1. Energy spectra of small scale dynamos with large Reynolds numbers
Nils Erland Leinebø Haugen
NTNU, Trondheim
Axel Brandenburg
NORDITA, Copenhagen

2. The simulations We use the ’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

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

4. Equations Momentum equation Induction equation: Continuity equation:
(isothermal, weakly compressible, sound speed cs):
Induction equation:
Continuity equation:

5. Helical vs. non-helical forcing

6. Magnetic field vectors (|B|>3Brms)

7. MHD spectra (Laplacian viscosity)
Haugen, Brandenburg & Dobler, Phys. Rev. E, 70, (2004)
MHD spectra (Laplacian viscosity)

8. DNS MHD energy spectra (1024^3)

9. Fvisc = n nu (+comp. terms)
Viscosity
Fvisc = n nu (+comp. terms)
The ordinary method:
-n=2
-n is constant
The hyper method:
-n=6
-n is constant (but small)
The Smagorinsky method:
-n=2
-n=nsmag=(Csmagl)2(2S:S)1/2

10. Pure hydrodynamical energy spectrum
Haugen & Brandenburg, Phys. Rev. E, 70, (2004)
Kaneda et al. Phys. Fluids 15, L21 (2003)
Pure hydrodynamical energy spectrum

11. Ordinary vs. artificial viscosity in MHD

12. MHD with artificial viscosity
Hyper viscosity (n=6)
Smagorinsky

13. Is this how the large Reynolds number spectra would look like?