Comparison of Early Evolutions of Mimas and Enceladus

Thermal history of Mimas and Enceladus is investigated from the beginning of accretion to 400 Myr. The numerical model of convection combined with the parameterized theory is used. The following heat sources are included: short lived and long lived radioactive isotopes, accretion, serpentinization, and phase changes. The heat transfer processes are: conduction, solid state convection, and liquid state convection. We find that temperature of Mimas’ interior was significantly lower than that of Enceladus. If Mimas accreted 1.8 Myr after CAI then the internal melting and differentiation did not occur at all. Comparison of thermal models of Mimas and Enceladus indicates that conditions favorable for the start of tidal heating lasted for a short time (~10⁷ yr) in Mimas and for ~10⁸ yr in Enceladus. This could explain the Mimas—Enceladus paradox. In fact, in view of the chronology based on cometary impact rate, one cannot discard a possibility that also Mimas was for some time active and it has the interior differentiated on porous core and icy mantle.     

Geophysical observations pertaining to solid-state convection in the terrestrial planets

We present a broad-based review of the observational evidence that pertains to or otherwise implies solid-state convection to be occurring (or have occurred) in the interiors of the terrestrial planets.For the Earth, the motion of the plates is prima facie evidence of large-scale mantle convection. Provided we understand upper-mantle thermal conductivity correctly, heat flow beneath the old ocean basins may be too high to be transported conductively from the upper mantle through the base of the lithosphere and therefore convection on a second smaller scale might be operative. The horizontal scale of plate dimensions implies, due to typical cell aspect ratios observed in convection, that the motion extends to the core-mantle boundary. Improved global data coverage and viscoelastic modeling of isostatic rebound due to Pleistocene deglaciation imply a uniform mantle viscosity, and thus indicate that whole-mantle convection could exist. Additionally, there is some seismic evidence of lithospheric penetration to depths deeper than 700 km. We discuss some salient features and assumption boundedness of arguments for convection confined to the upper mantle and for convection which acts throughout the mantle since the vertical length scale has a profound effect upon the relevance of geophysical observations. The horizontal form of mantle convection may be fully three-dimensional with complex planform and, therefore, searching for correlative gravity patterns in the ocean basins may not be useful without additional geophysical constraints. Many long-wavelength gravity anomalies may arise from beneath the lithosphere and must be supported dynamically, although thermal convection is not a unique explanation. Topography is an additional geophysical constraint, but for wavelengths greater than a few hundred kilometers, a general lack of correlation exists between oceanic residual gravity and topography, except at specific locations such as Hawaii. Theoretical calculations predict a complex relationship between these two observational types. Oceanic gravity data alone shows no regular planform and there is no correlation with any small-scale convective pattern predicted by laboratory experiments.All of the observational evidence argues against Martian plate tectonics occurring now or over much of the history of this planet, but lack of plate tectonics is not an argument against interior convection. The Tharsis uplift on Mars may have resulted from convective processes in the mantle, and the present-day gravity anomaly associated with Tharsis must be supported by the finite strength of the lithosphere or by mantle convection. Stresses imparted by the present topographic load would be greater than a kilobar, in excess of long-term finite strength. Observed fracture patterns are probably a direct result of this load, and the key question concerns the level of resultant strain relief. The global topographic and geomorphic dichotomy between the northern and southern hemisphere required a solid-state flow process to create the accompanying center-of-figure to center-of-mass offset.Lunar heat flow values, in analogy with oceanic heat flow on the Earth, strongly imply a convective mechanism of heat transport in the interior which, based on seismic Q values, is limited to the lower mantle. The presence of moonquakes in this region does not preclude solid-state convective processes. Lunar conductivity profiles provide no information on convection because of the difficulty in conductivity modeling, uniqueness of models, and the uncertainty in the conductivity-temperature relationship. The excess oblateness of the lunar figure over the hydrostatic value does not require convective support; in fact, such a mechanism is unlikely.The presence of a dipole magnetic field on Mercury does not provide a constraint on mantle convection unless its existence can be inextricably linked to a molten core. The non-hydrostatic shape of the equatorial figure, required for the observed $\text{3}\text{2}$ resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The $\text{3n}\text{2}$ resonance implies escape from a 2n resonance and, therefore, is related to the question of a molten core. Further dynamical data is needed to constrain interior models.Interpretation of limited radar imagery for the surface of Venus is enigmatic in terms of plate tectonics and therefore interior convection. Linear tensional and possibly compressional features are observed, but there are also crustal regions which appear to show large impact structures and are thus geologically old and may not have been recycled.     

