Magma flow in a volcanic conduit with account for nonequilibrium crystallization and heat exchange with surrounding rocks

Two-dimensional models of magma flow in a volcanic conduit with account for nonequilibrium crystallization, variable viscosity, heat exchange with surrounding rocks, and crystallization latent-heat release are presented. The viscosity depends on the temperature and the crystal concentration. It is assumed that magma may slip along the walls if a critical shear stress is reached. In the steady-state case the sigmoidal dependence of the flow-rate on the chamber pressure, earlier obtained within the framework of one-dimensional models, is found. It is shown that the parameter distribution across the conduit and thermal effects have a significant influence on the eruption dynamics.     

Gas-dynamic signs of explosive eruptions of volcanoes. 1. Hydrodynamic analogs of the pre-explosion state of volcanoes, dynamics of the three-phase magma state in decompression waves

Experimental data and results of numerical simulations of the magma state dynamics in explosive eruptions of volcanoes are presented. The pre-explosion state of volcanoes and the cavitation processes developed in the magma under explosive decompression are studied under the assumption that the intensity of explosive volcanoes does not exert any significant effect on the eruption mechanisms. In terms of the structural features of the pre-explosion state, a number of explosive volcanic systems are close to hydrodynamic shock-tube schemes proposed by Glass and Heuckroth. High-velocity processes initiated by shock-wave loading of the liquid may be considered as analogs of natural volcanic processes, which have common gas-dynamic features and common kinetics responsible for their mechanisms, regardless of the eruption intensity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 3–12, November–December, 2008.     

A Study of Magma Flows in the Case of Non-Equilibrium Diffusion of Water in the Melt

All volcanic eruptions are accompanied by the degasification of the magma, which results in the growth of gas bubbles in the silicate melt. The number and growth rate of the bubbles determine the character of the eruption. When the free-gas concentration is low, the eruption is weak and takes a short time. At high concentrations, the melt is fragmented and a gas-particle mixture is formed. This results in the catastrophic intensification of the eruption. In this study, for describing the magma flow in a volcano conduit with account for the mass transfer between the bubbles and the melt, we construct models in which the conduit magma flow is considered simultaneously with the dynamics of gas-bubble growth in the melt. The models describe the magma eruptions with equilibrium or weak growth of the bubbles and also with a moderate rate of bubble growth, which is more typical of volcanic systems. Using the models constructed, an intense steady-state eruption and the problem of the evolution of the eruption to the steady-state regime after the rupture of a plug near the top of the conduit are considered. The effect of gas diffusion on the intensity and duration of the eruption is indicated.     

Gasified magma flow in a volcanic conduit

A closed model for describing the magma flow in a volcanic conduit in the eruption regime characterized by quasisteady venting of a gas suspension jet is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 35–43, September–October, 1990.     

西安地铁二号线沿线地裂缝未来位错量估算及工程分级

地裂缝在地铁设计使用期内的最大垂直位错量是西安地铁二号线穿越地裂缝结构设计的一个十分重要的参数。本文以历史水准监测资料为基础,分析了西安地铁二号线沿线各地裂缝在不同历史阶段的活动特征与活动原因,对各地裂缝的未来活动趋势进行了预测。然后通过基于不同时间段地裂缝活动速率的最大垂直位错量估算结果的对比分析,得出了地铁设计使用期内各条地裂缝与地铁交汇点处地裂缝的最大垂直位错量,并以此为依据,将西安地铁二号线沿线地裂缝分为Ⅰ、Ⅱ、Ⅲ和Ⅳ级等4个工程级别。     

山西清徐地裂缝形变的InSAR监测分析

山西清徐地裂缝是近年汾渭盆地中活动最为剧烈的地裂缝之一,对耕地、道路和建筑物均造成了严重的破坏。为了监测该地裂缝的活动特征并推测其活动原因,采用差分合成孔径雷达干涉测量技术对该区域的地表形变进行了面状监测。由于受农田覆盖导致的严重时间去相干的影响,本文采用2007年时隔仅为70d的两景Envisat ASAR数据进行了解算,获取了该时间段清徐地区的整体地表形变,特别是清徐地裂缝两侧的形变梯度信息。结果显示: 清徐地裂缝南侧有一个长轴约为2km的地面沉降区域。进一步通过两条平行于地裂缝的剖线和多条垂直于地裂缝的剖线对该地裂缝形变的空间特征进行了分析,结果显示: 清徐地裂缝南侧为主要的形变区域,地裂缝最大的影响宽度达100m,而且地裂缝的不同地段的活动强度也不同, 70d的最大差异形变达5cm。从地裂缝与断裂的空间来看,该地裂缝位置受到交城断裂的控制,而推测近年地裂缝的异常活动则源于地裂缝南侧沉降中心的出现。     

