Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 2. Numerical solutions of the full equations
Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 2. Numerical solutions of the full equations
复制标题
DOI：
10.1017/jfm.2013.483
复制
发表时间：
2013-10
影响因子：
3.7
通讯作者：
R. Katz;Y. Takei
中科院分区：
文献类型：
--
作者：
R. Katz;Y. Takei
在地球部分熔融的地区，岩石和岩浆作为两相聚集体共存，其中固体岩石颗粒形成粘性变形的框架或基质。液态岩浆存在于颗粒之间的可渗透孔隙网络中。偏应力导致固体颗粒之间的接触面积的分布变得各向异性，这反过来又导致在连续尺度下的基质粘度的各向异性。在第二个两纸集，我们使用数值方法来解决这个系统的完整的，非线性的，时间依赖的方程。我们考虑孔隙度的演化在简单的剪切，Poistonille和扭转流。粘性各向异性下，有两种模式的孔隙度演化：基态偏析，修改域尺度的孔隙度分布，和增长的孔隙度扰动到熔体丰富的带。具有固定各向异性的模拟结果确认并扩展了第1部分的线性化分析（Takei & Katz，J. Fluid Mech.，第734卷，2013年，pp. 424-455）。最重要的是，数值解捕获的两种模式的相互作用：根据Poilluille流，基态偏析增强带的形成;扭转流，带被抑制。模拟结果还表明，低带角是由非线性过程，如高孔隙度段的重新连接和带之间的压实区域的反向旋转。动态各向异性的模拟修改了这些结果，进一步降低了平均带角。每个流的有效粘度由基态偏析控制;它在简单剪切下不发展，在Poiffille流中减少，在扭转中增加。我们提出了一个重新解释的粘性各向异性的后果方面的实验结果。
Abstract In partially molten regions of Earth, rock and magma coexist as a two-phase aggregate in which the solid grains of rock form a viscously deformable framework or matrix. Liquid magma resides within the permeable network of pores between grains. Deviatoric stress causes the distribution of contact area between solid grains to become anisotropic; this, in turn, causes anisotropy of the matrix viscosity at the continuum scale. In the second of a two-paper set, we use numerical methods to solve the full, nonlinear, time-dependent equations governing this system. We consider porosity evolution in simple shear, Poiseuille and torsional flow. Under viscous anisotropy, there are two modes of porosity evolution: base-state segregation, which modifies the domain-scale porosity distribution, and growth of porosity perturbations into melt-rich bands. Simulation results with fixed anisotropy confirm and extend the linearized analysis of Part 1 (Takei & Katz, J. Fluid Mech., vol. 734, 2013, pp. 424–455). Most importantly, numerical solutions capture the interaction of the two modes: under Poiseuille flow, base-state segregation enhances band formation; under torsional flow, bands are suppressed. Simulations also show that low band angle is maintained by nonlinear processes such as reconnection of high-porosity segments and by back-rotation of the compacted regions between bands. Simulations with dynamic anisotropy modify these results, further lowering the average band angle. The effective viscosity of each flow is controlled by base-state segregation; it does not evolve under simple shear, decreases in Poiseuille flow and increases in torsion. We propose a reinterpretation of experimental results in terms of the consequences of viscous anisotropy.