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1.
将地幔地震波速度异常转换为地幔横向黏度变化(达到3个数量级),在球坐标系下计算了瑞雷数为106、上边界为刚性、下边界为应力自由等温边界条件下的岩石层底部的地幔对流极型和环型应力场.结果表明,地幔对流极型应力场与地表大尺度构造具有良好的对应关系:俯冲带和碰撞带的应力呈现挤压状态,而洋中脊处的应力则呈现拉张状态.地幔对流环... 相似文献
2.
讨论了地幔内部的粘滞度及施加在地表和CMB 的边界条件对地幔对流环型场的激发分析表明,当粘滞度侧向均匀时,环型场与极型场自然解耦,且环型场不影响重力位,当粘滞度侧向不均时,环型场与极型场耦合在一起.两者共同影响重力位.当引入板块运动速度时,边界条件非零,也能激发环型场;对侧向均匀粘滞度地幔,零边界条件不能激发环型场 相似文献
3.
Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν0 + ν1 exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 107 and Rayleigh numbers of up to 108 are studied.For intermediate viscosity contrasts (around 103), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth zr (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 1015?5 × 1016 m2 s?1 for viscosity in the thermal boundary layer below the plate. 相似文献
4.
建立了三维黏度扰动下的变黏度地幔对流模型，并提供了在引入地幔的三维地震波速度结构下相应的求解方法. 依此反演了瑞利数Ra = 106时，两种不同边界条件下的极、环型场对流图像，这有助于深化对地幔物质流动和大地构造运动的深部动力学过程的认识和理解. 研究结果表明，不但地幔浅部的极型场对流图像显示出了与大地构造运动的相关性并揭示了其深部动力学过程，更重要的是，地幔浅部的环型场对流图像首次为我们认识和理解板块构造的水平与旋转运动提供了重要的信息：环型场速度剖面中在赤道附近存在一条大致南东东—北西西向的强对流条带，可能与环赤道附近大型剪切带的形成相关，进而表明可能是该带强震发生的深部动力学背景；在南北半球存在的旋转方向相反的对流环表明它们整体上可能存在差异旋转. 相似文献
5.
U.R. Christensen 《Physics of the Earth and Planetary Interiors》1984,35(4):264-282
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. 相似文献
6.
本文以板块绝对运动AM1-2模型为边界条件探讨了不同的瑞利数下地幔热对流模型.结果表明,瑞利数小于10000（529.41）时,地幔对流呈现以板块驱动图式,运动的极型场和环型场由板块运动激发,两种场占有差不多相同的功率.当瑞利数增加到接近或略超过最低临界值时（约1.5倍）,对流呈现出复杂状态:1.板块运动速率小于下伏地幔对流速率;2.区域性的双层对流环出现;3.对流谱成分发生变化;4.环型场仅在地幔很浅的区域中起作用,而在地幔深部对流图式中影响很小. 相似文献
7.
假定地幔为一个均匀的、粘滞系数为常数、同时均匀分布放射性热源的流体球层,其内部存在的对流则由流体力学3个基本方程:运动方程、能量方程和连续性方程确定.如果假定地幔处于低瑞利数的状态（临界瑞利数1.5倍左右）,那么上述方程中的非线性项可以忽略不计.作为一类可能的模型,本文计算一组用6个边界条件确定6个未知数的线性方程组.这些条件包括板块绝对运动极型场、地球大地水准面异常和地震层析结果提供的地幔密度分布横向不均匀相应的“刚性地球”水准面异常等.模型计算表明:1.地幔中流体运动格局不仅受地幔热动力学参数（瑞利数）控制,而且强烈地受边界条件的影响.2.若不限定下边界为等温边界,则上、下地幔之间并不呈现出活动性明显差异;但是在模型瑞利数加大到一定值时,核-幔边界附近将出现一些局部的小尺度对流环.3.当模型瑞利数从很小增加时,对流格局将发生变化,这些格局可能反应由地幔热动力学参数决定的地幔固有特性.4.当瑞利数为50000和80000时,核-幔边界形变与PcP波得到的结果吻合较好. 相似文献
8.
Gary A. Glatzmaier 《地球物理与天体物理流体动力学》2013,107(2):223-264
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. 相似文献
9.
Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection. 相似文献
10.
Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 105 and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated. 相似文献
11.
