D. A. Yuen

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

The effects of both depth-dependent thermal expansivity and depth-dependent viscosity on mantle convection have been examined with two-dimensional finite-element simulations in aspect-ratio ten boxes. Surface Rayleigh numbers between 107 and 6 × 107 have been considered. The effects of depth-dependent properties, acting singly or in concert, are to produce large-scale circulations with a few major upwellings. The interior of the mantle is cooled by the many cold instabilities, which are slowed down and eventually swept about by the large-scale circulation. The interior temperature of the mantle can be influenced by the trade-off between depth-dependent properties and internal heating. For chondritic abundance of internal-heating and depth-dependent thermal expansivity, the viscosity increase across the mantle can be no greater than a factor of around ten in order to keep the lower mantle adiabatic. The thermal contrasts between the cold blobs and the surrounding mantle are strongly reduced by depth-dependent properties, whereas the lateral differences between the hot upwelling and the ambient lower mantle can be significant, over several hundred degrees. Depth-dependent properties also encourage the formation of a stronger mean-flow in the upper mantle, which may be important for promoting long-term polar motions.

Rheological control of oceanic crust separation in the transition zone

Mineral physics observations suggest that distinct density and rheological differences exist between the crustal component of oceanic lithosphere and the underlying mantle. We have conducted numerical experiments to investigate the influence of both density and viscosity on the effectiveness of recycling of oceanic crust into the lower mantle. Confirming previous results, the density inversion at 670 km depth alone is not sufficient to prevent crustal recycling. However, a soft layer may exist between the strong garnet crust and cold slab interior. Models employing a simplified Newtonian sandwich model show that this thin, weak layer can effectively decouple the crust and slab. Once entrained into the lower mantle, the then lighter crust can rise sufficiently fast as a Rayleigh-Taylor instability to avoid further entrainment. These results suggest that the crustal component of slabs may be trapped at 670 km depth, leading to a garnet enriched transition zone.

Various influences on three-dimensional mantle convection with phase transitions

Abstract Three-dimensional numerical calculations of mantle convection with the two major phase transitions have been carried out in a 5 × 5 × 1 configuration to study the effects of increasing vigor of convection, internal heating and extremely negative Clapeyron slope of the spinel-perovskite phase transition. Depth-dependent properties of thermal expansivity, viscosity and thermal conductivity have been incorporated. Three-dimensional solutions for surface Rayleigh number (Ra s ) between 2 × 10 6 and 4 × 10 8 show that there is a distinct transition between Ra s = 4 × 10 7 and 10 8 in which the system changes from single-layered to layered convection with the mass flux decreasing to below 10% at Ra s = 10 8 . Surface heat flux does not decrease with increasing Ra s and with the accompanying decrease in the mass flux at the transition zone. The effects of internal heating are to reduce the wavelengths of the planforms which cause greater degree of layering in the system. Comparison between 2D and 3D results shows that there is a greater mass flux passing through the transition zone in the 2D models for the 5 × 5 × 1 ☐, but for larger aspect ratio (8 × 8 × 1) the 3D flows become more layered than the corresponding 2D solution. Increasing the magnitude of the negative Clapeyron slope by three times the experimental value can bring about a dramatic reduction in the amount of mass flux across the 670 km discontinuity. Results from a 8 × 8 × 1 ☐ show that a greater amount of layering is produced in the larger aspect-ratio configuration because of the shorter wavelengths of the developed planforms. Increasing the degrees of freedom in a 3D system by either greater amounts of convective vigor or arger domains may give rise to a greater tendency for layered convection. Three-dimensional spherical shell models may produce a greater degree of layering than the corresponding axisymmetric models.

Time‐domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a contrast of O(10 2 ) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(10 2 ) and O(10 4 ) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes

Non-linear effects from variable thermal conductivity and mantle internal heating: implications for massive melting and secular cooling of the mantle

Abstract The temperature-dependence of the phonon portion of the thermal conductivity k ( T , P ) devised by Hofmeister [Science 283 1699-1706] decreases with temperature, the same as in the dependence of mantle viscosity. Such a functional relationship of ∂k / ∂T ∂k / ∂T >0. Thus, there can be a tradeoff between the phonon and photon contributions in the conductivity in the presence of internal heating. We have conducted two-dimensional calculations of mantle convection up to a surface Rayleigh number of around five million and an internal heating of chondritic abundance, with the extended-Boussinesq approximation in which the dissipation number has been set to 0.47 and depth-dependent thermal expansivity, decreasing by a factor of 5 across the mantle. The value of the constant mantle viscosity and the amount of internal heating are varied. For an enhanced radiative contribution [J. Geophys. Res. 84 (B4) 1603-1610] the radiative component of the thermal conductivity can exceed the phonon contribution in the upper mantle. Our results show that in all cases with basal heating the average mantle temperature of the variable conductivity models are higher than those of the corresponding constant conductivity models. But the interior thermal difference between the two conductivity models decreases (1) with greater vigor of convection, (2) an increase of internal heating and (3) an increase in the radiative contribution to the conductivity. The interior mantle temperature is significantly hotter, more than 500xa0°C, than the constant conductivity model, for the k ( T , P ) model with the less enhanced radiative component [Science 283 1699–1706]. These results would suggest that some sort of massive melting in the young earth might have occurred with k ( T , P ) and that there should not be so much radioactivity in the lower mantle today without incurring the wrath of some melting. We have also studied the effects of k ( T , P ) on slowing down the mantle secular cooling process by monitoring the gradual decrease in mantle temperature following an imposition of an adiabatic boundary condition at the core-mantle boundary. A decay time of 3.6xa0Gy has been taken for the mantle radioactivity and we have varied the initial amount of radioactive heating from chondritic value to four times the chondritic value. A significant delay in the cooling process of at least 1–2xa0Gy is found for a surface Rayleigh number of between 5×10 6 to 5×10 7 . The mantle temperature can be heated up by 300–400xa0°C for initial radiogenic heating value characteristic of the Archean. We find the strongest deviations from the constant conductivity case for a silicate model by Hofmeister [Science 283 1699-1706] and intermediate values for an enhanced radiative conductivity model comparable to the model of Shankland et al. [J. Geophys. Res. 84 (B4) 1603-1610]. Such high mantle temperatures maintained for a long time by variable thermal conductivity would have important consequences on the thermal and petrological evolution of the mantle.

