Entrainment from a bed of particles by thermal convection

Differentiation in magma chambers, in the Earth's core and in the partially molten early Earth is a competitive process between sedimentation and re-entrainment of crystals in the presence of convection. Previous studies show that the particles suspended in convective layers eventually settle and do so almost as fast as in the absence of convection. However, the nature and magnitude of the competing entrainment has remained unclear. Here we provide a simple theory and experimental evidence showing that entrainment occurs at the crests of dunes created in the particle bed at the base of a convecting fluid. In both laminar and turbulent regimes, the dune formation and entrainment are driven by viscous stresses produced by thermal plumes. At sufficiently high Rayleigh numbers the particles are probably entrained by Reynolds stresses. Entrainment in the Earth's core is hardly possible because it requires unreasonably small crystals. Entrainment of 10⁻²–10⁻¹ cm diameter crystals is very likely in magma oceans. For magma chambers entrainment requires large viscosities (> 10⁶ P) and even when it occurs, the total amount of the suspended solid fraction is very small.     

Mantle and crustal contribution in the genesis of Recent basalts from off-rift zones in Iceland: Constraints from Th, Sr and O isotopes

Along the two volcanic off-rift zones in Iceland, the Snfellsnes volcanic zone (SNVZ) and the South Iceland volcanic zone (SIVZ), geochemical parameters vary regularly along the strike towards the centre of the island. Recent basalts from the SNVZ change from alkali basalts to tholeiites where the volcanic zone reaches the active rift axis, and their⁸⁷Sr/⁸⁶Sr andTh/U ratios decrease in the same direction. These variations are interpreted as the result of mixing between mantle melts from two distinct reservoirs below Snfellsnes. The mantle melt would be more depleted in incompatible elements, but with^a higher³He/⁴He ratio (R/Ra≈ 20) beneath the centre of Iceland than at the tip of the Snfellsnes volcanic zone (R/Ra≈ 7.5).

From southwest to northeast along the SIVZ, the basalts change from alkali basalts to FeTi basalts and quartz-normative tholeiites. TheTh/U ratio of the Recent basalts increases and both (²³⁰Th/²³²Th) andδ¹⁸O values decrease in the same direction. This reflects an important crustal contamination of the FeTi-rich basalts and the quartz tholeiites. The two types of basalts could be produced through assimilation and fractional crystallization in which primary alkali basaltic and olivine tholeiitic melts ‘erode’ and assimilate the base of the crust. The increasingly tholeiitic character of the basalts towards the centre of Iceland, which reflects a higher degree of partial melting, is qualitatively consistent with increasing geothermal gradient and negative gravity anomaly.

The highest Sr isotope ratio in Recent basalts from Iceland is observed inÖrfajökull volcano, which has a³He/⁴He ratio (R/Ra≈ 7.8) close to the MORB value, and this might represent a mantle source similar to that of Mauna Loa in Hawaii.     

瑞利数对热对流的影响——在地幔柱中的应用

本文分别在直角坐标系和柱坐标系下,研究瑞利数从104逐渐增大到107对热对流的影响,数值计算结果表明:瑞利数越大,地幔柱越窄,地幔柱上升速度也越快;源自上地幔的地幔柱半径的范围为9到210 km.根据峨眉山内带的半径推算出地幔的黏性系数约为3.8×1021Pa·s,地幔柱平均流动速度为2.5 cm/a.     

Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box

Numerical models are systematically presented for time-dependent thermal convection of Newtonian fluid with strongly temperature-dependent viscosity in a two-dimensional rectangular box of aspect ratio 3 at various values of the Rayleigh number Ra_b defined with viscosity at the bottom boundary up to 1.6×10⁸ and the viscosity contrast across the box r_η up to 10⁸. We found that there are two different series of bifurcations that take place as r_η increases. One series of bifurcations causes changes in the behavior of the thermal boundary layer along the surface boundary from small-viscosity-contrast (SVC) mode, through transitional (TR) mode, to stagnant-lid (ST) mode, or from SVC mode directly to ST mode, depending on Ra_b. Another series of bifurcations causes changes in the aspect ratio of convection cells; convection with an elongated cell can take place at moderate r_η (10³–10^5.5 at Ra_b=6×10⁶), while only convection of aspect ratio close to 1 takes place at small r_η and large r_η. The parameter range of r_η and Ra_b for elongated-cell convection overlaps the parameter range for SVC and ST modes and include the entire parameter range for TR mode. In the elongated-ST regime, the lid of highly viscous fluid along the top boundary is not literally ‘stagnant’ but can horizontally move at a velocity high enough to induce a convection cell with aspect ratio much larger than 1.     

