Influence of permeability on hydrothermal circulation in the sediment-buried oceanic crust

1 Introduction Hydrothermal circulation is the key process of hydrothermal activity. Modern seafloor hydrothermal circulation can be divided into three parts: convective cells in the oceanic curst, interface between seafloor and ocean and hydrothermal plume. Hydrothermal convection in the crust is the dominant part of the whole seafloor hydrothermal circulation. The distribu-tion and nature of hydrothermal system in the oceanic crust are controlled by crust thermal structures and permeability …     

Effects of Earth's rotation on convection in magma chambers

The rotation of the Earth is predicted to have a strong influence on the convective motions in basaltic magmas which cool at high and intermediate latitudes on the Earth's surface. Convection in layers greater than 100 m deep is characterised by large Taylor numbers and small Rossby numbers, for which laboratory experiments provide evidence of strong rotationally-induced flows. In the case of convection driven by either thermal or compositional buoyancy fluxes from horizontal top or bottom boundaries Coriolis forces induced by the Earth's rotation are expected to cause the turbulent convective motions to form into intense vortices whose axes tend to be close to the vertical. These vortices should be tall and thin, be very unsteady, and have rapid vertical motion in their cores. Earth's rotation is likely to have little or no effects on convection in very shallow convecting layers ( < 100 m) of basaltic magmas or in chambers of more viscous (granitic) magmas. When convection is driven by horizontal density differences (such as those produced by cooling or crystallization at sloping or vertical walls or by simple lateral variation of layer depth) in basaltic chambers of order 10 km or greater in width the rotation of the Earth may cause relatively rapid horizontal (geostrophic) circulation over the lateral scales of the chamber. These predictions involve some extrapolation of fluid dynamical principles from laboratory to magma chamber conditions. Speculative comments on some possible petrological implications are included.     

Interferometric observations of the temperature structure in water cooled or heated from above

Controlled laboratory experiments were performed in a water tank to study energy transfer during cooling and radiant reheating of water from above. Accurate instantaneous temperature measurements were obtained using a Mach-Zehnder interferometer which did not disturb the temperature, radiation, and flow fields. The buoyancy induced flow field was visualized by employing an electro-chemical dye production technique. Cooling of initially uniform layer of water and stratification-cooling-restratification were studied.The experimental observation during cooling of an initially uniform temperature column of water indicated intermittent free convection near the surface. The phenomenon was characterized by randomly descending cooler plumes penetrating 10 to 25 cm into the warmer underlying region. The cooling rate had a decisive influence on the frequency and intensity of the descending parcels of water. For lower cooling rates the colder water usually descended in a form of sheets.Observations during cooling of initially stratified water showed that buoyancy driven convection occurred near the surface. The motion had an initial regular roll pattern, but as the cooling continued the roll pattern in the convective (mixed) layer deteriorated into motion similar to that observed during cooling of an initially uniform temperature layer of water. When the water was restratified by radiant heating, the circulation in the convective layer was suppressed, and the temperature profiles obtained were similar to those observed in a fluid during free convection between two solid parallel walls.     

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.     

A model of thermal convection in the major planets with a strongly density-stratified atmospheric layer

Abstract

As an extension of a model by Busse (1983a), a two-layer model of thermal convection in the self-gravitating rotating spherical fluid is considered. The upper layer with arbitrary vertical distributions of density and potential temperature representing the atmospheric layer of major planets is imposed on the spherical Boussinesq fluid. The Prandtl number P and the ratio of the mass of the upper layer to that of the lower layer are used as small expansion parameters. The modification of the critical Rayleigh number by imposing the upper layer are clearly separated into two parts, proportional to (1) the mass of the upper layer and to (2) an integral representing a measure of convective instability of the upper layer. Some implications for atmospheric dynamics of the major planets are also presented.     

Planform of convection with strongly temperature-dependent viscosity

Abstract

This paper experimentally investigates the convective planform near critical in a fluid layer whose temperature-dependent viscosity varies from top to bottom by up to a factor of 1500. Convection occurs in three different planforms: rolls, hexagons and squares. The square planform, which appears only for fluids with viscosity variation greater than about 50, replaces the hexagonal convection pattern as the Rayleigh number increases much above critical. The large amplitude of hexagonal convection with strong viscosity variation precludes studying the hexagon-square transition with perturbation methods of the type used to study the hexagon-roll transitions at smaller viscosity variations.     

