首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
  相似文献   

2.
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   

3.
The rheology of the lower mantle of the Earth is examined from the viewpoint of solid state physics. Recent developments in high-pressure research suggest that the lower mantle contains a considerable amount of (Mg, Fe)O with Fe/Mg + Fe = 0.2–0.3. The pressure and temperature dependences of diffusion in (Mg, Fe)O are estimated by the theory of diffusion in ionic solids. Of the materials composing the lower mantle, (Mg, Fe)O may be the “softest”, and therefore the rheology of the lower mantle may be that of (Mg, Fe)O, unless the framework effect is important.Temperatures in the lower mantle are inferred from the depths of phase transitions and the melting temperatures of the core materials. A thermal boundary layer at the base of the mantle is suggested. The physical mechanisms of creep are examined based on a grain size-stress relation and non-Newtonian flow is shown to be the dominant flow mechanism in the Earth's mantle.The effective viscosity for the temperature models, with and without the thermal boundary layer, is calculated for constant stress and constant strain rate (with depth). For constant strain rate, which may be appropriate for discussing the mechanics of descending slabs, the increase in effective viscosity with depth is smaller than for the constant-stress case, which may be appropriate for discussing the flow induced by the surface motion of plates.The relatively small depth gradient of viscosity, for constant strain rate, suggests that the lower mantle could also participate in convection. The effective viscosity increases with depth, however, by at least 102 to 103 from the top to the bottom of the lower mantle, for a reasonable range of activation volumes and temperatures. There will be a low-viscosity layer at the base of the mantle, in contrast to the high-viscosity layer at the top of the mantle (plates), if a thermal boundary layer is present. The constant Newtonian viscosity inferred from rebound data may be an apparent feature resulting from the difference in deformation mechanisms between isostatic rebound and large-scale flow.  相似文献   

4.
A joint effect of weak zones, dividing lithospheric plates, and lateral viscosity variations (LVV) in the whole mantle on the observed geoid is investigated by a new numerical approach. This technique is based on the substantially revised method introduced by Zhang and Christensen (Geophys J Int 114:531–547, 1993) for solving the Navier–Stokes–Poisson equations in the spectral domain with strong LVV. Weak plate boundaries (WPB) are introduced based on an integrated global model of plate boundary deformations GSRM (Kreemer et al. in Geophys J Int 154:8–34, 2003). The effect of WPB on the geoid is significant and reaches ?40 to 70 m with RMS ~20 m. The peaks are observed over large subduction zones in South America and the southwestern Pacific in agreement with previous studies. The positive geoid anomaly in South America could be explained largely by a dynamic effect of decoupling of the Nazca and South American plates. The negative changes of the geoid mostly relate to mid-oceanic ridges. The amplitude of the effect depends on the viscosity contrasts at WPB compared with the plate viscosity until its value reaches the limit of 2.5–3 orders of magnitude. This value might be considered as a level at which the plates are effectively decoupled. The effect of WPB exceeds the effect of LVV in the whole mantle and generally does not correlate with it. However, inclusion of LVV reduces the geoid perturbations due to WPB by about 10 m. Therefore, it is important to consider all factors together. The geoid changes mainly result from changes of the dynamic topography, which are about ?300 to +500 m. The obtained results show that including WPB may significantly improve the reliability of instantaneous global dynamic models.  相似文献   

5.
The radial viscosity structure of the Earth is explored on the basis of the geoid observations. The variations of uncertainty in seismic tomography models are accounted for when finding the radial viscosity structure. The new methodology we propose attempts to fit more closely those features of the geoid that are better constrained by tomography models and avoids to fit those features that are poorly constrained. This approach is particularly important because the error of geoid predictions caused by uncertainties in seismic tomography models is overwhelmingly larger than the noise in the geoid measurements. The synthetic tests indicate that the viscosity structures obtained by disregarding the uncertainty variations in seismic tomography models can be biased depending on the geoid spectral band and on the ‘input’ seismic tomography model. When the uncertainty variations in seismic models are considered in the inversion process, results do not indicate a viscosity in the transition zone lower than in the upper mantle. A robust feature found with the new method is a viscosity in the upper mantle two orders of magnitude smaller than in the lower mantle. The error covariance of seismic tomography models is critical for the method we suggest. A covariance matrix rigorously derived by seismologists should help to even more reliably infer the viscosity structure and relation between anomalies in density and seismic velocities from surface observations such as the geoid, and thus lead to a better knowledge of the Earth interior.  相似文献   

