1. Does hyperviscosity spoil the inertial range? A. Brandenburg, N. E. L. Haugen Phys. Rev. E astro-ph/0402281

2. Brandenburg: hyperviscosity2 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)

3. Brandenburg: hyperviscosity3 Simulations at 512 3 With hyperviscosity Normal viscosity Biskamp & Müller (2000)

4. Brandenburg: hyperviscosity4 3 rd order hyperviscosity Different resolution: bottleneck & inertial range Traceless rate of strain tensor 3 rd order dynamical hyperviscosity  3 Hyperviscous heat

5. Brandenburg: hyperviscosity5 Bottleneck in the hydro Kaneda et al. (2003) on the Earth simulator, 4096 3 meshpoints Dobler et al. (2003), 1024 3 meshpoints, PRE 68, 026304

6. Brandenburg: hyperviscosity6 Comparison: hyper vs normal onset of bottleneck at same position height of bottleneck increased

7. Brandenburg: hyperviscosity7 Decay run with hyperviscosity Correction now compatible with She-Leveque Decay rate just as in ordinary turbulence

8. Brandenburg: hyperviscosity8 Visualization

9. 9 Dynamo saturation with hyperdiffusivity for ordinary hyperdiffusion ratio 125 instead of 5

10. Brandenburg: hyperviscosity10 Conclusions Hyperviscosity allows for a reasonable guess of what one might see a decade later using direct simulation