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obabko@uchicago

Simulation of Gallium experiment * §. Aleksandr Obabko Center for Magnetic-Self Organization Department of Astronomy and Astrophysics University of Chicago. obabko@uchicago.edu. * with Fausto Cattaneo (U of C) and Paul Fischer (ANL)

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obabko@uchicago

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  1. Simulation of Gallium experiment*§ Aleksandr Obabko Center for Magnetic-Self Organization Department of Astronomy and Astrophysics University of Chicago obabko@uchicago.edu *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) CMSO 2005

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

  3. Overview of Results • 2D & 3D hydro & MHD runs with vertical B.C. of periodicity, rings & lids • Re=620 … 6200, Pm=0.5 & Bz0=0 … 0.275 • Periodic: Stable Couette flow for Bz0→0 & Bz0→∞, 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 Bz0 • Rings setup is more suitable for study of MRI & angular momentum transport in laboratory CMSO 2005

  4. Couette flow Rings Lids Lids Rings 2D Steady Hydro Results for Re=620 Lids: Rings: • 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 CMSO 2005

  5. Couette flow 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 CMSO 2005

  6. 2D MHD: Re=6200, Rm=3100, B0=0.05, rings Couette flow Magnetic Total Hydro • 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 CMSO 2005

  7. 3D Results for Re=6200 Hydro with rings Periodic MHD, Bz0=0.05 2D 3D 2D 3D • Initial conditions: 2D flow solutions • Weak 3D dimensionality in hydro cases • Similar angular momentum transport • Smaller structures compared to 2D cases CMSO 2005

  8. 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 Bz0 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 (~106) 2D MHD Case Conclusion & Future Work CMSO 2005

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