Basal Heating Research Articles

Two‐stage evolution of the Earth's mantle inferred from numerical simulation of coupled magmatism‐mantle convection system with tectonic plates

AbstractSelf‐consistent numerical models are developed for a coupled magmatism‐mantle convection system with tectonic plates in a two‐dimensional rectangular box to understand the Earth's mantle evolution. The mantle evolves in two stages owing to decaying internal and basal heating, provided that the lithosphere is mechanically strong enough to inhibit spontaneous formation of new subduction zones by ridge push force. On the earlier stage that continues for the first 1–2 Gyr, the deep mantle is strongly heated, and hot materials there frequently ascend to the surface as bursts. The mantle bursts cause vigorous magmatism and make the lithosphere move chaotically. The thermostat effect of the vigorous magmatism keeps the average temperature in the upper mantle below about 1800 K no matter how strongly the mantle is heated. As the heating rate of the mantle declines, however, the mantle evolves into the later stage where mantle bursts subside, rigid tectonic plates emerge to move rather steadily, and subducted basaltic crusts accumulate on the core‐mantle boundary to form compositionally dense piles. Hot plumes occasionally ascend from the basaltic piles to cause magmatism. It takes time on the order of one billion years for the slabs that sink into the lower mantle to return back to the upper mantle, and the long overturn time makes the thermal history of the upper mantle, which has been petrologically constrained for the Earth, distinct from that of the whole mantle. The long overturn time also makes water injected into the mantle by slabs distribute heterogeneously.

Mantle dynamics in super-Earths: Post-perovskite rheology and self-regulation of viscosity

The discovery of extra-solar “super-Earth” planets with sizes up to twice that of Earth has prompted interest in their possible lithosphere and mantle dynamics and evolution. Simple scalings suggest that super-Earths are more likely than an equivalent Earth-sized planet to be undergoing plate tectonics. Generally, viscosity and thermal conductivity increase with pressure while thermal expansivity decreases, resulting in lower convective vigour in the deep mantle, which, if extralopated to the largest super-Earths might, according to conventional thinking, result in no convection in their deep mantles due to the very low effective Rayleigh number. Here we evaluate this. First, as the mantle of a super-Earth is made mostly of post-perovskite we here extend the density functional theory (DFT) calculations of post-perovskite activation enthalpy of to a pressure of 1TPa, for both slowest diffusion (upper-bound rheology) and fastest diffusion (lower-bound rheology) directions. Along a 1600K adiabat the upper-bound rheology would lead to a post-perovskite layer of a very high (∼1030Pas) but relatively uniform viscosity, whereas the lower-bound rheology leads to a post-perovskite viscosity increase of ∼7 orders of magnitude with depth; in both cases the deep mantle viscosity would be too high for convection. Second, we use these DFT-calculated values in statistically steady-state numerical simulations of mantle convection and lithosphere dynamics of planets with up to ten Earth masses. The models assume a compressible mantle including depth-dependence of material properties and plastic yielding induced plate-like lithospheric behaviour. Results confirm the likelihood of plate tectonics for planets with Earth-like surface conditions (temperature and water) and show a self-regulation of deep mantle temperature. The deep mantle is not adiabatic; instead feedback between internal heating, temperature and viscosity regulates the temperature such that the viscosity has the value needed to facilitate convective loss of the radiogenic heat, which results in a very hot perovskite layer for the upper-bound rheology, a super-adiabatic perovskite layer for the lower-bound rheology, and an azimuthally-averaged viscosity of no more than 1026Pas. Convection in large super-Earths is characterised by large upwellings (even with zero basal heating) and small, time-dependent downwellings, which for large super-Earths merge into broad downwellings. In the context of planetary evolution, if, as is likely, a super-Earth was extremely hot/molten after its formation, it is thus likely that even after billions of years its deep interior is still extremely hot and possibly substantially molten with a “super basal magma ocean” – a larger version of the proposal of Labrosse et al. (Labrosse, S., Hernlund, J.W., Coltice, N. [2007]. Nature 450, 866–869), although this depends on presently unknown melt–solid density contrast and solidus.