Effect of viscous dissipation on nonisothermal high-viscosity magma flow in a volcanic conduit

A two-dimensional nonisothermal model of magma flow in a volcanic conduit is proposed. The model makes it possible to investigate the effect of the processes of viscous dissipation and heat conduction on the magma flow. It is established that the effect of these processes is significant, particularly in the case of high flow rates. It is shown that in this case the conduit resistance calculated from the Poiseuille formula widely used in one-dimensional models is highly overestimated. This is related to the formation of a strongly heated fluid layer with reduced viscosity in the near-wall conduit zone. Within the framework of the proposed model it is possible to describe eruptions with flow rates which are several times higher than the flow rates obtained within the framework of one-dimensional models.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 21–32. Original Russian Text Copyright © 2004 by Barmin, Vedeneeva, and Melnik.     

On the Initiation of a Hydrothermal Eruption Using the Shock-Tube Model

In this work, the authors introduce the shock-tube model for a hydrothermal eruption in a geothermal reservoir. The governing equations, based on the multiphase Euler equations and a Darcy-type law, are solved using a three-phase weighted sub-system numerical solver. Results are then presented which show the importance of the geometry of the geothermal reservoir in predicting the initiation of a hydrothermal eruption. In particular, the porosity, permeability, and cohesion of the reservoir are shown to significantly affect the pressure difference required to initiate an eruption. Finally, the authors show the importance of the initial liquid water/water vapour volume fractions in determining the size of an eruption, and further show boiling to be of major importance.     

The Effect of Cracks and a Steam Cap on Hydrothermal Eruptions

The shock-tube model for a hydrothermal eruption in a geothermal reservoir (Fullard and Lynch, Trans Porous Med, 2011) is used to simulate eruptions that have a steam phase present near the surface in the form of a steam cap or a large crack. Simulations are performed with various steam cap/crack depths and it is shown that the presence of a steam phase greatly reduces the size of an eruption. We show that a steam cap type eruption is physically unlikely because of the large pressure differences required, but conclude that rock cracking is potentially a viable initiation mechanism for a hydrothermal eruption.     

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.     

A Model of Magma Solidification During Explosive Volcanic Eruptions

The paper considers the problem of magma solidification during an explosive volcanic eruption, which is characterized by release of a large amount of gases from the magma. This leads to considerable cooling and, hence, solidification of the magma. It is found that solidified magma has the structure of porous glass with crystalline inclusions.     

Two-dimensional models of magma flows in a volcanic conduit taking the magma compressibility and thermal effects into account

Two steady-state models of magma flow in a conduit are considered, with and without allowance for magma compressibility. As distinct from studies [{xc1}–{xc6}], in which either simplified equations were solved or unrealistic values of the parameters were used, in the present study the complete systems of equations are solved and the values of the parameters correspond to magma flow in a volcanic conduit. The secondary flows obtained in [{xc5}] for model conditions are not formed when the magma is simulated by an incompressible fluid and all the terms of the equations are taken into account. When the magma compressibility is taken into account, in the isothermal case and for constant magma viscosity the entire flow is adequately described by the one-dimensional isothermalmodel, although this approach is not formally applicable.     

Nucleation and growth of a gas bubble in magma

The dynamics of a “collective” gas bubble in the magma melt during its decompression was numerically studied on the basis of a complete mathematical models of an explosive volcanic eruption. It is shown that the bubble size distribution obtained for the nucleation process has one peak, which allows considering a “collective” bubble. The main stages of bubble growth due to gas diffusion and changes in the viscosity of the medium are determined. It is shown that the high viscosity of the melt makes possible the transition from the Rayleigh equation to a simpler relation for the radial velocity of the bubble.     

山西清徐县地裂缝灾害现状及类型分析

研究了山西省清徐县平泉村—武家坡村地裂缝地质灾害的现状和主要特征。清徐县平泉村至武家坡村等7个村庄自2002年春天出现地裂缝以来,其灾害呈现日趋加重的趋势,给当地村民的生产及生活带来了极大影响。经过对平泉村至武家坡村地裂缝的现场实地调查,认为清徐县平泉村-武家坡村地裂缝的分布情况复杂,影响带的宽度从3m左右到100多米不等,凡位于地裂缝带内的大部分建筑物都遭到了破坏。地裂缝带内的地面变形形式有陡降型和缓降型两类,其中位于陡降型变形带上的建筑物破坏最为严重。地裂缝引起建筑物的破坏主要有墙体开裂、地面倾斜、地基下沉、楼梯断裂、门窗变形等多种形式。清徐地裂缝目前仍处于活动阶段,这种活动趋势还将持续一段时间,建议地裂缝带内的村民应尽快搬迁,并限制其在地裂缝带内的工程活动,以免造成更大的损失。     

Simulation of the Effect of Water Injection on Volcanic Conduit Flow

The effect on the eruption process of water or steam injection into a volcanic conduit from an adjacent water-saturated stratum is studied. Both steady-state and unsteady processes are considered. The physical characteristics of these eruptions are identified. A mathematical model of such an eruption is proposed for the first time.     

