Plume Mode of Thermal Convection in the Earth’s Mantle

In our previous works, based on numerical models, it was shown that under certain conditions a hot material can rise in portions in the tails of thermal mantle plumes. The spectrum of these pulsations can correspond to the observed spectra of catastrophic hotspot eruptions. Since most of the existing numerical models of thermal convection for the mantle of the present Earth do not reveal these pulsations, in this work, we analyze the physical cause and initiation conditions of pulsations of thermal plumes. The results of a numerical solution of the thermal convection equations for a material with varying parameters in the extended Boussinesq approximation are presented. It is shown how the structure of the convection is transformed with the increase of convection intensity. At the Rayleigh numbers Ra > 10⁶, convection becomes unsteady, and the configuration of the ascending and descending flows changes. The new flow emerging at the mantle bottom acquires a mushroom shape with a head and a tail. After the rise of the plume’s head to the surface, the tail remains in the mantle in the form of a quasi-stationary hot steam. It turns out that at Ra ~ 5 × 10⁷, the thermal mantle plume becomes pulsating and its tail is in fact a heated channel through which the hot material rises in successive portions. At the Rayleigh numbers Ra > 5 × 10⁸, the tail of the thermal plume breaks and the plume becomes a regular conveyor of separate ascending portions of the hot material, which are referred to as thermals. Thus, thermal convection with pulsating plumes takes place at the transitional stage from the regime of quasi-stationary plumes to the regime of thermals.     

Numerical model for the generation of the ensemble of lithospheric plates and their penetration through the 660-km boundary

In the kinematic theory of lithospheric plate tectonics, the position and parameters of the plates are predetermined in the initial and boundary conditions. However, in the self-consistent dynamical theory, the properties of the oceanic plates (just as the structure of the mantle convection) should automatically result from the solution of differential equations for energy, mass, and momentum transfer in viscous fluid. Here, the viscosity of the mantle material as a function of temperature, pressure, shear stress, and chemical composition should be taken from the data of laboratory experiments. The aim of this study is to reproduce the generation of the ensemble of the lithospheric plates and to trace their behavior inside the mantle by numerically solving the convection equations with minimum a priori data. The models demonstrate how the rigid lithosphere can break up into the separate plates that dive into the mantle, how the sizes and the number of the plates change during the evolution of the convection, and how the ridges and subduction zones may migrate in this case. The models also demonstrate how the plates may bend and break up when passing the depth boundary of 660 km and how the plates and plumes may affect the structure of the convection. In contrast to the models of convection without lithospheric plates or regional models, the structure of the mantle flows is for the first time calculated in the entire mantle with quite a few plates. This model shows that the mantle material is transported to the mid-oceanic ridges by asthenospheric flows induced by the subducting plates rather than by the main vertical ascending flows rising from the lower mantle.     

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.     

Plume capture by divergent plate motions: implications for the distribution of hotspots,geochemistry of mid-ocean ridge basalts,and estimates of the heat flux at the core–mantle boundary

The coexistence of stationary mantle plumes with plate-scale flow is problematic in geodynamics. We present results from laboratory experiments aimed at understanding the effects of an imposed large-scale circulation on thermal convection at high Rayleigh number (10⁶≤Ra≤10⁹) in a fluid with a temperature-dependent viscosity. In a large tank, a layer of corn syrup is heated from below while being stirred by large-scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank. Three regimes are observed, depending on the ratio V of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary, and on the ratio λ of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary. When V≪1 and λ≥1, large-scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes. When V>10 and λ>100, plume formation is suppressed entirely, and the heat flux is carried by a sheet-like upwelling located in the center of the tank. At intermediate V, and depending on λ, established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling. Heat transfer across the layer occurs through a combination of ascending plumes and large-scale flow. Scaling analyses show that the bottom boundary layer thickness and, in turn, the basal heat flux q depend on the Peclet number, Pe, and λ. When λ>10, q∝Pe^1/2 and when λ→1, q∝(Peλ)^1/3, consistent with classical scalings. When applied to the Earth, our results suggest that plate-driven mantle flow focuses ascending plumes towards upwellings in the central Pacific and Africa as well as into mid-ocean ridges. Furthermore, plumes may be captured by strong upwelling flow beneath fast-spreading ridges. This behavior may explain why hotspots are more abundant near slow-spreading ridges than fast-spreading ridges and may also explain some observed variations of mid-ocean ridge basalt (MORB) geochemistry with spreading rate. Moreover, our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots.     