Energy reduction measures in agricultural greenhouses heating: Envelope, systems and solar energy collection

While a great reduction of the energy demand for the environmental control of civil buildings has been reached in recent years, still a great potential of energy savings lies in other sectors like the one of agricultural production. The scope of this paper is to investigate the energy performance of some of the recent envelope and systems technologies that best can contribute to a great reduction of the energy demand for the climatic control of a greenhouse for intensive crop production. This article concentrates on three aspects: the use of polycarbonate hollow sheets to reduce the thermal transmittance of the glazing, the application of polypropylene sheets as a basal heating system and the solar energy capture by means of low cost plastic solar collectors. A tunnel greenhouse for basil production of 40m of length and 10m of width was considered as a case study and modelled within the EnergyPlus simulation software. The climate locations that were considered refer to the north-west of Italy. The results show that savings of the order of 30% can be achieved by using more insulated transparent materials. On the contrary, the application of the solar collectors still remains problematic because of the large land use and lower global efficiencies.

On the scaling of heat transfer for mixed heating convection in a spherical shell

Planetary mantles and solid shells of icy satellites potentially undergoing natural convection are subjected to a mixed heating configuration including basal (from thermal exchanges with a subjacent, possibly liquid, layer) and internal (from radioactive decay or tidal dissipation) sources. In the quasi-static approximation, the average cooling/heating of the layer is also considered as an instantaneous internal heat source to model transient evolutions. In a previous study (Choblet and Parmentier, 2009), we have proposed simple scaling relationships to describe heat transfer for an isoviscous fluid in such a mixed heating configuration in the case of a Cartesian geometry. Here, we extend this analysis to the case of a spherical shell. A framework based on a temperature scale associated with the global surface heat flux is introduced. This enables a simple description of the cold boundary layer, independent of the heating configuration and of the relative radius of the inner boundary of the shell. When free-slip mechanical boundaries are prescribed, numerical experiments present a significant departure from the prediction (up to ≃30%). We show that this is caused by the impact of hot plumes on the cold boundary layer when a large amount of basal heating is prescribed. The results of no-slip calculations are well predicted by the scaling which thus could be applied to planetary mantles where convection occurs beneath a rigid lithosphere. The lower hot boundary layer is included in our analysis through the ratio of the temperature differences across both boundary layers: the simple scaling indicates that this ratio is independent of the Rayleigh number, and varies only with the amount of basal heating and with the curvature of the layer. This is shown to be valid in the no-slip case. In the free-slip case, a departure from this scaling is observed in the calculations but for the range of values corresponding to planetary bodies, the agreement is good. We conduct transient numerical experiments and show that the quasi-static approximation is valid in the configuration investigated here. Implications for more complex planetary set-ups are discussed.

The impact of a weak south pole on thermal convection in Enceladus’ ice shell

Enceladus exhibits a strong hemispheric dichotomy of tectonism and heat flux, with geologically young, heavily tectonized terrains and a high heat flux in the South Polar Terrain (SPT) and relatively ancient terrains with presumably lower heat fluxes over the rest of the satellite. To understand the convective pattern and its relationship with surface tectonics, we present three-dimensional numerical models of convection in Enceladus’ ice shell including basal heating and tidal heating. Our thermal boundary conditions exhibit no north–south asymmetries, but because the tectonism at the SPT may weaken the ice there, we impose a mechanically weak lithosphere within the SPT. The weakening is parameterized by adopting a reduced viscosity contrast within the SPT. Without such a weak zone, convection (if any) resides in stagnant-lid mode and exhibits no hemispheric dichotomy. In the presence of such an SPT weak zone, however, we find vigorous convection in the ice underneath the SPT, with convective plumes rising close to the surface. In contrast, only stagnant lid convection, or no convection at all, occurs elsewhere over the satellite. Away from the SPT, the heat flux in our models is small (5–10mWm−2) and the surface strains are small enough to imply surface ages >109years. Within the SPT, however, our models yield peak heat fluxes of ∼70–200mWm−2, implying heat flows integrated across the SPT of up to 5GW, similar to that inferred from Cassini thermal observations. The surface strains in our models are high enough near the south pole to cause intense tectonism and imply surface ages of ∼106–107years, consistent with age estimates of the SPT.

