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

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

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

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

5. ITP 2008 Small P m 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

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

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

8. ITP 2008 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  P m  0.1 4/3  0.046

9. ITP 2008 Amplitude effects Effective transport ( -  B  B r  ) 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 P m >>1

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

11. ITP 2008 From magneto-convection

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