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.     

Modelling the dynamics and thermodynamics of volcanic degassing

 The rates of passive degassing from volcanoes are investigated by modelling the convective overturn of dense degassed and less dense gas-rich magmas in a vertical conduit linking a shallow degassing zone with a deep magma chamber. Laboratory experiments are used to constrain our theoretical model of the overturn rate and to elaborate on the model of this process presented by Kazahaya et al. (1994). We also introduce the effects of a CO₂–saturated deep chamber and adiabatic cooling of ascending magma. We find that overturn occurs by concentric flow of the magmas along the conduit, although the details of the flow depend on the magmas' viscosity ratio. Where convective overturn limits the supply of gas-rich magma, then the gas emission rate is proportional to the flow rate of the overturning magmas (proportional to the density difference driving convection, the conduit radius to the fourth power, and inversely proportional to the degassed magma viscosity) and the mass fraction of water that is degassed. Efficient degassing enhances the density difference but increases the magma viscosity, and this dampens convection. Two degassing volcanoes were modelled. At Stromboli, assuming a 2 km deep, 30% crystalline basaltic chamber, containing 0.5 wt.% dissolved water, the ∼700 kg s^–1 magmatic water flux can be modelled with a 4–10 m radius conduit, degassing 20–100% of the available water and all of the 1 to 4 vol.% CO₂ chamber gas. At Mount St. Helens in June 1980, assuming a 7 km deep, 39% crystalline dacitic chamber, containing 4.6 wt.% dissolved water, the ∼500 kg s^–1 magmatic water flux can be modelled with a 22–60 m radius conduit, degassing ∼2–90% of the available water and all of the 0.1 to 3 vol.% CO₂ chamber gas. The range of these results is consistent with previous models and observations. Convection driven by degassing provides a plausible mechanism for transferring volatiles from deep magma chambers to the atmosphere, and it can explain the gas fluxes measured at many persistently active volcanoes. Received: 26 September 1997 / Accepted: 11 July 1998     

On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

Convection in rotating annular channels heated from below. Part 1. Linear stability and weakly nonlinear mean flows

Convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral rigid sidewalls, stress-free top and bottom, uniformly heated from below is investigated. The sidewalls are assumed to be either perfectly insulating or conducting. Three different types of convection are identified when the channel is rotating sufficiently fast: (i) global oscillatory convection preferred for small Prandtl numbers in channels with intermediate or large aspect ratios (width to height ratio), (ii) wall-localized oscillatory convection representing the most unstable mode for moderate or large Prandtl numbers in channels with intermediate or large aspect ratios and (iii) global stationary convection preferred in channels with sufficiently small aspect ratios regardless of the size of the Prandtl number. The corresponding weakly nonlinear problem describing differential rotation and meridional circulation is also examined, showing that geostrophic, multiple-peaked (two prograde and two retrograde) differential rotation can be maintained by the Reynolds stresses in wall-localized convective eddies in a rapidly rotating channel.     

An experimental study on the effects of phenocrysts on convection in magmas

The effect of phenocrysts on convection in magma chambers is investigated experimentally using small heavy particles in convecting fluids. The particles are initially uniformly distributed in a fluid which is either heated from below or cooled from above. The system is allowed to evolve, and temperature and particle concentration profiles are measured as functions of time. When the concentration of particles is sufficiently small, convection is basically unaffected by their presence. When the concentration is above a critical value, however, the convective motion is considerably altered. The effect of particles on the subsequent fluid behaviour is different in the cases of heating from below and cooling from above. In the former case, there are strong convective motions confined to a sedimentary layer of decreasing thickness beneath a clear layer which displays rather weak convective motions. With time, the destabilizing increase of temperature in the lower layer overcomes the stabilizing contribution to the bulk density due to the particles and the layer overturns quite suddenly. In the situation of cooling from above, a critical condition separates a case of continual overturn from a case of no overturn at all, with the sedimentary layer falling unimpeded to the bottom. Theoretical analysis suggests that the critical value is determined primarily by the ratio of the contribution to the bulk density of the suspension due to particles to the change in fluid density due to the thermal effect. The size distribution of the particles can also modify the fluid behaviour. Applying our general results to geological situations, we suggest that the presence of relatively small concentrations of phenocrysts can critically influence the mode of convection in magmas.     