板块运动是地幔对流的主要证据之一．同时，作为地球动力系统中一个相对独立部分，板块自身的存在和运动对地幔内部物质的流动形态有巨大影响．地幔内部的流动由两部分组成：一是由内部非绝热温度差异造成的自由对流解；另一部分是由在地表运动的板块所激发．作为系列工作的第一部分，本文研究球腔中的自由热对流问题．得到了对地幔对流研究有实际意义的下边界为自由、上边界为刚性情况下的临界瑞利数值，不同的瑞利数时球腔内流场和温度场的分布形态等． 相似文献
12.
Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y 2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core. 相似文献
13.
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. 相似文献
14.
Elizabeth M. Robinson Barry Parsons Stephen F. Daly 《Earth and Planetary Science Letters》1987,82(3-4)
A simple model for mid-plate swells is that of convection in a fluid which has a low viscosity layer lying between a rigid bed and a constant viscosity region. Finite element calculations have been used to determine the effects of the viscosity contrast, the layer thickness and the Rayleigh number on the flow and on the perceived compensation mechanism for the resulting topographic swell. As the viscosity decreases in the low viscosity zone, the effective local Rayleigh number for the top boundary layer of the convecting cell increases. Also, because the lower viscosity facilitates greater velocities in the low viscosity zone, the low viscosity layer produces proportionally greater horizontal flow near the conducting lid, causing the base of the conducting lid to appear like a free boundary. The change in the local Rayleigh number and in the effective boundary condition both cause the top boundary layer to thin. Through a Green's function analysis, we have found that the low viscosity zone damps the response of the surface topography to the temperature anomalies at depth, whereas it causes the gravity and geoid response functions to change sign at depth counteracting the positive contributions from the shallower temperature variations. By increasing the viscosity contrast, the conbined effects of the thinning of the boundary layer and the behaviour of the response functions allow the apparent depth of compensation to become arbitrarily small. Therefore, shallow depths of compensation cannot be used to argue against dynamic support of mid-plate swells. Furthermore, we compared the distribution of the effective compensating densities, which is used to obtain the geoid, to that of Pratt compensation, which is often used to calculate the depth of compensation from geoid and topography data for mid-plate swells. For all of our calculations including those with no low viscosity layer, the effective gravitational mass distribution is more complex than assumed in simple Pratt models, so that the Pratt models are not an appropriate gauge of the compensation mechanism. 相似文献
15.
The effects of variable viscosity on flow dynamics within spherical shells are investigated using a finite-element thermal convection model, and preliminary result for cases with relatively low Rayleigh numbers and small viscosity contrasts are reported. These results demonstrate some general effects of viscosity variation on mantle dynamics, and, in particular, the generation of toroidal energy. Since lateral viscosity variations are necessary in the generation of toroidal motion in a thermally driven convective system, it is not surprising our results show that flows with greater viscosity contrasts produce greater amounts of toroidal energy. Our preliminary study further shows that solutions become more time-dependent as viscosity contrasts increase. Increasing the Rayleigh number is also found to increase the magnitude of toroidal energy. Internal heating, on the other hand, appears to lead to less toroidal energy compared wth bottom heating because it tends to produce a thermally more uniform interior and thus smaller viscosity variations. 相似文献
16.
The observed plate velocities contain two types of motions. The poloidal component is related to the formation of ridges and subduction zones and the toroidal field expresses the shearing of surface plates. One very important consideration in modeling flow in the earth's mantle is the existence and motion of the lithospheric plates. The motion of plates represents a large-scale circulation with strong viscous coupling to the mantle underneath. The mantle flow probably is neither a purely free convection driven by buoyancy forces due to nonadiabatic temperature gradients in the mantle nor a forced convection generated by boundary forces, but a mixed convection that combines the effects of boundary and buoyancy forces. We present, in this paper, the mixed convection model resulting in a surface velocity field that contains both the observed poloidal and toroidal components. 相似文献
17.
We present the preliminary results of axisymmetric numerical simulations of thermal convection in the mantle with a phase transition boundary at 660 km depth and a viscosity interface at 1000 km depth. The results, obtained for Ra = 2 × 10
6
, are compared with the case when both the phase and the viscosity boundaries are located at the same depth of 660 km. 相似文献
18.