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

Abstract

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

An assessment of the effect of chemical scavenging within submarine hydrothermal plumes upon ocean geochemistry

Profiles of ²¹⁰Pb over the Endeavour and North Cleft Segments of the Juan de Fuca Ridge are used to model a time scale for the scavenging, by hydrothermal plumes, of reactive elements in seawater. The hydrothermal plumes above these ridge segments are sites of intense scavenging removal of ²¹⁰Pb. At Endeavour, the total ²¹⁰Pb activities within the plume are as low as 8 dpm/100 l and dissolved activities are as low as 3 dpm/100 l. At the North Cleft, which is characterized by higher particulate Fe concentrations, the total ²¹⁰Pb activities are 4.5 dpm/100 l, the dissolved activities are 1–2 dpm/100 l and the ²¹⁰Pb activities are deficient with respect to the activity of the ²¹⁰Po daughter. These are perhaps the lowest ²¹⁰Pb activities ever measured in the deep sea. The large gradient of ²¹⁰Pb between the plume and surrounding deep water suggests that scavenging is focused into the plumes through horizontal transport. The implication, therefore, is that this process might impact the ocean on a scale larger than that local to the ridge crest. By coupling published measurements of particle flux from Endeavour with ²¹⁰Pb activities on particles trapped at that site, the total volume of seawater stripped of ²¹⁰Pb per year for that site was calculated to be 7.4 × 10¹² l/y. Globally, the extrapolated volume flux of seawater stripped of reactive constituents is 5.7 × 10¹⁵ l/y, such that the entire ocean is processed in this manner in 2.4×10⁵ y. The geochemical cycle of elements with ocean residence times much shorter than this (e.g., Pb and Th) will not be greatly affected by hydrothermal scavenging. On the other hand, this process holds significance for the geochemistry of other elements scavenged by hydrothermal plumes, such as P and V, whose ocean residence times are > 10⁴ y.     

On the geodynamic setting of kimberlite genesis

The emplacement of kimberlites in the North American and African continents since the early Palaeozoic appears to have occurred during periods of relatively slow motion of these continents. The distribution of kimberlites in time may reflect the global pattern of convection, which forces individual plates to move faster or slower at different times. Two-dimensional numerical experiments on a convecting layer with a moving upper boundary show two different regimes: in the first, when the upper boundary velocity is high, heat is transferred by the large-scale circulation and in the second, when the upper boundary velocity is lower, heat is predominantly transferred by thermal plumes rising from the lower boundary layer. For a reasonable mantle solidus, this second regime can give rise to partial melting beneath the moving plate, far from the plate boundaries. The transition between these modes takes place over a small range of plate velocities; for a Rayleigh number of 10⁶ it occurs around 20 mm yr^?1. We suggest that the generation of kimberlite magmas may result from thermal plumes incident on the base of a slowly moving plate.     

Melting rates beneath Hawaii: Evidence from uranium series isotopes in recent lavas

²³⁸U, ²³²Th, ²³⁰Th and ²²⁶Ra abundances have been measured in six samples of recent Hawaiian basalt by high precision mass spectrometry, in an attempt to compare the melting process in plumes and at spreading ridges. The data reveal a very small range in (²³⁰Th/²³⁸U) activity ratio up to a maximum value of 1.02 ± 0.01, and (²²⁶Ra/²³⁰Th) activity ratios which lie between 1.10 ± 0.015 and 1.19 ± 0.02. UTh and RaTh abundances are linearly correlated demonstrating that the disequilibria predate crystallisation and differentiation. Using recently published estimates for the bulk partition coefficients of U and Th, the results are consistent with melting rates > 10⁻³ kg m⁻³ a⁻¹ at porosities < 10⁻³ for dynamic fractional melting in the garnet stability field.     