Crystal fractionation of granitic magma during its non-transport processes: A physics-based perspective

Granitic continental crust distinguishes the Earth from other planets in the Solar System. Consequently, for understanding terrestrial continent development, it is of great significance to investigate the formation and evolution of granite.Crystal fractionation is one of principal magma evolution mechanisms. Nevertheless, it is controversial whether crystal fractionation can effectively proceed in felsic magma systems because of the high viscosity and non-Newtonian behavior associated with granitic magmas. In this paper, we focus on the physical processes and evaluate the role of crystal fractionation in the evolution of granitic magmas during non-transport processes, i.e., in magma chambers and after emplacement. Based on physical calculations and analyses, we suggest that general mineral particles can settle only at tiny speed(~10~(-9)–10~(-7) m s~(-1))in a granitic magma body due to high viscosity of the magma; however, the cumulating can be interrupted with convection in magma chambers, and the components of magma chambers will tend to be homogeneous. Magma convection ceases once the magma chamber develops into a mush(crystallinity, F~40–50%). The interstitial melts can be extracted by hindered settling and compaction, accumulating gradually and forming a highly silicic melt layer. The high silica melts can further evolve into high-silica granite or high-silica rhyolite. At various crystallinities, multiple rejuvenation of the mush and the following magma intrusion may generate a granite complex with various components. While one special type of granites, represented by the South China lithium-and fluoride-rich granite, has lower viscosity and solidus relative to general granitic magmas, and may form vertical zonation in mineral-assemblage and composition through crystal fractionation. Similar fabrics in general intrusions that show various components on small lengthscales are not the result of gravitational settling. Rather, the flowage differentiation may play a key role. In general, granitic magma can undergo effective crystal fractionation; high-silica granite and volcanics with highly fractionated characteristics may be the products of crystal fractionation of felsic magmas, and many granitoids may be cumulates.     

Cumulate nodules as evidence for convective fractionation in a phonolite magma chamber

The physical mechanism by which chemical zonation develops in magma chambers has been controversial partly because unambiguous geological constraints have been lacking. The 11,000 years B.P. eruption of Laacher See Volcano produced a zoned tephra deposit and also ejected crystal-rich nodules which provide a snapshot of the materials crystallising at the magma chamber margins. New data on petrography and chemical compositions of nodules, their cumulate minerals and interstitial glasses are used to deduce the chemical evolution of the phonolite melt due to fractional crystallisation of the mineral assemblages. These data, together with those on the vertical zonation of the melt in the bulk of the chamber, are shown to be consistent with a model of stratification of the chamber by convective fractionation, in which a thin boundary layer of residual melt from fractional crystallisation ascends at the chamber side and accumulates at the roof. Crystallisation could have provided buoyancy to drive convection by enriching incompatible volatile components (mainly water) in the residual melt. Available fluid dynamic studies of single- and double-diffusive boundary layers are used to assess convection in the Laacher See chamber. The boundary layer is likely to have been: (1) laminar, which implies that the density gradient in the chamber steepened upwards; (2) in the counterflow regime, in which compositional and thermal layers flow in opposite directions; and (3) thin ( 10 cm), estimated from theory for a flat wall, suggesting that wall morphology could be important in determining boundary layer characteristics. Estimates of mass transfer rates due to this mechanism suggest that the chamber could have become stratified in a time of the order of 10³ years.     

Degassing of stratified magma by compositional convection

A new model is proposed for passive degassing from sub-volcanic magma chambers. The water content in stably stratified shallow magma chamber will be equated to its solubility at the upper boundary by convection. Water from a lower layer high in water content can enrich the contact zone of the upper layer and lead to further convective overturn of this boundary layer. A complete set of equations describing convection with bubble formation and dissolution is reduced to a simplified form by assuming a small bubble content. The development and pattern of flow driven by vesiculation is modeled numerically in a 2D magma chamber for relatively low Raleigh numbers (5×10⁵). Bubbles rising from the magma will collect near the roof in a layer of 8–10 vol% and then escape upward to fumaroles. The Stokes flux of bubbles escaping from an andesitic magma with viscosity 10⁴ P and a top surface of about 500×500 m corresponds with observed total magmatic water fluxes of 35 kg/s. Pressure within the chamber is buffered by elastic (and local visco-elastic) deformations in the solid rocks bounding the chamber to the range between ambient and close to lithostatic values. In a chamber closed to fresh magma inputs, the decrease in volume due to such gentle volatile escape lowers the reference pressure. Bubbles flux from the lower layer induced by variation of the saturation level around stratification boundary may be efficient mechanism for the water transport between layers.     

