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1.
Introduction The velocity field of surface plate motion can be split into a poloidal and a toroidal parts.At the Earth′s surface,the toroidal component is manifested by the existence of transform faults,and the poloidal component by the presence of convergence and divergence,i.e.spreading and subduc-tion zones.They have coupled each other and completely depicted the characteristics of plate tec-tonic motions.The mechanism of poloidal field has been studied fairly clearly which is related to …  相似文献   

2.
Abstract

Models of a differentially rotating compressible convection zone are calculated, considering the inertial forces in the poloidal components of the equations of motion. Two driving mechanisms have been considered: latitude dependent heat transport and anisotropic viscosity. In the former case a meridional circulation is induced initially which in turn generates differential rotation, whereas in the latter case differential rotation is directly driven by the anisotropic viscosity, and the meridional circulation is a secondary effect.

In the case of anisotropic viscosity the choice of boundary conditions has a big influence on the results: depending on whether or not the conditions of vanishing pressure perturbation are imposed at the bottom of the convection zone, one obtains differential rotation with a fast (≥ 10 ms?1) or a slow (～ 1 ms?1) circulation. In the latter case the rotation law is mainly a function of radius and the rotation rate increases inwards if the viscosity is larger in radial direction than in the horizontal directions.

The models with latitude dependent heat transport exhibit a strong dependence on the Prandtl number. For values of the Prandtl number less than 0.2 the pole-equator temperature difference and the surface velocity of the meridional circulation are compatible with observations. For sufficiently small values of the Prandtl number the convection zone becomes globally unstable like a layer of fluid for which the critical Rayleigh number is exceeded.  相似文献   

3.
Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler.  相似文献   

4.
Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection.  相似文献   

5.
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   

6.
Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers Rc for a wide class of parameters. Here, Rc is typically much less than in the case of a single layer, although the scaling Rc～T2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.  相似文献   

7.
Abstract

The transition between axisymmetric and non-axisymmetric régimes of flow in a rotating annulus of liquid subject to horizontal temperature gradient is known from previous experimental studies to depend largely on two dimensionless parameters. These are Θ, which is proportional to the impressed density contrast Δρ and inversely proportional to the square of the angular speed of rotation ω, and  (Taylor number), which is proportional to ω2 /v2 where v is the coefficient of kinematic viscosity. At moderate values of , around 107, the critical value of Θ above which axisymmetric flow is found to OCCUT and below which non-axisymmetric fully-developed baroclinic waves (sloping convection) occur, is fairly insensitive to . Though sharp, the transition exhibits marked hysteresis when the upper surface of the liquid is free (but not when the upper surface is in contact with a rigid lid), and it is argued on the basis of the experimental evidence supported by various results of baroclinic instability theory that both the sharpness of the transition and the hysteresis phenomenon are consequences of the combined effects of potential vorticity gradients and viscosity on the process of sloping convection.

We also present some new experiments on fully-developed baroclinic waves, conducted in a large rotating annulus using liquids of very low viscosity (di-ethyl ether), thus attaining values of  as high as 109 to 1010. The transition from axisymmetric to non-axisymmetric flow is found to lose its sharpness at such high values of , and it is argued that this occurs because viscosity is no longer able to inhibit instabilities at wavelengths less than the so-called ‘Eady short-wave cut-off’, which owe their existence to potential vorticity gradients in the main body of the fluid.  相似文献   

8.
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 32 resonance between Mercury's rotational and orbital periods, is most likely related to surface processes, as opposed to convection. The 3n2 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.  相似文献   

9.
Abstract

We apply a two-dimensional Cartesian finite element treatment to investigate infinite Prandtl number thermal convection with temperature, strain rate and yield stress dependent rheology using parameters in the range estimated for the mantles of the terrestrial planets. To handle the strong viscosity variations that arise from such nonlinear rheology in solving the momentum equation, we exploit a multigrid method based on matrix-dependent intergrid transfer and the Galerkin coarse grid approximation. We observe that the matrix-dependent transfer algorithm provides an exceptionally robust and efficient means for solving convection problems with extreme viscosity gradients. Our algorithm displays a convergence rate per multigrid cycle about five times better than what other published methods (e.g., CITCOM of Moresi and Solomatov, 1995) offer for cases with similar extreme viscosity variation. The algorithm is explained in detail in this paper.

When this method is applied to problems with temperature and strain rate dependent rheologies, we obtain strongly time dependent solutions characterized by episodic avalanching of cold material from the upper boundary layer to the bottom of the convecting domain for a significantly broad range of parameter values. In particular, we observe this behavior for the relatively simple case of temperature dependent Newtonian rheology with a plastic yield stress. The intensity and temporal character of the episodic behavior depends sensitively on the yield stress value. The regions most strongly affected by the yield stress are thickened portions of the cold upper boundary layer which can suddenly become unstable and form downgoing diapirs. These computational results suggest that the finite yield properties of silicate rocks must play a vitally important role in planetary mantle dynamics. Although our example calculations were selected mainly to illustrate the power of our multigrid method, they suggest that many possible exotic behaviors in planetary mantles have yet to be discovered.  相似文献   

10.
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   

11.
Abstract

Stability analysis is formulated for a two-layer fluid model in which the upper and lower layers are convectively stable and unstable, respectively. With discontinuities in viscosity and conductivity at the interface, the exchange of stability does not generally hold and overstability is possible. A detailed analytical treatment is presented for the case of small viscosity and conductivity in which viscous and conducting boundary layers are formed at the interface.