Three-dimensional convection in spherical shells

Abstract

In this study, the equations of the three-dimensional convective motion of an infinite Prandtl number fluid are solved in spherical geometry, for Rayleigh numbers up to 15 times the critical number. An iterative method is used to find stationary solutions. The spherical parts of the operators are treated using a Galerkin collocation method while the radial and time dependences are expressed using finite difference methods. A systematic search for stationary solutions has led to eight different stream patterns for a low Rayleigh number (1.28 times the critical number). They can be classified as:

I) Axisymmetrical solutions, analogous to rolls in plane geometry.

II) Solutions which have several ascending plumes within a large area of ascending current, and also several descending plumes within an area of descending current. This type of flow is analogous to bimodal circulation in plane geometry.

III) Solutions characterized by isolated ascending (or descending) plumes separated from each other by a closed polyhedral network of descending (or ascending) currents. This type of circulation is called ‘polygonal’ in analogy with hexagonal circulation in plane geometry.

The behaviour of each of the eight solutions has been studied by increasing the Rayleigh number up to 15 times the critical number. A trend towards transitions from type (I) and type (II) solutions to type (III) solutions is observed. It is inferred that only the “polygonal” solutions are stable for a Rayleigh number greater than 15 times the critical number.     

Influence of an endothermic phase transition on mass transfer between the upper and the lower mantle

Geochemical data indicate that two major reservoirs 1–2 Ga in age are present in the mantle. The upper mantle, feeding mid-ocean ridges, is depleted in chemical elements carried away into the continental crust. The lower mantle, feeding hotspot plumes, is close in composition to primordial matter. The 660-km depth of an endothermic phase transition in olivine has been considered over the last two decades as a possible boundary between the reservoirs. In this period, many models of mantle convection were constructed that used values of the phase transition parameters, which led to temporal (up to 1 Gyr long) convection layerings and periodic avalanche-induced mantle intermixing events. However, laboratory measurements with new improved instrumentation give other values of the phase transition parameters that require a revision of the majority of the existence of large-scale avalanches in the Earth’s history becomes disputable. The paper is devoted to comprehensive study of the phase transition effect on the structure of mantle flows with different values of phase transition parameters and Rayleigh numbers; in particular, the mass transfer through the phase boundary is calculated for different regimes of steady-state convection.     

Large aspect ratio cells in two-dimensional thermal convection

Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 10⁵ and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated.     

Plume Mode of Thermal Convection in the Earth’s Mantle

In our previous works, based on numerical models, it was shown that under certain conditions a hot material can rise in portions in the tails of thermal mantle plumes. The spectrum of these pulsations can correspond to the observed spectra of catastrophic hotspot eruptions. Since most of the existing numerical models of thermal convection for the mantle of the present Earth do not reveal these pulsations, in this work, we analyze the physical cause and initiation conditions of pulsations of thermal plumes. The results of a numerical solution of the thermal convection equations for a material with varying parameters in the extended Boussinesq approximation are presented. It is shown how the structure of the convection is transformed with the increase of convection intensity. At the Rayleigh numbers Ra > 10⁶, convection becomes unsteady, and the configuration of the ascending and descending flows changes. The new flow emerging at the mantle bottom acquires a mushroom shape with a head and a tail. After the rise of the plume’s head to the surface, the tail remains in the mantle in the form of a quasi-stationary hot steam. It turns out that at Ra ~ 5 × 10⁷, the thermal mantle plume becomes pulsating and its tail is in fact a heated channel through which the hot material rises in successive portions. At the Rayleigh numbers Ra > 5 × 10⁸, the tail of the thermal plume breaks and the plume becomes a regular conveyor of separate ascending portions of the hot material, which are referred to as thermals. Thus, thermal convection with pulsating plumes takes place at the transitional stage from the regime of quasi-stationary plumes to the regime of thermals.     