促成ナス栽培におけるトンネルと枝ダクトを組み合わせた株元加温システムの開発

ナスの促成栽培における暖房コストの削減を目的として，ナスの地際部に設置したトンネル内に暖房ダクトを挿入して株元部を加温するシステム（ダクト加温システム）を開発した．暖房機が稼動した期間ではダクト加温区の方が対照区より夜間の茎表面温度が6.3℃高く，暖房機が稼動しなかった期間でもダクト加温区の方が対照区より約3℃高かった．ダクト加温システムによって側枝の成長および果実の肥大が促進し，対照区より収穫果数が多くなり，商品果収量が増加した．10℃に暖房したハウスのダクト加温区の商品果収量は，12℃のハウスの対照区と同等であった．本システムは従来の暖房システムを改良して行うことができるため，資材費として10 a当たり約2万円／年の投資で対応できる．従って，ナスの促成栽培においてダクト加温システムは収穫果数を確保しつつ暖房コストを大幅に削減できる実用的な栽培技術であるといえる．

Partitioning effects from ocean and atmosphere on the calving stability of Kangerdlugssuaq Glacier, East Greenland

AbstractWe use the 7 km retreat of Kangerdlugssuaq Glacier (KG), East Greenland, to examine the mechanisms, interactions and relative significance of atmospheric forcing and ice/ocean interactions. Hydrographic data from 1991, 1993 and 2004 show that subtropical waters are common in Kangerdlugssuaq Fjord (KF), and that surface waters were warm in 2004 relative to 1991 and 1993. The main water column was nonetheless warmest in 1991. We contend that while flow of subtropical waters into fjords provides a setting in which rapid glacier retreat can occur, the triggering of retreat depends on additional environmental factors. The climatic variables standing out in our study of KG and KF are air temperature and katabatic winds. Both had strong positive anomalies during winter 2004/05, when KG retreated. We show that proglacial ice melange was absent and that fjord freeze-up did not occur until 11 April 2005, due to warm and windy conditions. We demonstrate that this setting is unusual and hypothesize that exposure to open water in winter months caused the retreat. Calculation of ice-front melt rates shows that discharge of basal meltwater, first from runoff and subsequently from frictional basal heating, should intensify the interaction between glacier and fjord.

Plate tectonics on super-Earths: Equally or more likely than on Earth

The discovery of extra-solar super-Earths has prompted interest in their possible mantle dynamics and evolution, and in whether their lithospheres are most likely to be undergoing active plate tectonics like on Earth, or be stagnant lids like on Mars and Venus. The origin of plate tectonics is poorly understood for Earth, likely involving a complex interplay of rheological, compositional, melting and thermal effects, which makes it challenging to make reliable predictions for other planets. Nevertheless, as a starting point it is common to parameterize the complex processes involved as a simple yield stress that is either constant or has a Byerlee's law dependence on pressure. Because the simplifying assumptions made in developing analytical scalings may not be valid over all parameter ranges, numerical simulations are needed; one numerical study on super-Earths finds that plate tectonics is less likely on a larger planet (O'Neill and Lenardic (2007)), in apparent contradiction of an analytical scaling study (Valencia et al. (2007)). To try and understand this we here present new calculations of yielding-induced plate tectonics as a function of planet size, focusing on the idealized end members of internal heating or basal heating as well as different strength profiles, and compared to analytical scalings. In the present study we model super-Earths as simple scaled up versions of Earth, i.e., assuming constant physical properties, keeping the ratio of core/mantle radii constant and applying the same temperature difference between top/bottom boundaries and the same internal heating rate. Effects that originate outside of the planet, such as tidal forces, meteor impacts and intense surface heating from a nearby star are not considered. We find that for internally-heated convection plate tectonics is equally likely for terrestrial planets of any size, whereas for basally-heated convection plate tectonics becomes more likely with increasing planet size. This is indicated both by analytical scalings and the presented numerical results, which agree with each other. When scalings are adjusted to account for increasing mean density with increasing planet size, plate tectonics becomes more likely with increasing planet size for all scenarios. The influence of the pressure variation of viscosity, thermal expansivity and conductivity may, however, act in the opposite sense and needs to be determined in future studies. At least in the simplest case, factors other than planet size, such as the presence of surface water, are likely most important for determining the presence or absence of plate tectonics.