Evolution of double diffusion convection in a felsic magma chamber

The onset of double diffusion convection (DDC) is modeled in a two-dimensional case in respect to magma chambers. The viscosity model for the melt takes into account the effects of temperature and concentration of the dissolved component (H₂O). The upper boundary of the convecting magma chamber is assumed to be anhydrous and at constant temperature, whereas the lower boundary is treated as being hydrous permeable with a temperature greater than that within the upper boundary. The case of positive compositional and thermal buoyancy of melt is studied assuming a H₂O diffusion coefficient small in comparison with thermal diffusivity. The DDC has been modeled using a system of equations solved by the finite difference method on a square grid. The convective pattern evolution has been studied for fixed boundary conditions as well as for cooling and degassing. Due to the higher viscosity in the upper zone, the upper boundary layer is thicker than the lower one. The variation of water concentration in this zone of the convective cell can be significant. In nature, the high gradient of water concentration can be responsible for the observed variations of water content in minerals crystallized from a granite melt (e.g., biotite). Because of a high Lewis number (= 100), temperature variations in the magma chamber decay much faster than the water concentration. In this case the intensive convection can continue at a constant temperature due to the non-zero water content in the chamber. In principle, the effect can be applied to the formation of magmatic bodies. If the cooling and degassing system reaches a uniform temperature distribution prior to the crystallization temperature, water content throughout the body may still remain variable.     

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.     

金星非单调冷却热演化历史分析

金星表层年龄和构造活动特点表明其岩石层在最近的地质历史时期经历过广泛的更新.这种全球性的表层改造与其内部热演化历史进程密切相关.如果金星存在相变形成的上、下地幔,依据现今所了解的金星物理性质和参量化的热对流理论,并且考虑金星地幔相变边界层状态对对流的控制作用,我们计算了金星热演化历史.结果表明,金星的热演化历史是一种非单调的冷却过程,在这种非单调的热演化历史进程中,金星地幔会出现大体等周期的翻转.由于参数选取的不同,翻转时金星上、下地幔的温差随时间可能出现稳定变化、逐渐加强、逐渐减弱三种不同演化模式,目前尚不能确定实际金星热演化历史究竟是哪一种模式.金星地幔相变边界层的穿透对流可能是推动其表层岩石层全球性更新的关键,导致其表层火山活动和地表构造以大致500 Ma时间间隔更新和重造.     

Concerning the multiscale structure of solar convection

The discrete scale spectrum of the convective flows observed on the Sun has not yet received a convincing explanation. Here, an attempt is made to find conditions for the coexistence of convective flows on various scales in a horizontal fluid layer heated from below, where the thermal diffusivity varies with temperature in such a way that the static temperature difference across a thin sublayer near the upper surface of the layer is many times larger than the temperature variation across the remainder of the layer. The equations of two-dimensional thermal convection are solved numerically in an extended Boussinesq approximation, which admits thermal-diffusivity variations. The no-slip conditions are assumed at the lower boundary of the layer; either no-slip or free-slip conditions, at the upper boundary. In the former case, stable large-scale rolls develop, which experience small deformations under the action of small structures concentrated near the horizontal boundaries. In the latter case, the flow structure is highly variable, different flow scales dominate at different heights, the number of large rolls is not constant, and a sort of intermittency occurs: the enhancement of the small-scale flow component is frequently accompanied by the weakening of the large-scale one, and vice versa. The scale-splitting effects revealed here should manifest themselves in one way or another in the structure of solar convection.     

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.     

Nonlinear modal analysis of penetrative convection

Abstract

The modal expansion procedure has been used to analyze penetrative convection that arises when a thin unstable layer is embedded between two stable regions. The Boussinesq approximation is applied in which the effect of compressibility and stratification are neglected. Various calculations have been made, with one and two modes, for Rayleigh numbers ranging from the critical value to more than 10⁵ times critical. The effect of decreasing the Prandtl number has also been investigated.

It is found that in the nonlinear regime, the convective motions penetrate substantially into the stable regions. The flux of kinetic energy plays a crucial role in such penetration, and its existence puts some requirements on the motions: in the single-mode case, they need to be three-dimensional. The extent of penetration amounts to about half of the thickness of the unstable layer on each side of it when the degree of instability and that of stability are comparable in the two domains; it increases as the stability of the outer region is lowered. The penetration depth appears to be independent of all other parameters defining the problem.     

The rapid dissipation of magnetic fields in highly conducting fluids

Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.     

Testing density-dependent groundwater models: two-dimensional steady state unstable convection in infinite,finite and inclined porous layers

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA––A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4π² and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature.     

现代板块运动驱动地幔块体置换度及地幔混合的研究

定义了描述地幔混合程度的新的统计学量度——地幔块体对流置换度和对流混合扩散度.地幔块体对流置换度等于至少被置换一次的块体数与地幔总块体数之比,对流混合扩散度等于示踪元初始体密度与示踪元终体密度之比.本研究假设地幔对流是稳定的,上地幔和下地幔的黏滞性存在差异,其驱动力为板块运动或地幔中密度异常分布.实验中地幔被划分为20736 个块体（5°×5°×300 km）,2376个示踪元被放置在地幔顶部100 km深度或底部100 km高度的5°×5°的网格点上.模型计算表明, 地幔块体对流置换度随运转时间变化.就全地幔而言,在系统运行四十亿年后,大多数模型对应的块体对流置换度均超过80%,而上地幔块体置换度则达到90%.这预示大多数的地幔块体将被来自其他位置的块体所取代.对于放置在地幔顶部或底部,浓缩于很小空间10°×10°(间距0.25°) 中的两组1681个示踪元而言,尽管其对流混合扩散度在开始有较大的差异,但是在运行一段时间之后,此两组对应的对流混合扩散度均趋于常数,示踪元比较均匀地分布于全地幔之中.由以上的结果可以推断,在经历了四十五亿年的演化过程后,由于对流的作用使地幔基本上已经均匀混合,地幔中不大可能存在尺度大于5°×5°×300 km的异常块体.     