The influence of particle composition on thorium scavenging in the NE Atlantic ocean (POMME experiment)

²³⁰Th, ²³²Th and ²³⁴Th were analyzed in sinking particles collected by moored and drifting sediment traps in the NE Atlantic Ocean (POMME experiment) in order to constrain the phase(s) carrying Th isotopes in the water column. It reveals a contrasted behaviour between ²³⁴Th and ²³⁰Th. ²³⁴Th is correlated to the particulate organic carbon suggesting that it is primarily scavenged by organic compounds in the surface waters. ²³⁰Th_xs is correlated with Mn, Ba and the lithogenic fraction that are enriched in small suspended particles and incorporated in the sinking particulate flux throughout the water column. The lack of correlation between ²³⁰Th_xs and CaCO₃ or biogenic silica (bSi) indicates that CaCO₃ and bSi are not responsible for ²³⁰Th scavenging in the deep waters of this oceanic region. ²³⁰Th is generally correlated with the lithogenic content of the trapped material but this correlation disappears in winter during strong atmospheric dust inputs suggesting that lithogenic matter is not directly responsible for ²³⁰Th scavenging in the deep waters or that sufficient time is required to achieve particle–solution equilibration. MnO₂ could be the prevalent ²³⁰Th_xs-bearing phase. The narrow range of K_{d_MnO2}^Th obtained for very contrasted oceanic environments supports a global control of ²³⁰Th_xs scavenging by MnO₂ and raises the possibility that the ²³⁰Th–²³¹Pa fractionation is controlled by the amount of colloidal MnO₂ in seawater.     

Influence of artificial groundwater lakes on the abundance and activity of bacteria in adjacent subsurface systems

Bacterial abundances and activity, estimated by 4′,6-diamidino-2-phenylindole staining (DAPI) and the reduction of 2-(p-iodophenyl)-3-(p-nitrophenyl)-5-phenyl tetrazolium chloride (INT), were investigated in two oligotrophic artificial groundwater lakes and the surrounding aquifers. To evaluate the effect of lake water on groundwater downstream, samples were taken from wells at different distances from the lakes, and the total number of bacteria and the number of active bacteria in these samples were compared with samples collected upstream. In addition, sterilized sandy sediments were exposed in groundwater wells to measure the number and activity of bacteria attached to particles. At one of the study sites, where the lake sediments were disturbed by dredging, total bacterial abundance and the number of respiring bacteria in the groundwater aquifer was clearly influenced by the lake water. The average bacterial abundances decreased from 2.6 ± 1.9 × 10⁵ cells ml⁻¹ in the well closest to the lake (S2) to 2.9 ± 3.8 × 10⁴ cells ml⁻¹ in the most distant one (S4), which was equivalent to cell numbers in the upstream well. The number of respiring bacteria showed a similar tendency with 1.3 ± 2.7 × 10⁴ active cells ml⁻¹ in S2 and 1.9 ± 1.5 × 10³ active cells ml⁻¹ in S4. At the second study site, which was not influenced by dredging, bacteria in the downstream wells seemed not to be affected by the lake water. The number and activity of bacteria, which colonized exposed sediments, were not significantly different in the upstream and downstream wells, indicating a minor influence of lake water on this habitat. Our results suggest that gravel-pit lakes may influence the free living bacterial assemblages in nearshore groundwater systems, but do not visibly affect numbers and activity of bacteria attached to the surface of aquifer sediments.     

