Endothermic Phase Boundary Research Articles

The mantle convection model with non-Newtonian rheology and phase transitions: The flow structure and stress fields

The mantle convection model with phase transitions, non-Newtonian viscosity, and internal heat sources is calculated for two-dimensional (2D) Cartesian geometry. The temperature dependence of viscosity is described by the Arrhenius law with a viscosity step of 50 at the boundary between the upper and lower mantle. The viscosity in the model ranges within 4.5 orders of magnitude. The use of the non-Newtonian rheology enabled us to model the processes of softening in the zone of bending and subduction of the oceanic plates. The yield stress in the model is assumed to be 50 MPa. Based on the obtained model, the structure of the mantle flows and the spatial fields of the stresses σ xz and σ xx in the Earth’s mantle are studied. The model demonstrates a stepwise migration of the subduction zones and reveals the sharp changes in the stress fields depending on the stage of the slab detachment. In contrast to the previous model (Bobrov and Baranov, 2014), the self-consistent appearance of the rigid moving lithospheric plates on the surface is observed. Here, the intense flows in the upper mantle cause the drift and bending of the top segments of the slabs and the displacement of the plumes. It is established that when the upwelling plume intersects the boundary between the lower and upper mantle, it assumes a characteristic two-level structure: in the upper mantle, the ascending jet of the mantle material gets thinner, whereas its velocity increases. This effect is caused by the jump in the viscosity at the boundary and is enhanced by the effect of the endothermic phase boundary which impedes the penetration of the plume material from the lower mantle to the upper mantle. The values and distribution of the shear stresses σ xz and superlithostatic horizontal stresses σ xx are calculated. In the model area of the subducting slabs the stresses are 60–80 MPa, which is by about an order of magnitude higher than in the other mantle regions. The character of the stress fields in the transition region of the phase boundaries and viscosity step by the plumes and slabs is analyzed. It is established that the viscosity step and endothermic phase boundary at a depth of 660 km induce heterogeneities in the stress fields at the upper/lower mantle boundary. With the assumed model parameters, the exothermic phase transition at 410 km barely affects the stress fields. The slab regions manifest themselves in the stress fields much stronger than the plume regions. This numerically demonstrates that it is the slabs, not the plumes that are the main drivers of the convection. The plumes partly drive the convection and are partly passively involved into the convection stirred by the sinking slabs.

Numerical studies of the effects of phase transitions on Venusian mantle convection

This paper presents a study on the effects of phase transitions on the mantle convection of Venus in a three-dimensional (3D) spherical shell domain. Our model includes strong depth- and temperature-dependent viscosity and exothermic phase change from olivine to spinel as well as endothermic phase change from spinel to perovskite. From extensive numerical simulations of the effects of Rayleigh number (Ra), and the Clapeyron slopes and depths of phase changes, we found the following: (1) The endothermic phase change prevents mass flow through the interface. Increasing the absolute value of the Clapeyron slopes decreases radial mass flux and normalized radial mass flux at the endothermic phase boundary, and decreases the number of mantle plumes. In other words, mass flow through the phase boundary decreases. The inhibition influence of phase changes increases, as do convective wavelengths. (2) Increasing Ra also increases the convective wavelength and decreases the number of mantle plumes, but it has less influence on the mass exchange. As Ra increases, the convective vigor increases along with the radial mass flux and the mass flow through the phase boundary; however, the normalized mass flux through the phase boundary varies little with Ra, which is different from the conclusion that increasing Ra will greatly increase the inhibition of mass flow through the phase boundary based on two-dimensional (2D) modeling. (3) Increasing the depth of endothermic phase change will slightly decrease the number of mantle plumes, but has little effect on the mass flow through the phase boundary. Consistent with previous studies, our results show that the phase change from spinel to perovskite could inhibit the mass flow through the phase boundary, but they also show that the buildup of hot materials under the endothermic phase boundary in the 3D model could not be so large as to cause strong episodic overturns of mantle materials, which is quite different from previous 2D studies. Our results suggest that it is difficult for phase changes to cause significant magmatism on Venus; in other words, phase changes may not be the primary cause of catastrophic resurfacing on Venus.