6.
New satellite technology to measure changes in the Earth’s gravity field gives new possibilities to detect layers of low viscosity inside the Earth. We used density models for the Earth mantle based on slab history as well as on tomography and fitted the viscosity by comparison of predicted gravity to the new CHAMP gravity model. We first confirm that the fit to the observed geoid is insensitive to the presence of a low viscosity anomaly in the upper mantle as long as the layer is thin ( 200 km) and the viscosity reduction is less than two orders of magnitude. Then we investigated the temporal change in geoid by comparing two stages of slablet sinking based on subduction history or by advection of tomography derived densities and compared the spectra of the geoid change for cases with and without a low viscosity layer, but about equal fit to the observed geoid. The presence of a low viscosity layer causes relaxation at smaller wavelength and thus leads to a spectrum with relatively stronger power in higher modes and a peak around degrees 5 and 6. Comparing the spectra to the expected degree resolution for GRACE data for a 5 years mission duration shows a weak possibility to detect changes in the Earth’s gravity field due to large scale mantle circulation, provided that other causes of geoid changes can be taken into account with sufficient accuracy. A discrimination between the two viscosity cases, however, demands a new generation of gravity field observing satellites.  相似文献   

7.
Seismic studies of the lowermost mantle suggest that the core-mantle boundary (CMB) region is strongly laterally heterogeneous over both local and global scales. These heterogeneities are likely to be associated with significant lateral viscosity variations that may influence the shape of the long-wavelength non-hydrostatic geoid. In the present paper we investigate the effect of these lateral viscosity variations on the solution of the inverse problem known as the inferences of viscosity from the geoid. We find that the presence of lateral viscosity variations in the CMB region can significantly improve the percentage fit of the predicted data with observations (from 42 to 70% in case of free-air gravity) while the basic characterisics of the mantle viscosity model, namely the viscosity increase with depth and the rate of layering, remain more or less the same as in the case of the best-fitting radially symmetric viscosity models. Assuming that viscosity is laterally dependent in the CMB region, and radially dependent elsewhere, we determine the largescale features of the viscosity structure in the lowermost mantle. The viscosity pattern found for the CMB region shows a high density of hotspots above the regions of higher-than-average viscosity. This result suggests an important role for petrological heterogeneities in the lowermost mantle, potentially associated with a post-perovskite phase transition. Another potential interpretation is that the lateral viscosity variations derived for the CMB region correspond in reality to lateral variations in the mechanical conditions at the CMB boundary or to large-scale undulations of a chemically distinct layer at the lowermost mantle.  相似文献   

8.
A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 1021 N s m–2 with a free-slip bottom boundary.  相似文献   

9.
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.  相似文献   

10.
《Journal of Geodynamics》2009,47(3-5):104-117
Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.  相似文献   

11.
Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.  相似文献   

12.
  相似文献   

13.
Water released from subducting slabs through a dehydration reaction may lower the viscosity of the mantle significantly. Thus, we may expect a low viscosity wedge (LVW) above the subducting slabs. The LVW coupled with a large-scale flow induced by the subducting slabs may allow the existence of roll-like small-scale convection whose axis is normal to the strike of the plate boundary. Such a roll structure may explain the origin of along-arc variations of mantle temperature proposed recently in northeast Japan. We study this possibility using both 2D and 3D models with/without pressure- and temperature-dependent viscosity. 2D models without pressure and temperature dependence of viscosity show that, with a reasonable geometry of the LVW and subduction speed, small-scale convection is likely to occur when the viscosity of the LVW is less than 1019 Pa s. Corresponding 3D model studies reveal that the wavelength of rolls depends on the depth of the LVW. The inclusion of temperature-dependent viscosity requires the existence of further low viscosity in the LVW, since temperature dependence suppresses the instability of the cold thermal boundary layer. Pressure (i.e. depth) dependence coupled with temperature dependence of the viscosity promotes short wavelength instabilities. The model, which shows a relatively moderate viscosity decrease in the LVW (most of the LVW viscosity is 1018∼1019 Pa s) and a wavelength of roll ∼80 km, has a rather small activation energy and volume (∼130 kJ/mol and ∼4 cm3/mol) of the viscosity. This small activation energy and volume may be possible, if we regard them as an effective viscosity of non-linear rheology.  相似文献   