Convective Instability of a Mushy Layer - I: Uniform Permeability

Mushy layers arise and are significant in a number of geophysical contexts, including freezing of sea ice, solidification of magma chambers and inner-core solidification. A mushy layer is a region of solid and liquid in phase equilibrium which commonly forms between the liquid and solid regions of a solidifying system composed of two or more constituents. We consider the convective instability of a plane mushy layer which advances steadily upwards as heat is withdrawn at a uniform rate from the bottom of a eutectic binary alloy. The solid which forms is assumed to be composed entirely of the denser constituent, making the residual liquid within the mush compositionally buoyant and thus prone to convective motion. In this article we focus on the large-scale mush mode of instability, arguing that the 'boundary-layer' mode is not amenable to the standard stability analysis, because convective motions occur on that scale for any non-zero value of the Rayleigh number. We quantify the minimum critical Rayleigh number and determine the structure of the convective modes of motion within the mush and the associated deflections of the mush-melt and mush-solid boundaries. This study of convective perturbations differs from previous analyses in two ways; the inhibition of motion and deformation of the mush-melt interface by the stable stratification of the overlying melt is properly quantified and deformation of the mush-solid interface is permitted and quantified. We find that the mush-melt interface is almost unaffected by convection while significant deformation of the mush-solid interface occurs. We show that each of these effects causes significant (unit-order) changes in the predicted critical Rayleigh number. The marginal modes depend on three dimensionless parameters: a scaled eutectic temperature, τ _e (which characterizes the eutectic temperature relative to the depression of the liquidus), a scaled superheat, τ_∞ (which measures the amount by which the temperature of the incoming melt exceeds the liquidus temperature) and the Stefan number, S (which measures the latent heat of crystallization). To survey parameter space, we focus on seven cases, a standard case having S = τ_∞ = τ _e = 1, and six others in which one of the parameters is either large or small compared with unity: a nearly pure case (τ _e = 100; having little of the light constituent), the large superheat limit (τ_∞→ ∞), a case of large latent heat (S = 100), the near eutectic limit (τ _e → 0), a case of small superheat (τ_∞ = 0.01) and the case of zero latent heat (S = 0). The critical Rayleigh number and the associated wavelength of the convection pattern are determined in each case. The eigenvector for each case is presented in terms of the streamlines and the isolines of the perturbation temperature and solid fraction.     

Numerical analysis for cooling effect of open boundary ripped-rock embankment on Qinghai-Tibetan railway

At present, the Qinghai-Tibetan railway is being built, and it will pass across more than 550-km perma-frost regions. Therefore, the key to the stability of therailway embankment lies in solving the permafrost problem. Because global warming and existence of railway tend to degrade the permafrost in these re-gions[1], more difficulties and problems are induced in the construction and maintenance of railway. In the area where the mean annual air temperature is higher than a certain value, the …     

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     

对流层上传重力波的非线性演化

利用二维全隐欧拉格式对重力波在可压、非等温大气中的非线性传播过程进行了数值模拟和分析.分析结果表明，从对流层顶激发的重力波能稳定地经平流层传到中层顶，从而将能量和动量从一个区域带到另一个区域；在向上传播过程中，重力波经历了发展、位温翻转、对流直至最终破碎的演变；重力波的破碎是对流和小尺度波动的重要的源，对流不稳定和翻转是非线性现象的一个基本特征.计算还显示，扰动源的大小直接影响着重力波的非线性传播过程，当扰动源足够小时，重力波能稳定传播，而大振幅扰动可以加速重力波的破碎.     

Evidence of free convection in groundwater: Field-based measurements beneath wind-tidal flats

Free convection caused by salinity differences had not been conclusively detected or measured in the field. A field experiment at wind-tidal flats on Padre Island National Seashore, Texas, documents salinity-driven free convection with both direct (head and salinity data) and indirect (time-lapse 3-D resistivity) methods. Evaporative concentration of groundwater near the water table created unstable inverted density gradients, reduced groundwater levels, and reversed hydraulic gradients. These factors allowed plumes or fingers of more saline, denser fluid to flow downward into less-dense fluid as observed in monitoring wells and 3-D surveys. The development of density inversions can overcome the dissipating forces of dispersion and diffusion to create a sufficiently large unstable gradient to induce free convection. The development of free convective flow of variable-density fluids in groundwater can be detected and monitored through field techniques.