Numerical Simulation of granular flows in 3D compressible astrophysical disks

Author: Luka Poniatowski
Keywords: Granular flow, Rheology, Planetary rings, Hydrodinamic stability
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We present the hydrodynamic study of granular flows rotating around a central gravitating object. For this purpose we employ rheological model of the granular fluid and describe the dissipative properties of the granular flow using a local constitutive equation. In the framework of our local viscosity model effects of the granular interactions can be described using the shear and pressure rheology parameters, derived as the partial derivatives of the viscosity parameter by the pressure and the second invariant of the deformation tensor, respectively. Analytic study is based on the linear stability analysis of the 3D incompressible granular flow in the local shearing sheet framework. We show that the epicyclic frequency that is normally a constant quantity in Keplerian flows, depends on the wave-numbers of the perturbations, showing leading-trailing asymmetry, depending on the shear rheology parameter of the flow. We have shown that such flows can exhibit new type of instability that is triggered by the interplay of the shear rheology and the differential rotation of incompressible dense granular fluids. Found visco-rotational instability sets in granular fluids, where the viscosity parameter grows faster than the square of the local shear rate (strain rate) at constant pressure. Numerical simulation of the compressible rheological granular flows is performed using the DNS code PLUTO. The standard Riemann solver of the PLUTO code is complemented by the new Rheo module that can be used to implement the dependence of the viscosity parameter on the flow pressure and deformation tensor. Direct numerical simulations has been carried out to identify the visco-rotational instability at nonlinear amplitudes. It seems that instability growth saturates at nonlinear amplitudes leading to a quasi-stationary self-sustained anticyclonic vortices in Keplerian flows. We have shown that hydrodynamic theory can be successfully applied to the investigation of the dense granular flows under central gravity. Found visco-rotational instability can play a crucial role in the dynamics of dense planetary rings and granular flows in protoplanetary disks.