Energy spectra of small scale dynamos with large Reynolds numbers

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Energy spectra of small scale dynamos with large
Reynolds numbers

• Nils Erland Leinebø Haugen
• NTNU, Trondheim
• Axel Brandenburg
• NORDITA, Copenhagen

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The simulations

• We use the Pencil-code
• http//www.nordita.dk/software/pencil-code/
• grid-based (sixth order finite difference)
• weakly compressible
• Force on wavenumbers between 1 and 2
• isotropic, nonhelical
• Periodic boundary conditions
• No imposed mean field
• Magnetic Prandtl number is unity
• Isothermal EOS

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Motivation

• Understand the physics of small scale dynamos
• Interstellar medium
• Hot inter galactic gas in galactic clusters?
• Sun?

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Equations
Momentum equation (isothermal, weakly
compressible, sound speed cs)
Continuity equation
Induction equation
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Helical vs. non-helical forcing
Non-helical
Helical
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Magnetic field vectors (Bgt3Brms)
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MHD spectra (Laplacian viscosity)
Haugen, Brandenburg Dobler, Phys. Rev. E, 70,
016308 (2004)
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DNS MHD energy spectra (10243)
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Viscosity
Fvisc n ?nu (comp. terms)
The ordinary method -n2 -n is constant
The hyper method -n6 -n is constant (but
small)
The Smagorinsky method -n2 -nnsmag(Csmagl)2(
2SS)1/2
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Pure hydrodynamical energy spectrum
Haugen Brandenburg, Phys. Rev. E, 70, 026405
(2004)
Kaneda et al. Phys. Fluids 15, L21 (2003)
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Ordinary vs. artificial viscosity in MHD
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MHD with artificial viscosity
Hyper viscosity (n6)
Smagorinsky
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Is this how the large Reynolds number spectra
would look like?