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cattaneo@flash.uchicago

MRI Driven turbulence and dynamo action. Fausto Cattaneo University of Chicago Argonne National Laboratory. cattaneo@flash.uchicago.edu. MRI in cylindrical annulus. Incompressible fluid Finite viscosity and magnetic diffusivity Periodic in the vertical. P m = 0.5

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cattaneo@flash.uchicago

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  1. MRI Driven turbulence and dynamo action Fausto Cattaneo University of Chicago Argonne National Laboratory cattaneo@flash.uchicago.edu ITP 2008

  2. MRI in cylindrical annulus • Incompressible fluid • Finite viscosity and magnetic diffusivity • Periodic in the vertical • Pm = 0.5 • Not a dynamo at Re=6,000 • Probably a dynamo at Re=60,000 inner cylinder velocity Simulations by Obabko, Fischer, FC ITP 2008

  3. What happens if Pm 0? Two issues: • Dynamo action becomes impossible. Turbulence decays. No enhanced transport • Dynamo action remain possible but amplitude of fluctuations decreases with decreasing Pm. Asymptotically enhanced transport becomes ineffective ITP 2008

  4. Dynamo action at small Pm Two possibilities: • There exist a critical value of Pm below which dynamo action is impossible for any Re • Dynamo action is always possible: • Asymptotically Rmcrit independent of Pm (σ=1) • Asymptotically Rmcrit increases with decreasing Pm Turbulence ITP 2008

  5. Small Pm regime Assume Re>>1. • Dynamo action driven by strongly fluctuating velocity. • Introduce roughness exponent  •  <1  rough velocity ( =1/3 corresponds to K41) • Related to energy spectrum: E(k)k-p  p=1+2 • At small scales ( O() ) action of viscosity is to smooth out velocity ITP 2008

  6. Structure functions • Shearing box simulation • Isothermal EOS • Finite vertical flux • Simulations using PLUTO • No explicit dissipation inertial Simulations by Bodo, Mignone, FC ITP 2008

  7. Kazantsev model From Boldyrev & FC Resolution parameter dynamo No dynamo increasing roughness ITP 2008

  8. What do we need? • Asymptotic regime is reached when η 50 x • If =1/3 dynamo action requires 30 η 1500 x ( 2 for periodic systems) • Requirement to reach asymptotic regime with =1/3 ν/η 0.1  Pm 0.14/3  0.046 ITP 2008

  9. Amplitude effects Effective transport ( - BBr ) depends on: • Correlations • Amplitude of fluctuating quantities (mostly B) For a flux rope in equilibrium with an axi-symmetric stagnation point flow, peak field satisfies (Galloway, Proctor & Weiss) Valid for Pm >>1 ITP 2008

  10. What happens if Pm < 1? Magneto-convection B-field (vertical) vorticity (vertical) Pm = 8.0 cold g hot Simulations by Emonet & FC Pm = 0.125 ITP 2008

  11. From magneto-convection ITP 2008

  12. Conclusion • Present simulations not suitable to inform us on small Pm regime • At present there is no result, theoretical or numerical indicating that dynamo action becomes impossible at small Pm • Results for Pm > 1 not representative of Pm <<1 • Informative simulations are possible, but very demanding ITP 2008

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