[M-GI33] Computational sciences on the universe, galaxies, stars, planets, and their environments

[MGI33-P03] Modeling of thermal convection by highly viscous fluid with non-Newtonian rheology

*Takatoshi Yanagisawa¹, Masanori Kameyama², Masaki Ogawa³ (1.Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology, 2.Geodynamics Research Center, Ehime University, 3.Graduate School of Arts and Sciences, University of Tokyo)

Keywords:magma, convection, non-Newtonian rheology

On the evolution of rocky planets, magmatism is one of the most important mechanisms. Magmatism controls mixing and cooling of the interior of planets, promotes differentiation of mantle such as formation of crust at shallow part, and also makes large impact on the atmosphere and ocean. It is essential to include magmatic processes on the modeling of planetary evolution. However, the behavior of magma is very complex and difficult to treat with a simple modeling. In addition to its high dependency of viscosity on temperature, magma shows non-Newtonian rheology in many cases. With emergence of small crystals in a totally molten magma, it is supposed that magma gets highly shear-thinning rheology. “Shear-thinning” means that viscosity decreases with the increase of shear rate. To explore these complexities of magma on heat transport, we introduced shear-thinning into three-dimensional numerical model of thermal convection. Assuming the situations such as magma chambers, conduits and dykes, we searched the dependency on one horizontal scale (aspect ratio) in enclosed boxes with no-slip velocity boundary conditions. We treated Boussinesq fluid with infinite Prandtl number, and its viscosity changes depending on temperature and shear rate at each position. Power law model and Carreau model are compared for expressing shear-thinning. Three parameters are used to characterize rheological features in both models, those are, the viscosity ratio of zero shear rate and infinite shear rate, starting value of shear rate of viscosity decrease, and the steepness of viscosity decrease. Heat transport is enhanced when the convective velocity exceeds a certain value with the occurrence of shear-thinning, and time-dependency of the flow pattern increases. These features of shear-thinning are more dominant for geometries of small aspect ratios due to the strong constraint of side walls.