Localization of toroidal motion and shear heating in 3-D high Rayleigh number convection with temperature-dependent viscosity

We have applied spectral-transform methods to study three-dimensional thermal convection with temperature-dependent viscosity. The viscosity varies exponentially with the form exp(-BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25×106, have been obtained for an aspect-ratio of 5×5×1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear-zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time-varying depth-dependent mean-flow is generated because of the correlation between laterally varying viscosity and velocity gradients.

Focussed time‐dependent martian volcanism from chemical differentiation coupled with variable thermal conductivity

Recently the Orbiter Camera on the Mars Global Surveyor imaged on some lava flows. The sparse cratering and thence young age of these flows indicates that volcanic activity on Mars is long-lived and perhaps pulsating. These pulses beg for an explanation, not yet provided by one-dimensional convection models simulating the thermal and compositional evolution of the Martian interior. We have, for the first time, simulated the thermochemical evolution of Mars with a two-dimensional model for the entire planetary history. Our results show that variable thermal conductivity k(T, P) can maintain sublithospheric “hot spots” over time scales of several hundred Ma and is essential in the focussing of hot mantle upwellings at almost the same location. This scenario can explain the persistent pulsating and focussed volcanism in the Tharsis region.

Is the long‐wavelength geoid sensitive to the presence of postperovskite above the core‐mantle boundary?

[1] The analysis of seismic data represents today the primary tool in the search for the presence of postperovskite in the lowermost mantle (D 00 ). This work aims at testing whether the inversion of gravitational data can also contribute to the detection of postperovskite in D 00 .W e assume that the transition from perovskite to postperovskite is accompanied by a reduction in viscosity and test the effects of such viscosity change on the prediction of the dynamic geoid with a numerical model of subducted lithosphere. Our results show that the long-wavelength component of the geoid is very sensitive to the presence of postperovskite areas in D 00 , especially if their viscosity is significantly lower than the viscosity of the surrounding perovskite and if these areas are located close to density � � � � � � � � � � � � � � � � � � � � � ��

Interplay of variable thermal conductivity and expansivity on the thermal structure of oceanic lithosphere

We have extended our previous analysis of the effects of constant vs. variable, i.e., pressure and temperature dependent thermal conductivity (k) and constant thermal expansivity (α) on the thermal structure of the oceanic lithosphere. We apply our analysis to the actual data set including information on the geoid slope. The heat flow and ocean floor depth data constrain the thermal expansivity (α ≈ 3 × 10−5 1/°C). Including geoid slope data may loosely constrain both the thermal expansivity and the thermal conductivity. The probable value of thermal conductivity is ≈3 W/m/°C for the constant k case and ≈4 W/m/°C (at ambient conditions) for the variable k case. These a and k are generally consistent with laboratory data of appropriate lithospheric materials. Our analysis supports the plate model with thin lithosphere and high bottom temperature, such as GDH1 (95 km; 1450°C). Variable k case requires slightly thinner and higher temperature lithosphere (≈85 km and ≈1500°C) and gives a slightly better fit to the geoid slope data.

The influences of composition-sand temperature-dependent rheology in thermal-chemical convection on entrainment of the D -layer

Abstract The entrainment dynamics in the D″-layer are influenced by multitudinous factors, such as thermal and compositional buoyancy, and temperature-xa0and composition-dependent viscosity. Here, we are focusing on the effect of compositionally dependent viscosity on the mixing dynamics of the D″-layer, arising from the less viscous but denser D″-material. The marker method, with one million markers, is used for portraying the fine scale features of the compositional components, D″-layer and lower-mantle. The D″-layer has a higher density but a lower viscosity than the ambient lower-mantle, as suggested by melting point systematics. Results from a two-dimensional finite-difference numerical model including the extended Boussinesq approximation with dissipation number Di=0.3, show that a D″-layer, less viscous than the ambient mantle by 1.5 orders of magnitude, cannot efficiently mix with the lower-mantle, even though the buoyancy parameter is as low as R ρ =0.6. However, very small-scale schlieren structures of D″-layer material are entrained into the lower-mantle. These small-scale lower-mantle heterogeneities have been imaged with one-dimensional wavelets in order to delineate quantitatively the multiscale features. They may offer an explanation for small-scale seismic heterogeneity inferred by seismic scattering in the lower-mantle.