Delamination-induced late-tectonic deformation and high-grade metamorphism of the Proterozoic Nampula Complex, northern Mozambique

Lithospheric thickening during protracted Ediacaran supercontinent assembly was dissipated in various ways along the “Pan-African” East African–Antarctic Orogen. In NE Mozambique, late-tectonic extension and plutonism south of the Lúrio Belt has been modelled in terms of lithosphere delamination, although rigorous testing of the hypothesis by structural analysis has not yet been undertaken.This study presents the first analyses of late-tectonic structures in both the Mesoproterozoic basement and the Cambrian cover sequences in the Nampula Complex, NE Mozambique, supported by, and integrated with, new geochronological data. Both late compressional and extensional fabrics overprint the main Pan-African collisional structures to a variable degree in identified structural domains. The long-lived northern boundary of the Nampula Complex, the Lúrio Belt high-strain zone, initiated in the Ediacaran, was reactivated and segmented during these later phases, with boundary-parallel shortening.U–Pb SIMS ages from selected latest-tectonic units in the Nampula Complex and the Lúrio Belt give consistent ages between 518±2 and 514±5Ma. They are coeval with migmatisation and granitoid plutonism in the Nampula Complex. U–Pb titanite (471±9Ma) and 40Ar/39Ar biotite (431±3Ma) data suggest subsequent slow cooling rates in the Nampula Complex, consistent with basal heating by asthenosphere uprise following lithosphere delamination. Consequently, we believe the new data suggest that the observed intense late polyphase deformation has preferentially occurred where the delaminated lithosphere was doubly weakened by loss of the mantle root and the resulting long-lived elevated temperature regime.

The basal chromospheric Mg ii h+k flux of evolved stars: probing the energy dissipation of giant chromospheres

Of a total of 177 cool G, K, and M giants and supergiants, we measured the Mg II h+k line emission of extended chromospheres in high-resolution (LWR) IUE spectra by using the IUE final data archive at STScI, and derived the respective stellar surface fluxes. They represent the chromospheric radiative energy losses presumably related to basal heating by the dissipation of acoustic waves, plus a highly variable contribution due to magnetic activity. Thanks to the large sample size, we find a very well defined lower limit, the basal chromospheric Mg II h+k line flux of cool giant chromospheres, as a function of T_eff. A total of 16 giants were observed several times, over a period of up to 20 years. Their respective minimal Mg II h+k line fluxes confirm the basal flux limit very well because none of their emissions dip beneath the empirically deduced basal flux line representative for the overall sample. Based on a total of 15 to 22 objects with very low Mg II h+k emission, we find as limit: log F_Mg_h+k = 7.33 log T_eff - 21.75 (cgs units; based on B-V). Within its uncertainties, this is almost the same relation as has been found in the past for the geometrically much thinner chromospheres of main sequence stars. Concerning any residual dependence of the basal flux on the surface gravity it can be stated that over a gravity range of more than four orders of magnitude (main-sequence stars to supergiants), the basal flux does not appear to vary by more than a factor of 2. These findings are in good agreement with the predictions by previous hydrodynamic models of acoustic wave propagation and energy dissipation, as well as with earlier empirical determinations. Finally, we discuss the idea that the ample energy flux of the chromospheric acoustic waves in a cool giant may yield, as a by-product, the energy flux required by its cool wind (i.e., non-dust-driven, "Reimers-type" mass-loss).

Radiative and magnetic properties of solar active regions

Context. Global relationships between the photospheric magnetic flux and the extreme ultraviolet emission integrated over active region area have been studied in a previous paper by Fludra & Ireland (2008, A&A, 483, 609). Spatially integrated EUVline intensities are tightly correlated with the total unsigned magnetic flux, and yet these global power laws have been shown to be insufficient for accurately determining the coronal heating mechanism owing to the mathematical ill-conditioning of the inverse problem. Aims. Our aim is to establish a relationship between the EUV line intensities and the photospheric magnetic flux density on small spatial scales in active regions and investigate whether it provides a way of identifying the process that heats the coronal loops. Methods. We compare spatially resolved EUV transition region emission and the photospheric magnetic flux density. This analysis is based on the O V 62.97 nm line recorded by the SOHO Coronal Diagnostic Spectrometer (CDS) and SOHO MDI magnetograms for six solar active regions. The magnetic flux density φ is converted to a simulated O V intensity using a model relationship I(φ,L) = Cφ δ L λ , where the loop length L is obtained from potential magnetic field extrapolations. This simulated spatial distribution of O V intensities is convolved with the CDS instrument’s point spread function and compared pixel by pixel with the observed O V line intensity. Parameters δ and λ are derived to give the best fit for the observed and simulated intensities. Results. Spatially-resolved analysis of the transition region emission reveals the complex nature of the heating processes in active regions. In some active regions, particularly large, local intensity enhancements up to a factor of five are present. When areas with O V intensities above 3000 erg cm −2 s −1 sr −1 are ignored, a power law has been fitted to the relationship between the local O V line intensity and the photospheric magnetic flux density in each active region. The average power index δ from all regions is 0.4 ± 0.1 and λ = −0.15 ± 0.07. However, the scatter of intensities in all regions is significantly greater than ±3σ from the fitted model. We therefore determine for the first time an empirical lower boundary for the IOV − φ relationship that is the same for five active regions. We postulate that it represents a basal heating. Because this boundary is present in the spatially-resolved data, this is compelling proof that the magnetic field is one of the major factors contributing to the basal component of the heating of the coronal plasma. We discuss the implications for the diagnostics of the coronal heating mechanism.