Effect of Bioremediation on the Microbial Community in Oiled Mangrove Sediments

Bioremediation was conducted in the field on a mature Rhizophora stylosa mangrove stand on land to be reclaimed near Fisherman’s Landing Wharf, Gladstone Australia. Gippsland crude oil was added to six large plots (>40 m²) and three plots were left untreated as controls. Bioremediation was used to treat three oiled plots and the remaining three were maintained as oiled only plots. The bioremediation strategy consisted of actively aerating the sediment and adding a slow-release fertilizer in order to promote oil biodegradation by indigenous micro-organisms. Oil addition stimulated the numbers of alkane-degrading bacteria slightly to levels of 10⁴–10⁵/g sediment. Bioremediation of the oiled sediment had a marked effect on the alkane-degrading population, increasing the population size by three orders of magnitude from 10⁵ to 10⁸ cells/g of sediment. An effect of bioremediation on the growth of aromatic-degraders was detected with numbers of aromatic-degraders increasing from 10⁴ to 10⁶ cells/g of sediment. Active aeration and nutrient addition significantly stimulated the growth of hydrocarbon-degraders in oiled mangrove sediment in the field.     

流变边界层及其对华北克拉通热/地震岩石圈底界差异的意义

二维热传导/对流数值模型显示,纯传导的固体岩石圈与纯对流的流体软流圈之间存在一过渡层,即流变边界层,其间传导与对流共同作用来传递热量.流变边界层厚度主要由软流圈黏性系数（η）控制,而受固体岩石圈厚度及热状态影响很小.随着η从1×10²¹Pa·s降低至1×10¹⁹ Pa·s,流变边界层也随之减薄,流变边界层的厚度与lg（η）成正比. 流变边界层的存在是造成热岩石圈与地震岩石圈厚度差异的重要因素. 全球典型克拉通岩石圈的对比结果表明,地震岩石圈厚度普遍大于热岩石圈厚度,二者的差异多数在70~90 km,很好地验证了流变边界层的存在. 研究发现二者的差异在华北克拉通自西向东逐渐减小：由西部鄂尔多斯的约80 km减少至渤海湾盆地的约20 km. 反映出华北克拉通岩石圈下部流变边界层厚度自西向东减薄,意味着软流圈黏性系数自西向东逐渐降低.这可能与中生代太平洋俯冲脱水形成的低黏大地幔楔有关,从一侧面印证了太平洋俯冲对华北克拉通破坏的影响.     

Geophysical evidence on the structure of the Taupo Volcanic Zone and its hydrothermal circulation

The Taupo Volcanic Zone (TVZ) of New Zealand is characterised by extensive volcanism and by high rates of magma production. Associated with this volcanism are numerous high-temperature (> 250 °C) geothermal systems through which the natural heat output of 4200 ± 500 MW is channelled. Outside the geothermal fields the heat flow is negligible. The average heat flux from the central 6000 km² of the TVZ, which contains most of the geothermal fields, is 700 mW/m³. This heat flux appears to be more concentrated along the eastern margin of the TVZ.Schlumberger resistivity measurements (AB/2 of 500 m and 1000 m) have identified 17 distinct geothermal fields with natural heat outputs greater than 20 MW. An additional six, low-heat-output geothermal fields also occur, and may represent formerly more active systems now in decline. Two extinct fields have also been identified. The average spacing between fields is 10–15 km. The distribution of geothermal fields does not appear to be directly associated with individual volcanic features except for the geothermal system that occurs within Lake Taupo and which occupies the vent of the 1800 yr.B.P. Taupo eruption. The positions of the geothermal fields do not appear to have varied for at least the last 200,000 years. These data are consistent with a model of large-scale convection occurring throughout the TVZ, in which the geothermal fields represent the upper portion of the rising, high-temperature, convective plumes. The majority of the recharge to the convection system is provided by the downward movement of cold meteoric water between the fields which suppresses the heat flow in these regions.Gravity measurements indicate that to a depth of about 2.5 km the upper layers of the TVZ consist of low-density pyroclastic infill. A seismic refraction interface with velocity change from 3.2 km/s to 5.5 km/s occurs at a similar depth. The cross-sectional area of the convection plumes (identified electrically) appears to increase at depths of 1–2 km, consistent with a decrease in permeability at the depth at which the velocity and density increase.The seismicity is dominated by swarm activity which accounts for about half of all earthquakes and is highly variable in both space and time. The small number of seismic events (and swarms) that have well determined depths show a cut off of seismicity at depths of 7–9 km. The depth of the transition from brittle to ductile behaviour of the rocks is identified with the transition from a regime where heat is transported by (hydrothermal) convection and pore pressures are near-hydrostatic to a regime where heat transport is dominantly conductive and pore pressures are lithostatic. Within the convective region, temperatures are moderated by the circulation of water so that the depth of the transition from convective to conductive heat transfer can be linked to the bottom of the seismogenic zone. Rocks must become ductile within about 1 km of the bottom of the overlying convective zone.Seismic refraction studies suggest that the crust beneath the TVZ is highly thinned with a seismic velocity of about 7.5 km/ s, typical of the upper mantle, occurring at depth of 15 km. Seismological studies indicate the upper mantle is highly attenuating beneath the TVZ. Conductive heat transfer between the bottom of the convective system, at about 8 km, and the base of the material with crustal velocities, at 15 km, is not able to provide all the heat that is discharged at the surface. Repeated intrusion from the mantle may provide the additional heat transport required.     

