Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.     

考虑多种因素影响的海上地震勘探气枪震源单枪子波数值模拟

在分析Ziolkowski气泡振动模型局限性的基础上,建立了多种实际因素影响下的海上地震勘探单枪子波模型。此模型考虑了气泡壁的热传导作用、枪口节流作用、气泡上浮、液体粘度和枪体本身等对气枪子波的影响。相对于Ziolkowski模型,改进模型所模拟的气枪子波主峰值减小,气泡振动衰减加快,与实测子波吻合性较好。实验分析表明：（1）枪口节流作用控制着气枪脉冲峰值振幅的大小,（2）上浮过程中气泡周围静水压力值减小,气泡振动的周期随之改变,（3）热传导作用和流体粘度是引起气泡振动衰减的主要因素。     

A Velocity-Based Approach to Visco-Elastic Flow of Rock

In structural geology, viscous creep is generally recognized as the major deformation mechanism in the folding of rock layers through geological time scales of hundreds of thousands of years. Moreover, since deformation of rock salt by creep takes already place on relatively small time scales—weeks to months, say—creep is a relevant phenomenon when studying salt mining, notably the convergence of mine cavities and the land subsidence caused by it. While creep is the dominant process on relatively long time scales, elasticity plays a dominant role in processes that take place on relatively short time scales. The elastic response to a stress is a displacement; the shape of the rock is deformed instantaneously with respect to its initial shape. However, the viscous response of a rock to a stress is a relatively low velocity in the order of millimeters per months or years, say. In this paper we consider the two deformation phenomena creep and elasticity. In general, elasticity is a compressible phenomenon, while creep is incompressible. Here we approximate creep by the introduction of a negligibly small amount of compressibility, which makes creep velocity calculations similar to conventional elastic displacement calculations. Using this procedure, a standard finite element package for elasticity can be applied to viscous problems, also in combination with elasticity. The method has been demonstrated to upscaling of creep viscosities.     

The influence of different rheological parameters on the surface deformation and stress field of the Aegean–Anatolian region

The Aegean–Anatolian region is characterised by an inhomogeneous deformation pattern with high strain rates and a high seismicity both at the boundaries and in the plate interior. This pattern is controlled by the geometry and rheology of the structural units involved and their tectonic setting. A numerical analysis with a finite-element model of the region is used to quantify the influence of different rheological parameters. Viscoelastic material behaviour is implemented for the mantle lithosphere, whereas the crust is modelled with an elastic–plastic rheology. The variation of the inelastic material properties (viscosity and plastic strength) quantifies the influence of these material parameters on the deformation, stress, and strain patterns. Comparison of the modelled results with geodetic and geophysical observations reveals that the viscosity of the mantle lithosphere is the key to explaining the inhomogeneous deformation pattern. The best-fit model yields a viscosity of 10²⁰ Pa s beneath Anatolia, whereas adjacent regions have viscosities between 10²¹ and 10²³ Pa s. The model also explains the intra-plate seismicity and the stress field as well as its partitioning into regions with strike-slip and normal faulting. The final model is in good agreement with seismological, geodetic, and geological observations. Local deviations can be tracked down to small-scale structures, which are not included in the model.     

Viscosity measurements of subliquidus magmas: Alkali olivine basalt from the Higashi-Matsuura district, Southwest Japan

