Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 2. Numerical solutions of the full equations

Abstract

AbstractIn 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.