Convective instabilities in a variable viscosity fluid cooled from above

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 z_r (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.     

Plume capture by divergent plate motions: implications for the distribution of hotspots,geochemistry of mid-ocean ridge basalts,and estimates of the heat flux at the core–mantle boundary

The coexistence of stationary mantle plumes with plate-scale flow is problematic in geodynamics. We present results from laboratory experiments aimed at understanding the effects of an imposed large-scale circulation on thermal convection at high Rayleigh number (10⁶≤Ra≤10⁹) in a fluid with a temperature-dependent viscosity. In a large tank, a layer of corn syrup is heated from below while being stirred by large-scale flow due to the opposing motions of a pair of conveyor belts immersed in the syrup at the top of the tank. Three regimes are observed, depending on the ratio V of the imposed horizontal flow velocity to the rise velocity of plumes ascending from the hot boundary, and on the ratio λ of the viscosity of the interior fluid to the viscosity of the hottest fluid in contact with the bottom boundary. When V≪1 and λ≥1, large-scale circulation has a negligible effect on convection and the heat flux is due to the formation and rise of randomly spaced plumes. When V>10 and λ>100, plume formation is suppressed entirely, and the heat flux is carried by a sheet-like upwelling located in the center of the tank. At intermediate V, and depending on λ, established plume conduits are advected along the bottom boundary and ascending plumes are focused towards the central upwelling. Heat transfer across the layer occurs through a combination of ascending plumes and large-scale flow. Scaling analyses show that the bottom boundary layer thickness and, in turn, the basal heat flux q depend on the Peclet number, Pe, and λ. When λ>10, q∝Pe^1/2 and when λ→1, q∝(Peλ)^1/3, consistent with classical scalings. When applied to the Earth, our results suggest that plate-driven mantle flow focuses ascending plumes towards upwellings in the central Pacific and Africa as well as into mid-ocean ridges. Furthermore, plumes may be captured by strong upwelling flow beneath fast-spreading ridges. This behavior may explain why hotspots are more abundant near slow-spreading ridges than fast-spreading ridges and may also explain some observed variations of mid-ocean ridge basalt (MORB) geochemistry with spreading rate. Moreover, our results suggest that a potentially significant fraction of the core heat flux is due to plumes that are drawn into upwelling flows beneath ridges and not observed as hotspots.     

Intermittent convection

Abstract

A theoretical analysis of pseudo two-dimensional, finite-amplitude, thermal convection is made for an infinite Prandtl number fluid which is subjected to a constant heat flux out of the top boundary and insulated at the bottom. For large Rayleigh numbers the convective flow becomes intermittent and the system is characterized by the following cyclic process: the formation of a thermal boundary layer by diffusion, the instability of this layer when it becomes sufficiently thick, the destruction of the layer by the convective flow, the dying down of the convection, and the reforming of the thermal boundary layer by diffusion. The periodicity and the horizontal wave number of the intermittent convective flow are found to be independent of the depth of the fluid layer but depend on the rate of cooling and the properties of the fluid.