Variety of plumes and the fate of subducted basaltic crusts

Subducted basaltic crusts induce various types of plumes in a recently developed self-consistent numerical model of mantle convection with tectonic plates and mantle magmatism. Subducted basaltic crusts segregate from the convecting mantle by their compositionally induced high density. The basaltic crusts are formed into a continuous layer along the core–mantle boundary, if there is no influence of subducting slabs; the layer induces classic hot mantle plumes by basal heating. When influenced by subducting slabs, the subducted basaltic crusts are formed into hot accumulations similar to the Earth's superplumes, provided that the internal heating is weaker than a threshold. Chemical discontinuities often develop within and along the boundaries of the basaltic accumulations, and hot plumes ascend from the uppermost parts of the accumulations. Some of the plumes hit plates, cause hot spot magmatism, and induces new spreading centers. The rest of the plumes often stagnate on the 660km phase boundary to form basaltic pools. Occasionally, secondary plumes grow from the pools to induce hot spot magmatism. The pools are also sucked up by the ridges that happen to be above the pools, and activate the ridge magmatism. Hot plumes ascend from basaltic accumulations more frequently as the internal heating becomes stronger. When the internal heating becomes too strong, however, the accumulations of subducted basaltic crusts become convectively unstable and no longer work as the sources of plumes. The various types of the plumes observed here are compared to the plumes in the Earth's mantle.

Temperature-dependent shear flow and the absence of thermal runaway in valley glaciers

We propose a two-dimensional model of a valley glacier in order to reconsider the question of whether thermal runaway could be a viable mechanism for the onset of creep instability in surging glaciers. We do this by providing an approximate solution for the temperature field based on the idea that shear is concentrated at the glacier bed. With this assumption, we show that a closed-form evolution equation for the glacier profile exists. While this is well known for isoviscous flows, it has not been previously derived for variable viscosity flows. During the process of deriving this equation, we show that thermal runaway does not occur. We provide numerical solutions of the model, and are led to infer that enhanced basal heating owing to refreezing of surface meltwater is an essential constituent in raising the bed temperature to the melting point.

Acoustic waves in the solar atmosphere at high spatial resolution

Aims. The energy supply for the radiative losses of the quiet solar chromosphere is studied. On the basis of high spatial resolution data, we investigate the amount of energy flux carried by acoustic waves in the solar photosphere. Methods. Time sequences from quiet Sun disc centre were obtained with the “Gottingen” Fabry-Perot spectrometer at the Vacuum Tower Telescope, Observatorio del Teide/Tenerife, in the non-magnetic Fe i 5576 A line. The data were reconstructed with speckle methods. The velocity and intensity fluctuations at line minimum were subjected to Fourier and wavelet analyses. The energy fluxes at frequencies higher than the acoustic cutoff frequency (period U ≈ 190 s) were corrected for the transmission of the solar atmosphere, which reduces the signal from short-period waves. Results. Both Fourier and wavelet analysis give an amount of energy flux of ∼3000 W m −2 at a height h = 250 km. Approximately 2/3 of it is carried by waves in the 5−10 mHz range, and 1/ 3i n the 10−20 mHz band. Extrapolation of the flux spectra gives an energy flux of 230−400 W m −2 at frequencies ν> 20 mHz. We find that the waves occur predominantly above inter-granular areas. Conclusions. We conclude that the acoustic flux in waves with periods shorter than the acoustic cutoff period can contribute to the basal heating of the solar chromosphere, in addition to the atmospheric gravity waves found recently.