On the heat budget of the moon and the surface temperature variation during a lunar eclipse

Summary The analysis of surface temperature variations of the moon is based on the equations of heat conduction and heat continuity in the interior of the moon andStefan's law. During a well-defined process, as exemplified by a lunar eclipse, the local heat budget equation establishes a boundary condition at the moon surface which must be satisfied by solutions of the thermal diffusion equation in the interior. Three simplified models of the general case are discussed. They are characterized by special assumptions regarding the depth and time dependency of the thermic qualities of the material underlying the moon's surface. In short, the thermal diffusivity is assumed to be constant in the first model, a linear depth function in the second and a time function in the third. A unique solution can be obtained for model No. I such that the absolute surface temperature is approximately inversely proportional to the 6th root of time during the phase of total eclipse.Epstein's conclusion that the average surface of the moon might consist of highly porous rocks or fine dust is confirmed by the order of magnitude of the heat conductivity which produces the best fit between the theoretical curves and a plot ofPettit's observational data during the lunar eclipse of 1939. Existing differences between the observed and theoretical curves during the totality phase of the eclipse can be reduced by the employment of the second model. A crude estimate shows that the average dust cover resting on more solid ground of lunar rocks might possibly have a thickness of approximately 0.5 meters.     

Two-dimensional mantle flow beneath a rigid accreting lithosphere

This study considers two-dimensional mantle flow beneath a rigid lithosphere. The lithosphere which forms the upper boundary of a convecting region moves with a prescribed uniform horizontal velocity, and thickens with distance from the accreting plate boundary as it cools. Beneath the lithosphere, the mantle deforms viscously by diffusion creep and is heated radiogenically from within. Solutions for thermal convection beneath the lithosphere are obtained by finite-difference methods. Two important conclusions have resulted from this study: (1) convective patterns of large aspect ratio are stable beneath a rigid moving lithosphere; (2) even for a lithosphere velocity as small as 3 cm/yr. and a Rayleigh number as large as 10⁶, mantle circulation with large aspect ratio is driven dominantly by the motion of the lithosphere rather than by temperature gradients within the flow. Gravity, topography and heat flow are determined and implications for convection in the upper mantle are discussed.     

The thermal state and strength of the lithosphere in the Spanish Central System and Tajo Basin from crustal heat production and thermal isostasy

In this work we have modeled the thermal structure of the lithosphere of the Spanish Central System and the Tajo Basin, and their implications for lithospheric strength. For this, we have used refined heat-producing elements (HPE) values to obtain new estimates of heat production rates in the Spanish Central System and Tajo Basin areas, which have been used joined to the relation between topography and thermal structure of the lithosphere to calculate the best-fit surface heat flows in the study area. Moreover, we have implemented a temperature-dependent thermal conductivity (appropriate for olivine) for the lithospheric mantle to improve the calculations of temperature profiles in the mantle. The geotherms so obtained, together with the implementation of a new rheological law for the upper lithospheric mantle, have been used to calculate refined estimations of the strength and effective elastic thickness of the lithosphere. We have obtained surface heat flow values of 84 mW m⁻² and ∼82 mW m⁻² for the Spanish Central System and the Tajo Basin, respectively. The thermal state of the lithosphere affects mantle temperatures, and hence may be playing an important role in the uplift and maintenance of the Spanish Central System.     

Internal constitution and evolution of the moon

The composition, structure and evolution of the moon's interior are narrowly constrained by a large assortment of physical and chemical data. Models of the thermal evolution of the moon that fit the chronology of igneous activity on the lunar surface, the stress history of the lunar lithosphere implied by the presence of mascons, and the surface concentrations of radioactive elements, involve extensive differentiation early in lunar history. This differentiation may be the result of rapid accretion and large-scale melting or of primary chemical layering during accretion; differences in present-day temperatures for these two possibilities are significant only in the inner 1000 km of the moon and may not be resolvable. If the Apollo 15 heat-flow result is representative of the moon, the average uranium concentration in the moon is 0.05–0.08 p.p.m.Density models for the moon, including the effects of temperature and pressure, can be made to satisfy the mass and moment of inertia of the moon and the presence of a low-density crust inferred from seismic refraction studies only if the lunar mantle is chemically or mineralogically inhomogeneous. The upper mantle must exceed the density of the lower mantle at similar conditions by at least 5%. The average mantle density is that of a pyroxenite or olivine pyroxenite, though the density of the upper mantle may exceed 3.5 g/cm³. The density of the lower mantle is less than that of the combined crust and upper mantle at similar temperature and pressure, thus reinforcing arguments for early moon-wide differentiation of both major and minor elements. The suggested density inversion is gravitationally unstable and implies stresses in the mantle 2–5 times those associated with the lunar gravitational field, a difficulty that can be explained or avoided by: (1) adopting lower values for the moment of inertia and/or crustal thickness, or (2) postulating that the strength of the lower mantle increases with depth or with time, either of which is possible for certain combinations of composition and thermal evolution.A small iron-rich core in the moon cannot be excluded by the moon's mass and moment of inertia. If such a core were molten at the time lunar surface rocks acquired remanent magnetization, then thermal-history models with initially cold interiors strongly depleted in radioactive heat sources as a primary accretional feature must be excluded. Further, the presence of ～||pre|40 K in a FeFeS core could significantly alter the thermal evolution and estimated present-day temperatures of the deep lunar interior.     