We carried out viscosity measurements and sampling of a crystal suspension derived from alkali olivine basalt from the Matsuura district, SW Japan, at subliquidus temperatures from 1230 °C to 1140 °C under 1 atm with NNO oxygen buffered conditions. Viscosity increased from 31 to 1235 Pa s with a decrease in temperature from 1230 to 1140 °C. On cooling, olivine first appeared at 1210 °C, followed by plagioclase at 1170 °C. The crystal content of the sample attained 31 vol.% at 1140 °C (plagioclase 22%, olivine 9%). Non-Newtonian behaviors, including thixotropy and shear thinning, were pronounced in the presence of tabular plagioclase crystals. The cause of such behavior is discussed in relation to shear-induced changes in melt–crystal textures. Relative viscosities, η_r (= η_s / η_m, where η_s and η_m are the viscosities of the suspension and the melt, respectively), were obtained by calculating melt viscosities from the melt composition and temperature at 1 atm using the equation proposed by Giordano and Dingwell [Giordano, D., Dingwell, D.B., 2003. Non-Arrhenian multicomponent melt viscosity: a model. Earth and Planetary Science Letters, 208, 337–349.]. The obtained relative viscosities are generally consistent with the Einstein–Roscoe relation, which represents η_r for suspensions that contain equant and equigranular crystals, even though the crystal suspension analyzed in the present experiments contained tabular plagioclase and granular olivine of various grain sizes. This consistency is attributed to the fact that the effect of crystal shape was counterbalanced by the effect of the dispersion of crystal size. The applicability of the Einstein–Roscoe equation with respect to crystal shape is discussed on the basis of the present experimental results. Our experiments and those of Sato [Sato, H., 2005. Viscosity measurement of subliquidus magmas: 1707 basalt of Fuji volcano. Journal of Mineralogical and Petrological Sciences, 100, 133–142.] show that the relationship between relative viscosity and crystal fraction is consistent with the Einstein–Roscoe relationship for axial ratios that are smaller than the critical value of 4–6.5, but discrepancies occur for higher ratios.     

Field observations,rheological testing and numerical modelling of a debris‐flow event

Debris flows generated from landslides are common processes and represent a severe hazard in mountain regions due to their high mobility and impact energy. We investigate the dynamics and the rheological properties of a 90 000 m³ debris‐flow event triggered by a rapid regressive landslide with high water content. Field evidence revealed a maximum flow depth of 7–8 m, with an estimated peak discharge of 350–400 m³ s^?1. Depositional evidence and grain‐size distribution of the debris pose the debris flow in an intermediate condition between the fluid‐mud and grain‐flow behaviour. The debris‐flow material has silt–clay content up to 15 per cent. The rheological behaviour of the finer matrix was directly assessed with the ball measuring system. The measurements, performed on two samples at 45–63 per cent in sediment concentration by volume, gave values of 3·5–577 Pa for the yield strength, and 0·6–27·9 Pa s for the viscosity. Based on field evidence, we have empirically estimated the yield strength and viscosity ranging between 4000 ± 200 Pa, and 108–134 Pa s, respectively. We used the Flo‐2D code to replicate the debris‐flow event. We applied the model with rheological properties estimated by means of direct measurements and back‐analyses. The results of these models show that the rheological behaviour of a debris‐flow mass containing coarse clasts can not be assessed solely on the contribution of the finer matrix and thus neglecting the effects of direct grain contacts. For debris flows composed by a significant number of coarse clasts a back‐analysis estimation of the rheological parameters is necessary to replicate satisfactorily the depositional extent of debris flows. In these cases, the back‐estimated coefficients do not adequately describe the rheological properties of the debris flow. Copyright © 2006 John Wiley & Sons, Ltd.     

粘性土的动力特性实验及数值模拟

使用产自日本的DTC-306型多功能电液伺服动态三轴仪,对粉质粘土进行动三轴试验。在试验提供的各种参数和数据的基础上,利用有限元程序ABAQUS建立动三轴试件的三维有限元模型,模拟在循环荷载作用下粉质粘土的动力变形特性;并通过与动三轴试验相关数据的大量对比分析,验证了模型的可靠性。然后在建立的三维有限元模型的基础上,进一步用数值模拟的方法研究了土体动力变形与各影响因素间的关系,得出如下结论:初始弹性模量、阻尼系数、受荷形式对土的塑性变形影响最大,应力幅值、围压、频率、加荷周数次之,加载波形的影响最小,不同波形对塑性变形的影响取决于荷载最大值时历时的长短。有限元数值模拟方法在一定程度上可以替代动三轴实验。     

扇形边界附近太阻风粘性的数学描写和物理效应

本文首先指出经典粘性理论应适用于扇形边界低速风,接着论证了常用太阳风粘性数学表式的不正确性,导出了螺旋磁场中径向球对称强磁化等离子体流动的各种经典粘性表式,并证明了这些公式的合理性;最后讨论了常用太阳风经典粘性表式出错原因,估计了具有正确粘性公式的扇形边界低速太阳风粘性模式应有的结果。