地球自转速率变化及其与地球物理现象关系研究的进展

作为地球的基本运动形式之一的地球自转变化表征着地球的整体运动状态和地球系统各圈层之间的相互作用过程,其变化形式非常复杂．研究表明,地球自转速率的变化与众多地球物理现象有密切联系,与地震活动、EN-SO事件等重大自然灾害存在一定的相关性．因此,对地球自转速率变化及其与地球物理现象之间关系的研究长期以来就受到天文学家、地球科学家和从事灾害研究领域专家的重视．本文主要介绍了该研究领域近年来的研究进展,并认为在此基础上开展更深入的研究对天文学和地球科学的发展都是有意义的．     

The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: the dependence on the prandlt numbers

The onset of Boussinesq convection in a horizontal layer of an electrically conducting incompressible fluid is considered. The layer rotating about a vertical axis is heated from below; a vertical magnetic field is imposed. Rigid electrically insulating boundaries are assumed. The loss of stability of the trivial steady state, which occurs as the Rayleigh numbers increase, can be accompanied by the development of a monotonic or an oscillatory instability, depending on the parameter values of the problem at hand (the Taylor number, the Chandrasekhar number, the kinematic and the magnetic Prandtl numbers). When the instability is monotonic, the emerging convective rolls themselves are also unstable if the Taylor number is sufficiently large (the so-called Küppers-Lortz instability takes place). In the present work it is studied how the critical value of the Rayleigh number, the type of the trivial steady state instability, and the critical value of the Taylor number for the Küppers-Lortz instability depend on the kinematic and the magnetic Prandtl numbers. We consider the values of the Prandtl number not exceeding 1, which is typical for the outer core of the Earth.     

Magma mixing and magma plumbing systems in island arcs

Petrographic features of mixed rocks in island arcs, especially those originating by the mixing of magmas with a large compositional and temperature difference, such as basalt and dacite, suggest that the whole mixing process from their first contact to the final cooling (= eruption) has occurred continuously and in a relatively short time period. This period is probably less than several months, considerably shorter than the whole volcanic history. There may also be a prolonged quiescent interval, lasting longer than several days, between the magmas' contact and the mechanical mixing. This interval will allow the basic magma to cool and produce a semi-solidified boundary which is later disrupted by flow movements to produce basic inclusions.Mixing of magmas of contrasting chemical composition need not be the inevitable consequence of the contact of the magmas. It is, however, made more probable by forced convection caused by motive force such as the injection of a basic magma into an acidic magma chamber. A short interval between their initial contact and the final eruption requires that the acid magma chamber has a small volume, of the same order or less than that the introduced basic magma.The volcanic activity of Myoko volcano, central Japan, of the last 100,000 years shows alternate eruptions of hybrid andesite by mixing of basaltic and dacitic magmas, and non-mixed basalt to basaltic andesite. There was a repose period of 20,000 to 30,000 years between eruptions. The acidic chamber, eventually producing the mixed andesite activity, is formed during the repose period by the « in situ » solidification of the original basic magma against its wall. The volume of the chamber is very small, probably about 10^–2 km³. Basaltic magma with constant chemical composition is supplied to the shallow chamber from another deep seated basaltic chamber. The volume of the shallow magma chamber may be critical to the characteristics of volcanic activity and its products.     

Physical and numerical experiments on layered convection in a density-Stratified fluid

Abstract

The formation and growth of horizontal layered convection cells in a density stratified solution of salt water subject to an impulsively applied lateral temperature gradient is investigated with physical and numerical experiments. Results indicate that lyers are induced by two mechanisms. One is the successive formation of layers due to the presence of the top and bottom boundaries. The other is the spontaneous occurrence of layers when a suitably defined Rayleigh number exceeds a critical value. It is found that well established layers are homogeneous in temperature and salinity and are separated by sharp gradients in density. Lateral heat transfer is of a periodic nature. Numerical experiments were carried out for finite and infinite geometry cases. For the finite geometry case, convection cells are generated successively inward from the horizontal boundaries. For the infinite geometry case, periodic conditions in the vertical direction are assumed. With continuous input of small perturbations, simultaneous occurrence of the convection cells is obtained at supercritical Rayleigh numbers. Criteria for determining the onset of spontaneous cells numerically are explored.     

Along-strike magma mixing beneath mid-ocean ridges: effects on isotopic ratios

The effects of mixing processes on the isotopic variability of mid-ocean ridge basalts are studied. The processes considered are porous flow dispersion and convective mixing in magma chambers. Porous flow dispersion is capable of mixing magmas over distances of only a few tens of meters. Convective mixing, on the other hand, is found to produce mixing over scales of kilometers to hundreds of kilometers. Calculations of convective mixing are carried out for continuous magma chambers, where mixing is limited by convective processes, and for discontinuous chambers, where mixing is limited by chamber size. Preliminary comparison of our calculations with observations along the mid-ocean ridges shows that the calculations are consistent with the existence of a correlation between bathymetry and isotopic ratio at long, but not at short, wavelengths. They are also capable of explaining a decrease in isotopic variability with increasing spreading rate.     