基于InSAR的西安地面沉降与地裂缝发育特征研究

哺乳动物细胞胞质分裂过程中伴随着一系列形态学改变,随着分裂沟不断收缩,形成连接两 个子细胞的细胞间桥. 间桥不断拉长、变细,直至断裂、生成两个子细胞. 采用细胞力学 和形态学测量及分析方法,通过施加肌球蛋白II抑制剂,定量研究了NRK细胞间桥变细动力 学; 采用细胞免疫荧光技术, 检测了早期胞质分裂肌动蛋白的分布,揭示肌球蛋白II缺失细 胞胞质分裂可能的机制. 结果表明：施加肌球蛋白II抑制剂的NRK细胞, 其整体形态学和细胞 间桥形态学曲线明显不同于0.3%DMSO组. 根据流体力学特性和所测量的力学参数对曲线 进行模拟发现,表面张力对肌球蛋白II抑制组细胞的间桥动力学曲线轨迹影响很大. 研究结 果提示由细胞力学特性决定的拉普拉斯压力和细胞运动共同参与了肌球蛋白II缺失细胞胞 质分裂的调节.     

地裂缝错动对地铁区间隧道影响的三维离散元分析

拟建西安地铁2号线穿越10条地裂缝,地裂缝活动将影响地铁2号线的安全运营。应用三维离散元程序3DEC建立三维计算模型,分析了裂缝带错动对地铁区间隧道盾构管线的影响,得出了不同错距工况下隧道衬砌的变形和应力。通过计算得知,当土体上下盘底部竖向错距由10cm增大到93cm时,引起的衬砌竖向变形量由0. 712cm增大到13. 99cm,且最大变形均发生在沿纵向约35～36m处,距裂缝带距离约为9. 5～8. 5m;引起的管道纵向最大拉应力则由0. 65MPa增大到18. 43MPa,最大压应力由0. 611MPa增大到16. 9MPa,且最大应力区与最大变形区一致。这一结论的获得可为地铁设计、施工及其安全运营提供科学的理论指导及设计依据。     

One-dimensional,time-dependent,homogeneous, two-phase flow in volcanic conduits

A one-dimensional, time-dependent, isothermal, homogeneous, two-phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor-corrector procedure and by means of a predictor-corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady-state, homogeneous, two-phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non-equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time-dependent behavior of real volcanic eruptions.     

Hydrodynamic aspects of explosive eruptions of volcanoes: simulation problems

The paper offers a short survey of experimental results on simulation of processes of explosive volcano eruptions, based on the method of hydrodynamic pulse shock tubes. The experiments show that the development of cavitation in the magma under the effect of decompression waves is characterized by the formation of bubbly clusters and their transformation into a system of arbitrary distributed slugs as a result of bubble coalescence. As a consequence, the magma flow turns out to be stratified into a system of vertical jets of spatial form, which then disintegrate into individual fragments. An unsteady multiphase mathematical model is created to study the dynamics of the magma state at the initial stage of the explosive eruption. This model takes into account nucleation and diffusive processes, gravity, and dynamically changing viscosity. The results of numerical studies performed within the framework of this model showed that the magma state in 6–7 s (after the beginning of decompression) is characterized by the flow glass transition, if the processes of bubble coalescence are ignored. The flow includes “frozen-in” 0.3-mm-thick bubbles, and the magma viscosity increases by 6–7 orders in the degassing process.     

Entropy generation in a square enclosure with partial heating from a vertical lateral wall

The entropy generation during the transient laminar natural convection in a square enclosure that is partially heated from a vertical lateral wall is numerically investigated. The active sites referring to the main irreversibility locations are determined. The Boussinesq approximation is used in the natural convection modelling. The effects of Prandtl (Pr) and Rayleigh (Ra) number combinations on the entropy generation are investigated. The study is restricted to the fluids of Prandtl number from 0.01 to 1.0, and Rayleigh numbers in the range of 10²–10⁸. It is found that the upper corner of the heated part of the side wall is the active site where the entropy generation initiates due to irreversibilities representing the energy loss.