Dynamics of plumes in a compressible mantle with phase changes: Implications for phase boundary topography

While plumes rising from the deep mantle may be responsible for hotspot volcanism, their existence has not yet been unambiguously confirmed by seismological studies. Several seismic studies reported that the topography of the 670-km discontinuity is flat below hotspots, which disagrees with the elevation expected due to its negative Clapeyron slope and plume excess temperature. An improved numerical method that includes compressibility and consistently implemented phase transitions is used to study plume evolution in the Earth’s mantle. The influence of latent heat on plume behavior for varying convective vigor and Clapeyron slope of the endothermic phase change at 670km depth is studied in axisymmetric spherical shell geometry. Minor differences in plume dynamics are found for models considering and neglecting latent heat. Three regimes of plume behavior at the endothermic phase boundary are observed: besides complete plume inhibition and penetration along the symmetry axis an intermediate regime in which the plume forms a ring around the symmetry axis is found.These models also predict that the 670-km discontinuity is flat below hotspots due to a large plume head in the lower mantle of about 1000km diameter that significantly thins as it rises into the upper mantle. This is explained by the lower viscosity in the upper mantle and the spreading of the temporarily inhibited plume below the endothermic phase boundary, which reconciles the flat 670-km discontinuity with a deep mantle plume origin.

The combined effects of continents and the 660 km-depth endothermic phase boundary on the thermal regime in the mantle

We explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in simple two-dimensional convection calculations. Phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. Our study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. We show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flow decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flow is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. We also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. Our results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. We find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.

Phase transitions and the three‐dimensional planform of thermal convection in the Martian mantle

Previous convection models for Earth have shown that the endothermic phase transition from spinel to perovskite plus magnesiowüstite at 660 km depth has a strong effect on mantle convection. For Mars, the depth of the main phase transitions is estimated using a set of 32,000 density models with randomly perturbed input parameters. It is found that, on average, the depth of the spinel to perovskite transformation is 1910 km. Thus a perovskite layer exists in the Martian mantle only if the core radius is less than 0.45 of the planetary radius. Recent results on the density of FeS at pressure and temperature conditions relevant to the Martiam core indicate that such a small core size is consistent with the cosmochemical estimate of around 14% sulphur content of the core. Numerical simulations of three‐dimensional spherical convection demonstrate that the presence of the endothermic phase transition close to the core‐mantle boundary is the crucial factor determining the style of convection. In addition to the endothermic phase boundary, the simulations assume an isoviscous mantle, which is heated both from below and within, a rigid upper boundary, and Rayleigh numbers of the order of 106. Under these conditions, it is shown that the natural planform of mantle convection exhibits only one or two strong mantle plumes. The number of plumes decreases with time during planetary evolution. For high Rayleigh numbers, the plumes start to oscillate about a mean position and pulsate in time. Strongly localized mantle upwellings are obtained even when the proportion of basal heating is only 10%. These results are robust in the sense that they do not critically depend on the parameters of the phase transition, the Rayleigh number, or the rate of basal heating. This planform of mantle convection is consistent with the volcanic history of Mars, where early volcanism was widespread, but later concentrated in two provinces, Tharsis and Elysium, and finally in Tharsis alone.

Dynamical effects of a temperature- and pressure-dependent lower-mantle rheology on the interaction of upwellings with the transition zone

We have examined the consequences of a temperature- and pressure-dependent lower-mantle viscosity on the interaction of upwellings with the two major phase transitions. The viscosity used is only temperature-dependent in the upper-mantle but assumes both temperature- and pressure dependences in the lower-mantle. The activation enthalpy increases with depth dependence scaled after experimental melting curves of lower-mantle components. We have employed a two-dimensional cartesian box with an aspect-ratio of five and a mantle layer thickness of 2900 km, using an extended Boussinesq model with a depth-dependent thermal expansivity. Latent heat release and viscous dissipation have been included in the temperature equation. We have considered models both without and with a viscosity jump (a factor of 8) across the 660 km boundary. The range of averaged Rayleigh numbers (Ra) considered lies between 2 × 10 6 and 10 7. A major effect of this temperature- and pressure-dependent rheology is the stabilization of the upwelling plumes and the increase of viscous heating in the bottom portion of these plumes. The impingement of these heated plumes at the endothermic phase boundary causes the development of secondary plumes to rise into the upper-mantle. Shear-heating together with the latent heat release produces large temperature increases in the plumes passing through the transition zone, which may cause melting in the deep upper-mantle. Although the average Rayleigh number in the case of temperature- and pressure-dependent viscosity is around a factor of 5 lower than in a case with purely temperature-dependent viscosity, the resulting flow is only slightly less layered, which is contrary to the earlier finding of Christensen and Yuen (1985). The tendencies for the development of secondary plumes and high temperatures inside the upwellings are enhanced by the viscosity jump at the 660 km boundary. In this situation few nearly steady, vigorous upwellings exist in the lower mantle, while in the upper mantle vigorous time-dependent convection takes place. For an averaged Rayleigh number of 10 7, the system becomes layered with many thin plumes appearing in the lower mantle.