Free polyamine variations in rooting of Vitis rootstock 140 Ruggeri.

The rooting of Vitis (rootstock 140 Ruggeri) woody cuttings, collected in field from mother plants over a five-month period (October 1999-February 2000), was recorded from 0 to 60 days of basal heating. The material was collected directly in field and/or submitted to different treatments: a) cold treatment of the shoots at 2°C in cold chamber from October; b) dipping in water at the bottom end of the cuttings. Both treatments were able to modify rooting time and amount. During basal heating, at 0, 20, 40 and 60 days, rooting percentage was recorded; concomitantly, from the basal end of cuttings, free-poly amines were extracted to evaluate their endogenous levels. Results show that positive variations in rooting, induced by the treatments, are related to increases in free-polyamine levels, suggesting that an increase in the endogenous putrescine could be correlated with primordia formation time. The pattern of spermine variations appears to be similar to that of putrescine, while spermidine does not appear to be correlated to the rooting process. Both spermine and spermidine amounts are present at far lower levels than putrescine.

Mantle convection with longest‐wavelength thermal heterogeneity in a 3‐D spherical model: Degree one or two?

The formation of longest‐wavelength mantle convection in the sluggish‐lid regime is investigated using a three‐dimensional spherical model. The bottom Rayleigh number is fixed at 107. Considering temperature‐dependent rheology, degree‐one dominant thermal convection occurs for both purely basal heating and mixed (i.e., basal and internal) heating modes. For the purely basal heating mode, degree‐one convection occurs when the viscosity contrast due to temperature‐dependent rheology is 103–104 in both Boussinesq and extended‐Boussinesq fluids. However, with extended‐Boussinesq fluid, degree‐one convection may only occur in the basal heating mode: In the mixed heating mode, degree‐one convection shifts to one with high‐degree modes, presumably because of enhanced viscous dissipation in the highly viscous lid over up/downwelling plumes. The geophysically relevant degree‐two convection with sheet‐like downwellings is not observed in this study. The inclusion of visco‐plastic rheology in the top part of the mantle breaks down degree‐one convection.

Convective interactions between oceanic lithosphere and asthenosphere: Influence of a transform fault

Current estimates of the asthenospheric viscosity favor the occurrence of small-scale convection (SSC) beneath oceanic lithosphere of sufficient age. Since transform faults (TFs) juxtapose lithospheres of distinct ages (and thicknesses), they are likely to influence their dynamics. In this paper, we describe 3D numerical models of oceanic spreading for two ridge segments offset by a TF in domains that are sufficiently large for SSC to fully develop. A framework based on thermal convection with temperature-dependent viscosity and both internal and basal heating is adopted and parameters such as surface velocity, age offset at the TF, activation energy, mantle viscosity, and internal heating rate are explored. In our numerical experiments, the onset time for SSC is identical on each side of the fracture zone (FZ). It is not modified by the presence of a TF. Moreover, scaling relationships for the onset time obtained in 2D experiments remain valid. Earlier studies focused on the influence of a TF based on 2D experiments corresponding to slices parallel to the ridge axis. They noted the rapid development of a sinking thermal instability located at the step in the lithospheric relief. Our results indicate that the wake of the TF is characterized by the development of a lateral, “edge-driven”, buoyant flow, from the younger (thinner) side to the older (thicker) side of the FZ. However, due to the global shearing context, this instability does not sink before the onset of SSC (characterized by small-scale instabilities on each side of the FZ, as observed in earlier studies). The essentially 3D velocity field, combining this lateral flow and the prescribed surface spreading velocity, results in an angle formed by the TF trail with the spreading direction. We describe the parameters controlling this angle in our experiments and propose a scaling relationship. In oceanic settings, the specific geometry of the ridge axis (segment length, orientation of the TFs) may affect this angle. In addition, a large scale mantle flow of other geodynamical origin could interact with the spreading flow, and also modify the TF trail angle. This departure at depth of the boundary between the thick and thin lithospheres from the surface FZ may explain the presence of oceanic volcanoes on the older side of the FZ (usually considered as thicker).

