non-Newtonian flow has an activation enthalpy only about half as large as that of the nonlinear flow.

The effects of nonlinear viscosity on convection need to be determined for three-dimensional flows. A few steady-state three-dimensional solutions with non-Newtonian, power-law viscosity are in the literature and the effect of a non-Newtonian surface sheet on three-dimensional convection has also been studied. However, there are no studies of three-dimensional convection with non-Newtonian viscosity in vigorously convecting, time-dependent cases. It is possible that nonlinear viscosity will influence three-dimensional convection in unanticipated ways because of the spatial complexity of flow patterns in three dimensions. However, as the two-dimensional calculations emphasize, this should be done by simultaneously incorporating the temperature and pressure dependence of viscosity and probably compressibility as well. Compressibility and nonlinear viscosity are tied together through the influence of viscous dissipation on compressible convection and through the dependence of viscosity on temperature and pressure. If the combined effect of all the variables which influence viscosity is to moderate viscosity variations in the flow, then mantle convection may be closer to constant viscosity convection than would be expected on the basis of the individual dependences of mantle viscosity on temperature, pressure, and stress.

15.7.4 Compressibility

Compressibility is significant in mantle convection because the density of the Earth's mantle increases by about 60% from the top of the mantle to the bottom (accounting for phase and/or compositional changes). The effects of compressibility have been considered in two-dimensional Cartesian and axisymmetric studies of convection and in three-dimensional studies. Compressible models of convection must also incorporate viscous dissipation to be valid [Question 10.11].

Compressibility has dramatic effects on convection only when the superadiabatic temperature change across the spherical shell is small compared with the adiabatic temperature change. In the Earth's mantle, the superadiabatic temperature change is comparable to the adiabatic temperature change and compressibility should not particularly influence convection.

The results of some numerical models suggest that compressibility might stabilize the bottom of the mantle and lead to penetrative convection. In some two-dimensional, plane layer, liquid anelastic models the dissipation number is assumed constant and the magnitude of the adiabatic temperature gradient increases exponentially with depth. The stabilization of the bottom of the layer in this model is a consequence of the steep adiabat. The adiabat in the Earth's mantle does not steepen in this manner with depth and compressibility does not stabilize the lower mantle. A form of penetrative convection in the Earth's lower mantle has been suggested, but this is associated with density changes across 660 km depth. Realistic variations with depth in the density and thermal structure of the deep mantle as a consequence of compressibility do not lead to stabilization and penetrative convection in the lower mantle.

Laboratory experiments and theoretical studies have shown that thermal expansivity in the Earth's mantle decreases with depth due to the compressibility of rocks under high pressure [Question 9.12]. This effect has been incorporated into two-dimensional numerical models of compressible convection which show that it is a significant influence on the style of convection (e.g., the occurrence and structure of plumes). A decrease of thermal expansivity with depth is a standard feature in most three-dimensional compressible convection models. While the depth dependence of thermal expansivity must be accounted for in realistic models of mantle convection, the variation of thermal expansivity with depth is not a major influence on the style of compressible convection. Variations in viscosity with depth are much more important.

Compressibility affects convection through the complex interplay of a number of material properties and the distribution of heat sources, but overall, the effects of compressibility on mantle convection appear to be relatively minor. The interpretation of the seismic velocity anomalies obtained in mantle tomography requires an understanding of the relative roles of temperature, composition, and melting [Questions 5.2, 9.2].

15.7.5 Viscous Dissipation

The role of viscous heating in mantle convection has been studied in several compressible convection models. Viscous dissipation in these models is significant in small-scale structures such as boundary layers, plumes, and sheet-like downflows [Question 9.13]. Viscous heating is strong where upwelling plumes meet the top thermal boundary layer. Accordingly, viscous heating could play an important role in lithospheric thinning.

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