Finite-Amplitude thermal convection within a self-gravitating fluid sphere

Abstract

Finite-difference calculations have been carried out to determine the structure of finite-amplitude thermal convection within a self-gravitating fluid sphere with uniform heat release. For a fixed-surface boundary condition single-cell convection breaks up into double-cell convection at a Rayleigh number of 3 × 10⁴, at a Rayleigh number of 5 × 10⁵ four-cell convection is observed. With a free-surface boundary condition only single cell convection is obtained up to a Rayleigh number of 5 × 10⁶.     

The existence of a thin low-viscosity layer beneath the lithosphere

The horizontal temperature gradient at the base of the lithosphere at an oceanic fracture zone, where plate of different ages is juxtaposed, is expected to drive a local circulation, the characteristics of which can be constrained by the amplitude, wavelength and age-dependence of the geoid. Two-dimensional numerical models of convection in a fluid layer overlain by a solid conducting lid have been used to generate theoretical geoid profiles at right angles to the fracture zone. Only a thin, low-viscosity layer provides a reasonable fit to the data. The best model so far obtained has a fluid layer 150 km thick with viscosity 1.5 × 10¹⁹ Pa s under a 75 km lid. Such a layer, which is incapable of transmitting strong horizontal shear stresses, could provide the decoupling mechanism between plate and deep mantle flow required to balance the forces on the plates.     

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers (Ra) is 10⁴?10⁷ and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number (Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln(Nu)/? ln(Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.     

On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

Thermal-rheological structure of lithosphere beneath the northern flank of Tarim Basin, western China: Implications for geodynamics

Based on the data of geo-temperature and thermophysical parameters of rocks in the Kuqa Depression and the Tabei Uplift, northern flank of the Tarim Basin, in terms of the analytical solution of 1-D heat transfer equation, the thermal structure of the lithosphere under this region is determined. Our results show that the average surface heat flow of the northern flank of the Tarim Basin is 45 mW/m2, and the mantle heat flow is between 20 and 23 mW/m2; the temperature at crust-mantle boundary (Moho) ranges from 514℃ to 603℃ and the thermal lithosphere where the heat conduction dominates is 138-182 km thick. Furthermore, in combination with the P wave velocity structure resulting from the deep seismic sounding profile across this region and rheological modeling, we have studied the local composition of the lithosphere and its rheological profile, as well as the strength distribution. We find that the rheological stratification of the lithosphere in this region is apparent. The lowermost of the lower crust is ductile; however,the uppermost of the mantle and the upper and middle parts of the crust are both brittle layers,which is typically the so-called sandwich-like structure. Lithospheric strength is also characterized by the lateral variation, and the uplift region is stronger than the depression region. The lithospheric strength of the northem flank of the Tarim Basin decreases gradually from south to north; the Kuqa Depression has the lowest strength and the south of the Tabei Uplift is strongest.The total lithospheric strength of this region is 4.77× 1012-5.03 × 1013 N/m under extension, and 6.5 × 1012-9.4× 1013 N/m under compression. The lithospheric brittle-ductile transition depth is between 20 km and 33 km. In conclusion, the lithosphere of the northern flank of the Tarim Basin is relatively cold with higher strength, so it behaves rigidly and deforms as a whole, which is also supported by the seismic activity in this region. This rigidity of the Tarim lithosphere makes it little deform interior, but only into flexure under the sedimentation and tectonic loading associated with the rapid uplift of the Tianshan at its northern margin during the Indian-Eurasian continental collision following the Late Eocene. Finally, the influences of factors, such as heat flow, temperature,crustal thickness, and especially basin sediment thickness, on the lithospheric strength are discussed here.     

