Does hyperviscosity spoil the inertial range

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Does hyperviscosity spoilthe inertial range?

• A. Brandenburg, N. E. L. Haugen

Phys. Rev. E astro-ph/0402281
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Hydromagnetic turbulence and subgrid scale models?

• Want to shorten diffusive subrange
• Waste of resources
• Want to prolong inertial range
• Focus of essential physics
• Reasons to be worried about hyperviscosity
• Shallower spectra
• Wrong amplitudes of resulting large scale fields
  (Brandenburg Sarson 2002, PRL 88, 055003)

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Simulations at 5123
Biskamp Müller (2000)
Normal viscosity
With hyperviscosity
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3rd order hyperviscosity
Different resolution bottleneck inertial range
Traceless rate of strain tensor
Hyperviscous heat
3rd order dynamical hyperviscosity m3
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Bottleneck in the hydro
Kaneda et al. (2003) on the Earth simulator,
40963 meshpoints
Dobler et al. (2003), 10243 meshpoints, PRE 68,
026304
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Comparison hyper vs normal
height of bottleneck increased
onset of bottleneck at same position
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Decay run with hyperviscosity
Decay rate just as in ordinary turbulence
Correction now compatible with She-Leveque
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Visualization
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Dynamo saturation with hyperdiffusivity
for ordinary hyperdiffusion
ratio 125 instead of 5
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Conclusions

• Hyperviscosity allows for a reasonable guess of
  what one might see a decade later using direct
  simulation