地幔对流的实验研究:非立柱状幔柱和地幔涡旋

地幔对流的物理模拟实验结果表明 ,在地幔介质和温度非均匀分布的复杂条件下 ,热卷流 (地幔柱 )往往由立柱状转变为非立柱状 (含斜柱状、涡旋状等 )。在忽略科里奥利力的情况下 ,板块的下插和滞积下沉、岩石圈根的存在以及地幔介质粘度的非均匀分布等都可能构成不同形状的障碍 -导流体 ,导致地幔的涡旋运动。软流圈中的水平涡旋环带属于对数螺线型 ,环带旋转半径及线速度逐渐减小 ,最终在旋转中心处下沉 ,而旋转角速度大致保持恒定     

Plume-induced geoid anomalies from 2D axi-symmetric temperature- and pressure-dependent mantle convection models

A collection of numerical simulations of 2D axi-symmetric thermal convection is presented here. The aim is to investigate the shape of geoid anomalies and dynamic topography above a plume. The simulation is based on the Boussinesq approximation and infinite Prandtl number and is carried out in the spherical shell with strongly temperature- and depth-dependent Arrhenius-type viscosity. According to the Arrhenius law, plume models with purely depth-dependent rheology are unphysical and should be taken with care. The strongly coupled temperature- and depth-dependent viscosity enables us to better understand the plume's behavior inside the Earth.The topography and geoid anomalies produced from plumes are sensitive to rheology of the mantle and rheology of the plume; both have effects on shape and amplitude of the geoid anomalies. We determined different categories of the geoid which are related to various rheology. Depth-dependent viscosity models show a geoid with a negative sign above the plume, and temperature-dependent viscosity models depict a bell-shaped geoid. We identified different behaviors in the combined model with temperature- and pressure-dependent viscosity.     

On the rise of strongly tilted mantle plume tails

The rise of an initially horizontal, buoyant cylinder of fluid through a denser fluid at low Reynolds number is used to look at the ascent of strongly tilted mantle plumes through the mantle. Such ascents are characterized by (1) the growth of instabilities and (2) the development of a thermal wake downstream. Three-dimensional numerical experiments were carried out to examine these features. An hybrid particle-in-cell finite element method was used to look at the rise of non-diffusing cylinders and, a standard finite element method was used to look at the diffusing case. First the experiments show that the timescale of the fastest growing instability vary with the Rayleigh number and the viscosity ratio. In particular the growth rate decreases as the Rayleigh number decreases, in agreement with our analysis of the laboratory experiments of Kerr et al. (2008). Second the experiments show that the length of the thermal wake increases with the Rayleigh number but the change in viscosity has almost no influence on the wake length. Applied to strongly tilted mantle plumes we conclude that such plumes cannot be unstable given the plume timescales. We also discuss the application of this conclusion to weakly tilted plumes. Besides, this study allows to predict that mantle plumes are unlikely to have developed a significant thermal wake by the time they reach the surface. Finally, the resolution that is required to allow for the growth of mantle plume tails by combined diffusion and thermal entrainment is shown to represent a challenge for the large scale mantle convection simulations.     

Lower mantle dynamics with the post-perovskite phase change, radiative thermal conductivity, temperature- and depth-dependent viscosity

The new post-perovskite phase near the core-mantle boundary has important ramifications on lower mantle dynamics. We have investigated the dynamical impact arising from the interaction of temperature- and depth-dependent viscosity with radiative thermal conductivity, up to a lateral viscosity contrast of 10⁴, on both the ascending and descending flows in the presence of both the endothermic phase change at 670 km depth and an exothermic post-perovskite transition at 2650 km depth. The phase boundaries are approximated as localized zones. We have employed a two-dimensional Cartesian model, using a box with an aspect-ratio of 10, within the framework of the extended Boussinesq approximation. Our results for temperature- and depth-dependent viscosity corroborate the previous results for depth-dependent viscosity in that a sufficiently strong radiative thermal conductivity plays an important role for sustaining superplumes in the lower mantle, once the post-perovskite phase change is brought into play. This aspect is especially emphasized, when the radiative thermal conductivity is restricted only to the post-perovskite phase. These results revealed a greater degree of asymmetry is produced in the vertical flow structures of the mantle by the phase transitions. Mass and heat transfer between the upper and lower mantle will deviate substantially from the traditional whole-mantle convection model. Streamlines revealed that an overall complete communication between the top and lower mantle is difficult to be achieved.     