The influence of trench migration on slab penetration into the lower mantle

A two-dimensional numerical convection model in cartesian geometry is used to study the influence of trench migration on the ability of subducted slabs to penetrate an endothermic phase boundary at 660 km depth. The transient subduction history of an oceanic plate is modelled by imposing plate and trench motion at the surface. The viscosity depends on temperature and depth. A variety of styles of slab behaviour is found, depending predominantly on the trench velocity. When trench retreat is faster than 2–4 cm/a, the descending slab flattens above the phase boundary. At slower rates it penetrates straight into the lower mantle, although flattening in the transition zone may occur later, leading to a complex slab morphology. The slab can buckle, independent of whether it penetrates or not, especially when there is a localised increase in viscosity at the phase boundary. Flattened slabs are only temporarily arrested in the transition zone and sink ultimately into the lower mantle. The results offer a framework for understanding the variety in slab geometry revealed by seismic tomography.

A one-plume model of martian mantle convection

FOR at least the past two billion years, volcanism on Mars has been restricted to the Tharsis region1. In addition, most tectonic activity on Mars2, together with the long-wavelength topography and the non-hydrostatic gravity field3, are strongly correlated with Tharsis, implying a close connection with deep mantle processes. These observations have motivated suggestions4 that the thermal convection in the martian mantle is very different from that in the Earth's mantle, being dominated by a single large upwelling under Tharsis. Two-dimensional convection modelling has shown that the presence of an endothermic phase boundary in the lowermost mantle of a planet has a strong influence on convection, suppressing all but one or two upwellings5. Recent experiments6 indicate that such a boundary may indeed exist on Mars. Here we investigate the convective evolution of the martian mantle using a three-dimensional model which incorporates an endothermic phase transition close to the core–mantle boundary. We find that a single-plume pattern of convection gradually develops, and we show that this is consistent with the distribution of volcanism, the shape of the gravity field, and the gross tectonic stress pattern of Mars.

The effects of temperature-dependent viscosity on mantle convection with the two major phase transitions

We have studied the consequences of including temperature-dependent viscosity in mantle convection with both of the major phase transitions included. We have employed a two-dimensional cartesian model in a box of aspect ratio four. The time-dependent equations have been cast within an extended Boussinesq framework in which each of the phase changes has been simulated by an enhanced thermal expansivity. Both latent heat release and viscous dissipation have been considered. Two different forms of temperature-dependent viscosity, the Arrhenius and the Frank-Kamenetzky forms, have been employed. We have considered both models with a constant temperature (equilibrium) boundary condition at the core-mantle boundary and models with a time-varying (non-equilibrium) temperature boundary condition from cooling of the core. The effects of temperature-dependent viscosity are to enhance the tendency of the convective system to be layered because of the influences of the latent heat release and the mechanical heating on creating a sharp viscosity drop across the transition zone. We have found that there is a non-linear coupling between latent heat release from the interaction of the hot plume with the endothermic phase transition and the temperature-dependent viscosity. This positive feedback process can give rise to the production of very high temperatures in the transition zone, which may cause melting in the region between the two major phase transitions. Flushing events produced by the non-equilibrium boundary condition are much more dramatic than those generated by the equilibrium boundary condition. The non-linear coupling between latent heat release and temperature-dependent viscosity is also stronger in the non-equilibrium models. Comparison with models without the presence of latent heat release and viscous dissipation shows that the models without the heating terms produce a greater degree of mass flux across the endothermic phase boundary because of the lack of the viscosity stratification in the interior of the convective flow. Results of this moded can be applied to other types of endothermic phase transition found in the lithosphere or to the spinel-perovskite transition in the deep portion of the Martian mantle.