On the origin and significance of subadiabatic temperature gradients in the mantle

It is well established that the temperature gradients in the interiors of internally heated mantle convection models are subadiabatic. The subadiabatic gradients have been explained as arising because of a balance between vertical advection and internal heating; however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this paper, we examine in detail the energy balance in a suite of simple, two‐dimensional convection calculations with mixed internal and basal heating, depth‐dependent viscosity, and continents. We find that there are three causes of subadiabatic gradients. One is the above mentioned balance, which becomes significant when the ratio of internal heating to total surface heat flow is large. The second mechanism involves the growth of the “overshoot” of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time‐dependent calculations, we find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time‐averaged geotherm. We also compare the basal heat flow with parameterized calculations based on the temperature drop at the core‐mantle boundary, calculated both with and without taking the subadiabatic gradient into account, and we find a significantly improved fit with its inclusion.

The influence of plate-like surface motion on upwelling dynamics in numerical mantle convection models

Tectonic plate geometry organises the planform of convection in the Earth's mantle and is therefore expected to strongly influence mantle upwelling dynamics. We present the findings from two- and three-dimensional mantle convection simulations with plate-like surface motion and analyse how convective patterns and time-dependence change as surface plate geometry is transformed from a simple configuration permitted in 2D experiments (allowing only divergent and convergent plate boundaries) into arrangements requiring three-dimensional modelling. Our experiments model vigorous convection ( Ra = 10 7 based on the upper mantle viscosity) in a stratified viscosity system featuring both internal and basal heating. We first consider a suite of two-dimensional experiments and determine an estimate for a uniform surface velocity that is comparable in magnitude to the mean transit time for the upwellings associated with the system. We argue that a surface velocity that neither forces nor resists the convectively driven flow meets this requirement but show that temporally varying and constant plate velocities can both satisfy this condition over a given period of time with different results. For the partially internally heated, aspect ratio 4 cases considered here, we choose a fixed velocity boundary condition and find this velocity is about 23% lower than the mean velocity obtained with a free-slip surface condition in an otherwise identical model. The plate velocity obtained from our two-dimensional experiments is then adopted for our three-dimensional calculations that include plates as plate geometry is systematically varied. For the parameters specified in our study (which result in a basal heat flux of approximately 50% the surface value and a viscosity contrast of a factor of 30 between the upper and lower mantle) steady plume-like upwellings are present in both free-slip and rigid surface calculations. However, a surface boundary condition featuring a pair of congruent plates moving in opposing directions with a velocity comparable to the plume transit time forces the convective planform into a roll-like pattern featuring essentially sheet-like upwellings positioned below the divergent plate boundary. When plate geometries are specified in a way that produces offset segments of convergent and divergent boundary joined by boundaries characterised by strike-slip motion, the planform of the underlying convection organises into patterns featuring columnar, plume-like, upwellings. Using calculations of upwelling advective heat flux to determine plume locations, we track plume motion in the upper and lower mantle over periods of several plume rise times. We show that long-lived, nearly stationary, plumes appear in calculations featuring surface velocities comparable to the mean vertical velocity of the upwellings and that the associated plume heads remain positioned below intraplate positions for periods that can exceed tens of millions of years.

Dipole moment scaling for convection-driven planetary dynamos

Scaling laws are derived for the time-average magnetic dipole moment in rotating convection-driven numerical dynamo models. Results from 145 dynamo models with a variety of boundary conditions and heating modes, covering a wide section of parameter space, show that the time-average dipole moment depends on the convective buoyancy flux F. Two distinct regimes are found above the critical magnetic Reynolds number for onset of dynamo action. In the first regime the external magnetic field is dipole-dominant, whereas for larger buoyancy flux or slower rotation the external field is dominated by higher multipoles and the dipole moment is reduced by a factor of 10 or more relative to the dipolar regime. For dynamos driven by basal heating, the dipole moment M increases like M ∼ F 1/3 in the dipolar regime. Reversing dipolar dynamos tend to cluster near the multipolar transition, which is shown to depend on a local Rossby number parameter. The geodynamo lies close to this transition, suggesting an explanation for polarity reversals and the possibility of a weaker dipole earlier in Earth history. Internally heated dynamos generate smaller dipole moments overall and show a gradual transition from dipolar to multipolar states. Our scaling yields order of magnitude agreement with the dipole moments of Earth, Jupiter, Saturn, Uranus, Neptune, and Ganymede, and predicts a multipolar-type dynamo for Mercury.