The structure of convection in the spherical mantle with internal heating

Thermal convection in the mantle is caused by the heat transported upwards from the core and by the heat produced by the internal radioactive sources. According to the data on the heat transfer by the mantle plumes and geochemical evidence, only 20% of the total heat of the Earth is supplied to the mantle from the core, whereas most of the heat is generated by the internal sources. Along with the models that correctly allow for the internal heat sources, there are also many publications (including monographs) on the models of mantle convection that completely ignore the internal heating or the heat flux from below. In this study, we analyze to what extent these approximations could be correct. The analytical distributions of temperature and heat flux in the case of internal heating without convection and the results of the numerical modeling for convection with different intensity are presented. It is shown that the structure of thermal convection is governed by the distribution of the heat flux in the mantle but not by the heat balance, as it is typically implicitly assumed in most works. Heat production by the internal sources causes the growth of the heat flux as a function of radius. However, in the spherical mantle of the Earth, the heat flux decreases with radius due to the geometry. It turned out that with the parameters of the present Earth, both these effects compensate each other to a considerable extent, and the resulting heat flux turns out to be nearly constant as a function of radius. Since the structure of the convective flows in the mantle is determined by the distributions of heat flux and total heat flux, in the Cartesian models of the mantle convection the effective contribution of internal heating is small, and ignoring the heat flux from the core significantly distorts the structure of the convective currents and temperature distributions in the mantle.     

地幔对流与深部物质运移研究的新进展

现代固体地球科学已经认识到,地幔对流不再是少数动力学家的假想,它是地幔热动力系统的主要构架.地幔对流和板块运动驱动机理关系的研究已经从简单的主动或被动驱动的讨论转向对统一热动力系统的探讨.包括地幔热柱在内的地幔对流的深入研究不仅成为研究地幔热动力系统演化的主线,也成为研究大陆形成和演化驱动机理的主线.与此同时,以地震层析成像为主体的地震、地球物理观测资料和以地幔岩石化学组份为主体的地球化学观测成为认识地幔对流的强有力的工具.然而,地球化学和地球物理观测之间存在明显的差异,一些依赖于地球化学数据构思的新的热动力学框架对地幔对流的研究构成了强烈的挑战.     

Numerical models of subduction of the oceanic crust with basaltic plateaus

Light continents and islands characterized by a crustal thickness of more than 30 km float over a convective mantle, while the thin basaltic oceanic crust sinks completely in subduction zones. The normal oceanic crust is 7 km thick. However, anomalously thick basaltic plateaus forming as a result of emplacement of mantle plumes into moving oceanic lithospheric plates are also pulled into the mantle. One of the largest basaltic plateaus is the Ontong Java plateau on the Pacific plate, which arose during the intrusion of a giant superplume into the plate ～100 Myr ago. Notwithstanding its large thickness (averaging ～30 km), the Ontong Java plateau is still experiencing slow subduction. On the basis of numerical modeling, the paper analyzes the oceanic crust subduction process as a function of the mantle convection vigorousness and the density, thickness, viscosity, and shape of the crust. Even a simplified model of thermocompositional convection in the upper mantle is capable of explaining the observed facts indicating that the oceanic crust and sediments are pulled into the mantle and the continental crust is floating on the mantle.     

Constraints on the dynamics of mantle plumes from uplift of the Hawaiian Islands

The ∼0.2 mm/yr uplift of Hawaiian islands Lanai and Molokai and Hawaiian swell topography pose important constraints on the structure and dynamics of mantle plumes. We have formulated 3-D models of mantle convection to investigate the effects of plume-plate interactions on surface vertical motions and swell topography. In our models, the controlling parameters are plume radius, excess plume temperature, and upper mantle viscosity. We have found that swell height and swell width constraints limit the radius of the Hawaiian plume to be smaller than 70 km. The additional constraint from the uplift at Lanai requires excess plume temperature to be greater than 400 K. If excess plume temperature is 400 K, models with plume radius between 50 and 70 km and upper mantle viscosity between 10²⁰ and 3×10²⁰ Pa s satisfy all the constraints. Our results indicate that mantle plume in the upper mantle may be significantly hotter than previously suggested. This has important implications for mantle convection and mantle melting. In addition to constraining plume dynamics, our models also provide a mechanism to produce the observed uplift at Lanai and Molokai that has never been satisfactorily explained before.     

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.     

Influence of an endothermic phase transition on mass transfer between the upper and the lower mantle

Geochemical data indicate that two major reservoirs 1–2 Ga in age are present in the mantle. The upper mantle, feeding mid-ocean ridges, is depleted in chemical elements carried away into the continental crust. The lower mantle, feeding hotspot plumes, is close in composition to primordial matter. The 660-km depth of an endothermic phase transition in olivine has been considered over the last two decades as a possible boundary between the reservoirs. In this period, many models of mantle convection were constructed that used values of the phase transition parameters, which led to temporal (up to 1 Gyr long) convection layerings and periodic avalanche-induced mantle intermixing events. However, laboratory measurements with new improved instrumentation give other values of the phase transition parameters that require a revision of the majority of the existence of large-scale avalanches in the Earth’s history becomes disputable. The paper is devoted to comprehensive study of the phase transition effect on the structure of mantle flows with different values of phase transition parameters and Rayleigh numbers; in particular, the mass transfer through the phase boundary is calculated for different regimes of steady-state convection.     

