High Reynolds Number Simulations of Circular and Magnetized Couette Flows in a Cylindrical Annulus

Event Sponsor: 
Mathematics and Computer Science Division Seminar
Start Date: 
Nov 12 2008 (All day)
Bldg: 221, Conference Room A216
Argonne National Laboratory
Aleks Obabko
Speaker(s) Title: 
University of Chicago

Turbulence is the most promising mechanism to explain the anomalous enhancement of angular momentum transport (AMT) in astrophysical accretion discs that power some of the most energetic phenomena in the universe. The presence of even weak magnetic fields can destabilize an otherwise (Rayleigh-) stable Keplerian disc leading to the development of the magneto-rotational instability (MRI) and to MRI driven turbulence. Inspired by the Princeton MRI liquid gallium experiment, we present numerical simulations of circular and magnetized Couette flow in axisymmetric and fully three-dimensional geometry of the cylindrical annulus. The incompressible Navier-Stokes and magneto-hydrodynamical equations are solved with the spectral element code Nek5000 incorporating realistic boundary conditions corresponding to differentially rotating rings. Our results** demonstrate a significant enhancement of AMT and its dependence on Reynolds number, horizontal boundary conditions and external magnetic field strength through the onset of unsteadiness and three-dimensionality. Finally, at high enough magnetic Reynolds number, the MRI driven turbulence becomes an efficient dynamo capable of sustaining the magnetic fields necessary to induce MRI in the first place. This implies that MRI-driven turbulence in a real disc is likely to be self-regulating and universal depending only on the properties of the disc itself.

Miscellaneous Information: 

In collaboration with Fausto Cattaneo (University of Chicago, Argonne National Lab) and Paul Fischer (ANL).

Acknowledge the support of NSF and use of the resources of Argonne Leadership Computing Facility and Division of Mathematics and Computer Science (ANL), of NERSC (Lawrence Berkeley National Lab, INCITE 2005), and of IBM Thomas J. Watson Research Center (Blue Gene/W)