Convection model of post-glacial uplift

A new approach to analytical and numerical study of the process of the post-glacial uplifting of the Earth’s surface was proposed within the framework of a viscous model. Displacement of the Earth’s surface is considered as the motion of the density boundary due to chemico-density convection. It is shown that the incorporation of the non-Newtonian rheology at observed velocities of post-glacial uplifts requires an obligatory presence of faults in the lithosphere and gives rise to quasi-uniform motion of the mantle material, whose viscosity under the lithosphere is, on the average, sufficiently small and amounts to ～10¹⁹ Pa. The study of the stability of the constructed model of the post-glacial uplift considered as the chemico-density convection relative to the thermal convection shows that the velocity of thermal convection developing in the presence of a quasiuniform mantle flow related to the post-glacial recovery is ～1 m/yr.     

Gravitational energy of core evolution: implications for thermal history and geodynamo power

Using density–pressure relationships for mantle silicate and core alloy closely matching PREM we have constructed six models of the Earth in different evolutionary states. Gravitational energies and elastic strain energies are calculated for models with homogeneous composition, separated mantle and liquid core, separated inner and outer cores with the inner core either liquid or solid and models with increased densities, representing cooling of either the mantle or core. In this way we have isolated the gravitational energy released by each of several evolutionary processes and subtracted the consequent increase in strain energy to obtain the net energy released as heat or geodynamo power. Radiogenic heat (∼7.8×10³⁰ J) is found to contribute only about 25% of the total heat budget, the balance originating as residual gravitational energy from the original accretion and from core separation (14×10³⁰ J). The total energy of compositional convection, driven by inner core formation, is 3.68×10²⁸ J and this is the most important (or even the only) energy source for the dynamo for the most recent 2 billion years. It appears unlikely that the inner core existed much before that time. The total net (gravitational minus strain) energy released in the core by the process of inner core formation, 11.92×10²⁸ J, is not much less than the thermal energy released in this process, 15.1×10²⁸ J. In the mantle the net (gravitational minus strain) energy released by thermal contraction is about 20% of the heat release. All of the numerical results are presented in a manner that allows simple rescaling to any revised density estimates.     

Stability of the oceanic lithosphere with variable viscosity: an initial-value approach

We have studied the problem concerning the onset of convective instabilities below the oceanic lithosphere. A system of linear partial differential equations, in which the background temperature field is time-dependent, is integrated in time to monitor the evolution of incipient disturbances. Two types of rheologies have been examined. One depends strongly on temperature. The other involves a viscosity which is both temperature- and pressure-dependent. The results from this initial-value approach, in which the viscosity profiles migrate downward with time, reveal the importance of considering temperature- and pressure-dependent rheology in issues regarding the development of local instabilities in upper mantle convection. For temperature-dependent viscosity, viscosities of 0(10²⁰P) are required to produce instabilities with growth-rates of 0(.1/Ma). In contrast, these same growth rates can be attained for a temperature- and pressure-dependent viscosity profile with a mean value close to 0(10²⁰P) in the upper mantle, owing to the presence of a low viscosity zone, 0(10²⁰P), existing right below the lithosphere. Unlike the results of temperature-dependent viscosity, whose growth-rates increase with time, the amplification of disturbances in a fluid medium with temperature- and pressure-dependent rheology reaches a maximum at an early age, < 50 Ma, and decreases thereafter with time. This suggests the potential importance played by initial disturbances in the evolution of the oceanic lithosphere.     

The structure of thermal convection and geotherms beneath a continent and ocean

The formation of the thermal cross section of the lithosphere and mantle upon the interaction between the mantle convection and the immobile continent surrounded by the oceanic lithosphere is studied by numerical modeling. The convective temperature and velocity fields and then the averaged geotherms for subcontinental and suboceanic regions up to the boundary with the core are calculated from the solution of convection equations with a jump in viscosity in the continental zone. Using the experimental data on the solidus temperature in the rocks of the upper mantle, the average thickness of the continental and oceanic lithosphere is estimated at 190 and 30 km, respectively. The effect of a hot spot formed in the subcontinental upper mantle at a depth of 250–500 km, which has not been previously noted, is revealed. Although the temperature in this zone is typically assumed to be close to adiabatic, the calculations show that it is actually higher than adiabatic by up to 200°C. The physical mechanism responsible for this effect is associated with the accumulation of convective heat beneath the thermally insulating layer of the continental lithosphere. The revealed anomalies can be important in studying the phase and mineral transformations at the base of the lithosphere and in the regional geodynamical reconstructions.     