Spatial fields of temperature, velocity, overlithostatic pressure, and horizontal stresses in the Earth’s mantle are studied
in two-dimensional (2D) numerical Cartesian models of mantle convection with variable viscosity. The calculations are carried
out for three different patterns of the viscosity distribution in the mantle: (a) an isoviscous model, (b) a four-layer viscosity
model, and (c) a temperature- and pressure-dependent viscosity model. The pattern of flows, the stresses, and the surface
heat flow are strongly controlled by the viscosity distribution. This is connected with the formation of a cold highly viscous
layer on the surface, which is analogous to the oceanic lithosphere and impedes the heat transfer. For the Rayleigh number
Ra = 107, the Nusselt number, which characterizes the heat transfer, is Nu = 34, 28, and 15 in models with constant, four-layered,
and p, T-dependent viscosity, respectively. In all three models, the values of overlithostatic pressure and horizontal stresses σ
xx
in a vast central region of the mantle, which occupies the bulk of the entire volume of the computation domain, are approximately
similar, varying within ±5 MPa (±50 bar). This follows from the fact that the dimensionless mantle viscosity averaged over
volume is almost similar in all these models. In the case of temperature- and pressure-dependent viscosity, the overlithostatic
pressure and stress σ
xx
fields exhibit much stronger concentration towards the horizontal boundaries of the computation domain compared to the isoviscous
model. This effect occurs because the upwellings and downwellings in a highly viscous region experience strong variations
in both amplitude and direction of flow velocity near the horizontal boundaries. In the models considered with the parameters
used, the stresses in the upper and lower mantle are approximately identical, that is, there is no denser concentration of
stresses in the upper or lower mantle. In contrast to the overlithostatic pressure field, the fields of horizontal stresses
σ
xx
in all models do not exhibit deep roots of highly viscous downwelling flows. 相似文献
19.
Important though indirect information about the internal structure of Venus is provided by its topography and geoid. In the last decades this information has been used to constrain the Venus mantle viscosity structure and its dynamic regime. Recently, the geodynamic inversion of the Venus?? geoid and topography resulted in a group of best fitting viscosity profiles. We use these viscosity models here as an input to our mantle convection code. We carry out simulations of the Venus?? mantle evolution in a 3D spherical shell with depth dependent viscosity and check whether the character of the dynamic topography and the geoid represented by their power spectra fits the observed quantities. We compare the results with several other models obtained for different viscosity stratifications (constant, constant with highly viscous lithosphere, linear increase of viscosity). Further, we estimate the effect of other factors such as internal heating and varying Rayleigh number. We use a 2D spherical axisymmetric convection code to study the effect of lateral viscosity variations. In these 2D models we monitor the topography and the geoid developing above the axisymmetric plume and compare them with the observed elevations of Venus?? geoid and topography in several Regia. Though none of the models fits observed data perfectly, we can generally conclude, that the best fit between the observed and predicted quantities is reached for viscosity profiles with 200 km thick lithosphere followed by a gradual increase of viscosity with depth and with the upper mantle viscosity of 2 × 10 21 Pa s. For all viscosity profiles the predicted geoid and topography spectra match the observed ones only up to the degree 40, thus indicating other than dynamic origin of these quantities for higher degrees. 相似文献
20.
Abstract Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell with and without inhomogeneous temperature anomalies on the top boundary have been carried out using a three-dimensional, time-dependent, spectral-transform code. The spherical shell of Boussinesq fluid has inner and outer radii the same as those of the Earth's liquid outer core. The Taylor number is 107, the Prandtl number is 1, and the Rayleigh number R is 5Rc (Rc is the critical value of R for the onset of convection when the top boundary is isothermal and R is based on the spherically averaged temperature difference across the shell). The shell is heated from below and cooled from above; there is no internal heating. The lower boundary of the shell is isothermal and both boundaries are rigid and impermeable. Three cases are considered. In one, the upper boundary is isothermal while in the others, temperature anomalies with (l,m) = (3,2) and (6,4) are imposed on the top boundary. The spherically averaged temperature difference across the shell is the same in all three cases. The amplitudes of the imposed temperature anomalies are equal to one-half of the spherically averaged temperature difference across the shell. Convective structures are strongly controlled by both rotation and the imposed temperature anomalies suggesting that thermal inhomogeneities imposed by the mantle on the core have a significant influence on the motions inside the core. The imposed temperature anomaly locks the thermal perturbation structure in the outer part of the spherical shell onto the upper boundary and significantly modifies the velocity structure in the same region. However, the radial velocity structure in the outer part of the shell is different from the temperature perturbation structure. The influence of the imposed temperature anomaly decreases with depth in the shell. Thermal structure and velocity structure are similar and convective rolls are more columnar in the inner part of the shell where the effects of rotation are most dominant. 相似文献