The usual damping effect due to the energy dissipation by viscosity and thermal conductivity exists irrespective of whether the mode is the convection or the gravity wave, but, for larger horizontal wave lengths, the effect of the boundary layer can become more important. The jump in the thermal conductivity in the boundary layer can give rise to overstability of the gravity wave in agreement with Souffrin and Spiegel (1967). The jump in the viscosity provides a self-catalytic action for the unstable flow if the viscosity is assumed to be the nonlinear turbulent viscosity due to the motion itself. The effect, however, is not strong enough to overcome the usual viscous damping.  相似文献   

12.
Abstract

We study the bifurcation to steady two-dimensional convection with the heat flux prescribed on the fluid boundaries. The fluid is weakly non-Boussinesq on account of a slight temperature dependence of its material properties. Using expansions in the spirit of shallow water theory based on the preference for large horizontal scales in fixed flux convection, we derive an evolution equation for the horizontal structure of convective cells. In the steady state, this reduces to a simple nonlinear ordinary differential equation. When the horizontal scales of the cells exceed a certain critical size, the bifurcation to steady convection is subcritical and the degree of subcriticality increases with increasing cell size.  相似文献   

13.

Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.  相似文献   

14.
Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.  相似文献   

15.
Abstract

A laboratory model of thermal convection under a central force field has been constructed using a strong, alternating electric field gradient in a dielectric liquid. Both the electric field gradient and a temperature gradient are maintained between concentric vertical cylinders. The onset of thermal convection is detected by heat transfer and temperature measurements. It is governed by an electrical Rayleigh number, in which the electric force replaces gravity. Marginal stability analysis gives a critical electrical Rayleigh number in agreement with the experimentally determined value.  相似文献   

16.
In a traditional analytical method, the convective features of Earth’s mantle have been inferred from surface signatures obtained by the geodynamic model only with depth-dependent viscosity structure. The moving and subducting plates, however, bring lateral viscosity variations in the mantle. To clarify the effects of lateral viscosity variations caused by the plate-tectonic mechanism, I have first studied systematically instantaneous dynamic flow calculations using new density-viscosity models only with vertical viscosity variations in a three-dimensional spherical shell. I find that the geoid high arises over subduction zones only when the vertical viscosity contrast between the upper mantle and the lower mantle is O(103) to O(104), which seems to be much larger than the viscosity contrast suggested by other studies. I next show that this discrepancy may be removed when I consider the lateral viscosity variation caused by the plate-tectonic mechanism using two-dimensional numerical models of mantle convection with self-consistently moving and subducting plates, and suggest that the observed geoid anomaly on the Earth’s surface is significantly affected by plate-tectonic mechanism as a first-order effect.  相似文献   

17.
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18.
Emplacement of a large igneous province is usually accompanied by kilometre-scale uplift over an area of ∼106 km2. We have developed a method for mapping the dynamically supported swell associated with the North Atlantic Igneous Province by inverting palaeo-topographic information from continental margins. In the forward model, latest Palaeocene palaeo-topography around Britain and Ireland is calculated by correcting present-day topography for global sea-level change, denudation and dynamic support. We initially assume a Gaussian, axially symmetric dynamic support profile. Modelled coastlines are compared with palaeo-coastlines mapped on 2D and 3D reflection seismic data. In the inverse model, the amplitude, width and centre of the dynamically supported swell are determined by minimising misfit between modelled and observed coastlines. Uncertainties associated with global sea-level variation and denudation have little effect on this calculation. The best-fit dynamic support profile from inverting palaeo-coastline positions is in good agreement with dynamic support estimates from subsidence anomalies measured in extensional sedimentary basins fringing Britain and Ireland. However, a circular planform of dynamic support cannot simultaneously account for palaeo-coastlines, subsidence anomalies and the spatial extent of the North Atlantic Igneous Province. In combination, these data suggest that the swell was more irregular in planform. This inference can be tested in future by modelling stratigraphic data from offshore Norway, Greenland and Canada. The large areal extent and short time interval for inflation of the dynamically supported swell are best explained by rapid convective emplacement of an abnormally hot mantle layer horizontally beneath the lithosphere, during the starting phase of the Icelandic convective system. We emphasise the need to interpret the igneous record jointly with the dynamic support history when discussing models of large igneous province formation and mantle convection.  相似文献   

19.
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20.
张晨  张双喜 《地震学报》2014,36(5):872-882
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.   相似文献   

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