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CMSO 2005 obabko@uchicago.edu Simulation of Gallium experiment * § Aleksandr Obabko Center for Magnetic-Self Organization Department of Astronomy and Astrophysics University of Chicago * with Fausto Cattaneo (U of C) and Paul Fischer (ANL) § used NERSC resources supported by the Office of Science of the US DOE under Contract No. DE-AC03-76SF00098 (INCITE 2005)

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CMSO 2005 Problem formulation Incompressible viscous resistive MHD equations in cylindrical geometry of MRI experiment at PPPL Boundary conditions: Solved numerically by MHD version of ANL spectral element code nek5000

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CMSO 2005 Overview of Results Periodic: Stable Couette flow for Bz 0 0 & Bz 0, otherwise, MRI (for Rm>100…300) Rings diminish Ekman circulation (and torque) as compared to cases with lids & exhibit similar growth of torque with increase of Bz 0 Rings setup is more suitable for study of MRI & angular momentum transport in laboratory 2D & 3D hydro & MHD runs with vertical B.C. of periodicity, rings & lids Re=620 … 6200, Pm=0.5 & Bz 0 =0 … 0.275

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CMSO 2005 2D Steady Hydro Results for Re=620 Angular momentum transport outward both by outward radial flow of high angular momentum and by inward radial flow of low angular momentum (like convection) Rings diminish Ekman circulation and hydro angular momentum transport restored Couette flow profile Lids:Rings: Couette flow Lids Rings Lids Rings

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CMSO 2005 2D Unsteady Results for Re=6200 with rings Smaller viscous boundary & shear layers Oscillating vertical jets Short radial jet outward at midplane of z=H/2 Couette flow

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CMSO 2005 2D MHD: Re=6200, Rm=3100, B 0 =0.05, rings The reversal of radial flow (toward the inner cylinder along the plane at z=H/2) Higher torques compared to hydro case Hydro angular momentum transport near boundaries, magnetic – near z=H/2 Couette flow Total Hydro Magnetic

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CMSO 2005 3D Results for Re=6200 Initial conditions: 2D flow solutions Weak 3D dimensionality in hydro cases Similar angular momentum transport Smaller structures compared to 2D cases 2D Hydro with rings 3D Periodic MHD, Bz 0 =0.05 2D3D

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CMSO 2005 Conclusion & Future Work Conducted 2D & 3D Hydro & 2D MHD computations with vertical B.C. of periodicity, rings & lids in geometrical setup of Princeton MRI experiment Observed diminished Ekman circulation and angular momentum transport in hydro cases with rings as compared to the cases with lids Found similar behavior of torque with increase of external axial magnetic field Bz 0 for 2D MHD cases with rings as compared to the periodic case with MRI Suitability of the ring setup for study of MRI and angular momentum transport in laboratory Angular momentum transport is reminiscent of transport of thermal energy in convection … Ongoing 3D MHD calculations … Plans for high-Re (~10 6 ) 2D MHD Case

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