14.
Predictions of present day secular variations in the Earth's long wavelength geopotential driven by glacial isostatic adjustment (GIA) have previously been analyzed to infer the radial profile of mantle viscosity and to constrain ongoing cryospheric mass balance. These predictions have been based on spherically symmetric Earth models. We explore the impact of lateral variations in mantle viscosity using a new finite-volume formulation for computing the response of 3-D Maxwell viscoelastic Earth models. The geometry of the viscosity field is constrained from seismic-to-mographic images of mantle structure, while the amplitude of the lateral viscosity variations is tuned by a free parameter in the modeling. We focus on the zonal J˙? harmonics for degrees ? = 2,…,8 and demonstrate that large-scale lateral viscosity variations of two to three orders of magnitude have a modest, 5-10%, impact on predictions of J˙2. In contrast, predictions of higher degree harmonics show a much greater sensitivity to lateral variation in viscosity structure. We conclude that future analyses of secular trends (for degree ? > 2) estimated from ongoing (GRACE, CHAMP) satellite missions must incorporate GIA predictions based on 3-D viscoelastic Earth models.  相似文献   

15.
—Recently a high-resolution tomographic model, the P1200, based on P-wave travel times was developed, which allowed for detailed imaging of the top 1200 km of the mantle. This model was used in diverse ways to study mantle viscosity structure and geodynamical processes. In the spatial domain there are lateral variations in the transition zone, suggesting interaction between the lower-mantle plumes and the region from 600 km to 1000 km. Some examples shown here include the continental region underneath Manchuria, Ukraine and South Africa, where horizontal structures lie above or below the 660 km discontinuity. The blockage of upwelling is observed under central Africa and the interaction between the upwelling and the transition zone under the slow Icelandic region appears to be complex. An expansion of the aspherical seismic velocities has been taken out to spherical harmonics of degree 60. For degrees exceeding around 10, the spectra at various depths decay with a power-law like dependence on the degree, with the logarithmic slopes in the asymptotic portion of the spectra containing values between 2 and 2.6. These spectral results may suggest the time-dependent nature of mantle convection. Details of the viscosity structure in the top 1200 km of the mantle have been inferred both from global and regional geoid data and from the high-resolution tomographic model. We have considered only the intermediate degrees (l = 12–25) in the nonlinear inversion with a genetic algorithm approach. Several families of acceptable viscosity profiles are found for both oceanic and global data. The families of solutions for the two data sets have different characteristics. Most of the solutions asociated with the global geoid data show the presence of asthenosphere below the lithosphere. In other families a low viscosity zone between 400 and 600 km depth is found to lie atop a viscosity jump. Other families evidence a viscosity decrease across the 660 km discontinuity. Solutions from oceanic geoid show basically two low viscosity zones one lying right below the lithosphere; the other right under 660-km depth. All of these results bespeak clearly the plausible existence of strong vertical viscosity stratification in the top 1000 km of the mantle. The presence of the second asthenosphere may have important dynamical ramifications on issues pertaining to layered mantle convection. Numerical modelling of mantle convection with two phase transitions and a realistic temperature- and pressure-dependent viscosity demonstrates that a low viscosity region under the endothermic phase transition can indeed be generated self-consistently in time-dependent situations involving a partially layered configuration in an axisymmetric spherical-shell model.  相似文献   

16.
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   

17.
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   

18.
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.  相似文献   

19.
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 σxz and σxx 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 σxz and superlithostatic horizontal stresses σxx 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.  相似文献   

20.
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   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号