A simple parameterized model of Earth's thermal history with the transition from layered to whole mantle convection

Recent studies of mantle convection suggest a possible scenario for Earth's history in which the convection has changed its style from layered to whole mantle because of the existence of an endothermic phase boundary. To understand the possible thermal consequence of this ‘transition’, we shall re-examine the thermal history of Earth with different types of convection mode (i.e., whole mantle convection, layered mantle convection and convection with a transition) using a simple parameterized scheme. For the whole mantle convection model we shall confirm the results presented by previous workers (i.e., a small β of <0.1 (the index of the power-law relation between the Nusselt and Rayleigh numbers) is required for a low Urey ratio (∼ 0.4) Earth. For the layered case the Urey ratio, β and the concentration of the radiogenic heat source in the lower mantle are restricted by the melting constraints. In order to avoid massive melting of the mantle at present and in the past, a depleted lower mantle is required, which confirms the results of the previous studies, although the amount of depletion is not so large as previous estimates. We shall also show that a low β (e.g., < 0.1) and low Urey ratio (∼ 0.4) Earth are not favourable for layered convection models, because they will predict massive melting of the mantle in the past and at the present. For the transition-type convection model, we find that early transition (e.g., older than 1 Ga B.P. is allowed for low β (< 0.1) with a low Urey ratio (∼ 0.4) or for high β (> 0.2) with a high Urey ratio (∼ 0.8). This is almost identical to the whole mantle case. The implication is that, because whole mantle convection is powerful enough, Earth may loose the memory of early layering that may have existed more than 1 Ga B.P. The change in flow velocity associated with the transition is expected to be a factor of five or more. The temperature of the upper mantle before the transition took place may be lower than the present mantle temperature.

Model for Convective Cooling of Mantle with Phase Changes: Effects of Aspect Ratios and Initial Conditions.

The effects of the aspect ratios and initial conditions on a cooling mantle with phase changes are studied using a 2-D Cartesian convection model without internal heating. The aspect ratio is either 3 or 5 and the side-boundaries are periodic. The initial condition is either a quasi-equilibrium state of convective flow or linear temperature increase from the top to the bottom surface. Bottom or core temperature is changed to match the core cooling by the convective heat transfer. Considerable qualitative and quantitative differences exist among the models with different initial conditions and aspect ratios. For example, we cannot find the convenient criterion, such as critical Rayleigh number, for the massive overturn of the upper and lower mantle associated with the endothermic phase transition (flushing). The presence of the thermal boundary layer at the endothermic phase boundary plays an important role in cooling both the upper and lower mantles. A common feature is that the upper mantle becomes hottest during the flushing event. In some cases, we find qualitatively similar in which the style of flow changes. These events reflect the physical properties of the upper and lower mantles. Geological information of the past may be necessary to constrain the different models.

Layered convection induced by phase transitions

We report a systematic study on the conditions under which an endothermic phase transition can enforce layered convection. Two‐dimensional numerical calculations of convection in a domain containing a divariant phase change were performed in the framework of the “extended Boussinesq approximation,” i.e., considering the effects of adiabatic gradient, latent heat, and frictional heating in the energy equation. We find that the critical value of the negative Clapeyron slope, which must be surpassed in order to induce layered convection, decreases in magnitude with increasing Rayleigh number Ra in the range 104 ≤ Ra ≤ 2×106. Near the critical Clapeyron slope, vacillations between double‐ and single‐layer convection or strongly leaking double‐layer convection are possible. The breakdown into layers is influenced very little by the latent heat release but depends solely on the phase boundary deflection caused by lateral temperature differences. The value of the critical Clapeyron slope also seems little affected by the width of the transition zone or by its depth. A possible superplastic rheology within the transition zone would tend to favor layered convection. Scaling the model results to the 670‐km discontinuity in the earth's mantle as a possible endothermic phase boundary, we estimate the critical Clapeyron slope to be in the range of −4 to −8 MPa/K (−40 to −80 bar/K). The possibility that the spinel → perovskite + periclase transition is within this range appears to be remote but certainly cannot be neglected.