Emergent anisotropy and flow alignment in viscous rock

A novel class of nonlinear, visco-elastic rheologies has recently been developed by MUHLHAUS et al. (2002a, b). The theory was originally developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock. The orientation of the layer surfaces or slip planes in the context of crystallographic slip is determined by the normal vector the so-called director of these surfaces. Here the model (MUHLHAUS et al., 2002a, b) is generalized to include thermal effects; it is shown that in 2-D steady states the director is given by the gradient of the flow potential. The model is applied to anisotropic simple shear where the directors are initially parallel to the shear direction. The relative effects of textural hardening and thermal softening are demonstrated. We then turn to natural convection and compare the time evolution and approximately steady states of isotropic and anisotropic convection for a Rayleigh number Ra=5.64x10(5) for aspect ratios of the experimental domain of 1 and 2, respectively. The isotropic case has a simple steady-state solution, whereas in the orthotropic convection model patterns evolve continuously in the core of the convection cell, which makes only a near-steady condition possible. This near-steady state condition shows well aligned boundary layers, and the number of convection cells which develop appears to be reduced in the orthotropic case. At the moderate Rayleigh numbers explored here we found only minor influences in the change from aspect ratio one to two in the model domain.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

Anisotropy model for mantle convection

The paper presents a new theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including folding and kinking in multi-layered visco-elastic rock. The orientation of slip planes in the context of crystallographic slip is determined by the normal vector, the so-called director of these surfaces. The model is applied to simulate anisotropic natural mantle convection. We compare the evolution of the director and approximately steady states of isotropic and anisotropic convection. The isotropic case has a simple steady state solution, whereas the orthotropic convection model produces a continuously evolving patterning in tile core of the convection cell which makes only a near-steady condition possible, in which the thermal boundary layer appears to be well aligned with the flow and hence as observed in seismic tomomgraphy strong anistropic.