Implication for mantle flow from the Hawaiian-Emperor chain

Assuming that Rayleigh-Benard flow occurs within the upper mantle, ascending plumes must undergo horizontal displacement during ascent that can be traced at the surface. It is shown that the Hawaiian-Emperor bend cannot be formed if the convection rate is of the same order of magnitude as the ascent rate of the plumes. The plume patterns obtained by push-pull or lithospheric sliding are similar to that of the Hawaiian-Emperor chain. Hence the present results support the sliding model.     

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.     

Mantle plume,large igneous province and continental breakup——Additionally discussing the Cenozoic and Mesozoic mantle plume problems in East China

Based on the former workers study results such as numerical simulation of fluid mechanics,seismic tomography of the whole earth and igneous rocks,the basic characteristics of mantle plumes are summarized in detail,namely the mantle plume,from the D″layer near the core-mantle bouundary(CMB)of 2900 km deep,is characterized by the spape of large head and thin narrow conduit,by the physical property of high temperature and low viscosity.The LIP(large igneous province)is the best exhibition when the mantle plume ascends to the surface.According to the basic characteristics of the mantle plumes and the LIP,as well as the temporal-spatial relationships between the mantle plume and continental breakup,the detailed research on petrology,geochemistry,temporal-spatial distribution,tectonic background of the Cenozoic-Mesozoic igneous rocks and gravity anomaly distribution in East China has been done.As a result,the Mesozoic igneous rocks in Southeast China should not be regarded as an example of typical LIP related to mantle plumes.for their related characteristics are not consitent with those of the typical LIPs related to mantle plumes.The Cenozoic igneous rocks in Northeast China have no the typical characteristics of mantle plumes and hotspots,so the Cenozoic volcanism in Northeast China might have no the direct relationships with the activity of mantle plumes.     

基于随温度变化的热系数模拟板块俯冲动力学过程

热传导系数和热膨胀系数是影响板块俯冲动力学过程的两个重要参数. 由于地球介质的不均匀性,热系数也会随深度发生变化.然而,这种变化在地球动力学模拟研究中往往被忽略.本文针对随温度变化的热传导系数和热膨胀系数, 模拟板块俯冲的动力学过程,分析热系数、黏度对板块俯冲形态的影响及其对应的地幔对流特征.结果表明,依温度变化的热传导系数和热膨胀系数会影响地幔温度及黏度分布,进而改变板块的俯冲角度;黏度是控制板块俯冲动力学演化过程的重要因素;地幔对流受黏度结构的影响,呈现分层对流及局部多个对流环等多种不同形态的对流场特征.      

On the interaction between small- and large-scale convection and postglacial rebound flow in a power-law mantle

Some consequences arising from the superposition of flows of two different kinds or scales in a non-Newtonian mantle are discussed and applied to the cases mantle convection plus postglacial rebound flow as well as small- plus large-scale mantle convection. If the two flow types have similar magnitude, the apparent rheology of both flows becomes anisotropic and the apparent viscosity for one flow depends on the geometry of the other. If one flow has a magnitude significantly larger than the other, the apparent viscosity for the weak flow is linear but develops direction-dependent variations about a factorn (n being the power exponent of the rheology). For the rebound flow lateral variations of the apparent viscosity about at least 3 are predicted and changes in the flow geometry and relaxation time are possible. On the other hand, rebound flow may weaken the apparent viscosity for convection. Secondary convection under moving plates may be influenced by the apparent anisotropic rheology. Other mechanisms leading to viscous anisotropy during shearing may increase this effect. A linear stability analysis for the onset of convection with anisotropic linear rheology shows that the critical Rayleigh number decreases and the aspect ratio of the movement cells increases for decreasing horizontal shear viscosity (normal viscosity held constant). Applied to the mantle, this model weakens the preference of convection rolls along the direction of plate motion. Under slowly moving plates, rolls perpendicular to the plate motion seem to have a slight preference. These results could be useful for resolving the question of Newtonian versus non-Newtonian or isotropic versus anisotropic mantle rheology.     

Numerical studies of non-Newtonian mantle convection

Numerical model computations have been carried out to determine how the stress-dependence of non-Newtonian viscosity affects the flow structure of thermal convection. The viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology, based on the diffusion and dislocation creep laws of olivine. The results show that there are important differences between the structures of Newtonian and non-Newtonian convection. While the Newtonian models are insufficient in some respects, the non-Newtonian solutions can explain the characteristics of the real mantle flow. However, this may require a faster plastic deformation than power law dislocation creep, at least in the high-stress regions of the mantle, e.g. at the active plate margins.