Numerical simulations of mantle convection: Time-dependent,three-dimensional,compressible, spherical shell

Abstract

We describe nonlinear time-dependent numerical simulations of whole mantle convection for a Newtonian, infinite Prandtl number, anelastic fluid in a three-dimensional spherical shell for conditions that approximate the Earth's mantle. Each dependent variable is expanded in a series of 4,096 spherical harmonics to resolve its horizontal structure and in 61 Chebyshev polynomials to resolve its radial structure. A semiimplicit time-integration scheme is used with a spectral transform method. In grid space there are 61 unequally-spaced Chebyshev radial levels, 96 Legendre colatitudinal levels, and 192 Fourier longitudinal levels. For this preliminary study we consider four scenarios, all having the same radially-dependent reference state and no internal heating. They differ by their radially-dependent linear viscous and thermal diffusivities and by the specified temperatures on their isothermal, impermeable, stress-free boundaries. We have found that the structure of convection changes dramatically as the Rayleigh number increases from 10⁵ to 10⁶ to 10⁷. The differences also depend on how the Rayleigh number is increased. That is, increasing the superadiabatic temperature drop, δT, across the mantle produces a greater effect than decreasing the diffusivities. The simulation with a Rayleigh number of 10⁷ is approximately 10,000 times critical, close to estimates of that for the Earth's mantle. However, although the velocity structure for this highest Rayleigh number scenario may be adequately resolved, its thermodynamic structure requires greater horizontal resolution. The velocity and thermodynamic structures of the scenarios at Rayleigh numbers of 10⁵ and 10⁶ appear to be adequately resolved. The 10⁵ Rayleigh number solution has a small number of broad regions of warm upflow embedded in a network of narrow cold downflow regions; whereas, the higher Rayleigh number solutions (with large δT) have a large number of small hot upflow plumes embedded in a broad weak background of downflow. In addition, as would be expected, these higher Rayleigh number solutions have thinner thermal boundary layers and larger convective velocities, temperatures perturbations, and heat fluxes. These differences emphasize the importance of developing even more realistic models at realistic Rayleigh numbers if one wishes to investigate by numerical simulation the type of convection that occurs in the Earth's mantle.     

地幔热导率的选取对动力学数值模拟的影响——以岩石圈张裂过程为例

目前存在有多种地幔热导率模型,不同模型在数值和随温压变化的特征上有明显的差异.为探究不同热导率模型对动力学数值模拟结果的影响,本文对不同模型下的岩石圈张裂过程进行模拟研究,探讨地幔热导率对岩石圈热传输、变形和熔融过程的影响及其作用机理.结果显示,不同热导率模型下,岩石圈的变形和熔融特征表现出明显差异.高热导率模型下,岩石圈破裂较晚,形成陆缘较为宽阔,地壳熔融强烈而地幔熔融较弱;低热导率模型下,岩石圈破裂较早,形成陆缘较为狭窄,地幔熔融强烈而地壳熔融较弱.这种差异源于不同地幔热导率下岩石圈和地幔热状态的变化及相应力学性质的改变.高热导率下,热传导的增温效应显著,岩石圈呈现较热的状态,其强度整体较低,壳幔耦合减弱;而低热导率下,热对流的增温效应显著,岩石圈呈较冷的状态,其强度整体较高,壳幔耦合增强.基于模拟结果,本文认为地幔热导率的选取对动力学模拟的结果有着较为显著的影响,相对于随温压的变化,热导率数值的差异对动力学数值模拟的结果影响更大,尤其是对于地幔熔融过程的影响.

     

月表温度对于月幔对流影响的数值模拟研究

行星内部对流计算中, 一般都将其表面温度作为常温处理.但在月球、水星等无大气的天体表面, 温度与纬度明显相关, 月球两极和赤道的平均温度相差可以达到100 K以上.纬度相关的温度边界条件, 是否会影响天体早期对流特征与内部热状态, 过去没有得到重视和研究.本文使用有限元方法进行了二维球壳对流模型的热演化模拟, 以评估无大气行星上, 与纬度高度相关的表面温度对其内部对流和演化的影响.模拟计算结果表明, 表面温度会对月球对流形态产生较大影响, 两极因为相对更冷而易于形成下降流, 上升流更倾向于从赤道位置开始, 在早期演化中表现得尤为明显.受边界条件影响, 月球两极与赤道的岩石圈厚度差异可以达到400 km以上.今后在研究太阳系内月球、水星一类没有大气的天体演化、特别是早期演化时, 对于表面温度纬度相关分布的影响应该予以考虑.

     

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.