Linear Stability of Thermal Convection in Rotating Systems with Fixed Heat Flux Boundaries

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

The imprint of basalt on the geochemistry of silicic magmas

We propose that the fluid mechanics of magma chamber replenishment leads to a novel process whereby silicic magmas can acquire an important part of their chemical signatures. When flows of basaltic magma enter silicic magma chambers, they assume a ‘fingered' morphology that creates a large surface area of contact between the two magmas. This large surface area provides an opportunity for significant chemical exchange between the magmas by diffusion that is enhanced by continuous flow of silicic liquid traversing the basalt through thin veins. A quantitative analysis shows that a basaltic magma may thereby impart its trace-element and isotopic characteristics to a silicic magma. Depending on concentration differences and diffusion coefficients for the given components, this new mechanism may be as important as crystal fractionation and assimilation in producing the compositional diversity of silicic magmas. It may explain concentration gradients in silicic ash-flow tuffs and should be considered when interpreting the isotopic signatures of silicic rocks, even in the overt absence of mixing. For example, we show that, for several well studied, compositionally graded ash-flow tuffs, the concentrations and isotopic ratios of important geochemical tracers such as strontium could be largely due to this flow-enhanced diffusion process.     

Simultaneous crystallization and melting at both the roof and floor of crustal magma chambers: Experimental study using NH4Cl–H2O binary eutectic system

Thermal and compositional evolution of magmas after emplacement of basalt into continental crust has been investigated by means of fluid dynamic experiments using a cold solid mixture with eutectic composition and a hot liquid with higher salinity in the NH₄Cl–H₂O binary eutectic system. The experiments were designed to simulate cases where crystallization of a basalt magma is accompanied by melting at both the roof and floor of a crustal magma chamber. The results show that thermal and compositional convection occur simultaneously in the solution; the thermal convection is driven by cooling at the roof and the compositional convection is driven by melting and crystallization at the floor. The roof was rapidly melted by the convective heat flux, which resulted in formation of a separate eutectic melt layer (the upper liquid layer) with negligible mixing of the underlying liquid (the lower liquid layer). On the other hand, a mushy layer formed at the floor. The compositional convection at the floor carried a low heat flux, so that the heat transfer at the floor was basically explained by simple heat conduction. The thermal boundary layer in the lower liquid layer at the interface with the upper liquid layer became thicker with time and subsequently temperature decreased upward throughout the lower liquid layer. Compositional gradient with NH₄Cl content decreasing upward formed by compositional convection in the lower liquid layer. The formation of these gradients resulted in formation of double-diffusive convecting layers in the lower liquid layer. The upward heat transfer was suppressed when compared with the case where the liquid region is homogenized by vigorous convection.These experimental results imply that, when a basalt magma is emplaced in continental crust, floor melting does not always enhance the cooling of the magma, but it may even reduce the total heat loss from the magma to the crusts due to suppression of convection by formation of a stabilizing compositional gradient.     

Baroclinic,Kelvin and inertia-gravity waves in the barostrat instability experiment

The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment.     

Convective heat transfer in magmas near the liquidus

Natural convection in magmas at subliquidus temperatures is analyzed using Bingham plastic and power-law rheology models. Heat flux measurements were obtained at liquidus and subliquidus temperatures for degassed basaltic lava at atmospheric pressure. These measurements of heat flux ranged from 2 to 40 kW/m² and were obtained using two different types of convective heat flux probes. The agreement between the two different instruments and the theoretical calculations is excellent. A noticeable change in the trend of the convective heat flux data is observed in the vicinity of the liquidus temperature. Subliquidus convective heat flux rates (6–15 kW/m²) are attractive for energy extraction applications.     

An experimental investigation of volatile exsolution in evolving magma chambers

Previous laboratory experiments investigating the fluid dynamics of replenished magma chambers have been extended to model effects resulting from the release of gas. Turbulent transfer of heat between a layer of dense, hot and volatile-rich mafic magma overlying cooler more evolved magma can lead to crystallization and exsolution of volatiles in the lower layer. Small gas bubbles can cause the bulk density to decrease to that of the upper layer and thus produce sudden overturning and initiate mixing, followed by further exsolution of gas and explosive eruption. These processes have been modelled in the laboratory using a chemical reaction between sodium or potassium carbonate and nitric acid to release small bubbles of CO₂. We have investigated both the initial overturning produced by gas release in the lower layer, and the subsequent evolution of gas due to intimate mixing of the two layers. The latter experiments, in which the reactants remained isolated in the two layers until overturning occurred, demonstrated unambiguously that the fluxes of chemical components across the interfaces between convecting layers are very slow compared to the flux of heat. This shows that the evolution of layers of magma of different origins and composition can take place nearly independently of each other. The magmas can coexist in the same stratified chamber, until their bulk densities become equal and they mix together. The processes illustrated in these experiments could occur in H₂O-bearing magmas such as in the calcalkaline association and in CO₂-bearing mafic magmas such as in silica undersaturated suites.