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Advancements in Turbulence Research at Nordita

Explore the latest research at Nordita, focusing on turbulence studies, bottleneck effects, and magnetic fields. Learn about the innovative Pencil Code software, its features, and applications in various fields. Discover the implications of passive scalar diffusion in turbulence simulations.

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Advancements in Turbulence Research at Nordita

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  1. Turbulence research at Nordita • Bottleneck effect • Magnetic fields (active vector) • Passive scalar diffusion Haugen & Brandenburg (2006, Phys. Fl. 18, 075106) Brandenburg & Subramanian (2005, Phys. Rep., 417, 1) Brandenburg (2001, ApJ 550, 824; and 2005, ApJ 625, 539) Brandenburg et al. (2004, Phys. Fl. 16, 1020)

  2. Nordita in Stockholm Nordita in Stockholm

  3. Nordita in Stockholm • ~6 new post-docs Nordic+non-Nordic • ~2-3 new assist. profs • ~5 programs/year • visiting professors (1/2-2yr) • Nordita-days next August

  4. Pencil Code • Started in Sept. 2001 with Wolfgang Dobler • High order (6th order in space, 3rd order in time) • Cache & memory efficient • MPI, can run PacxMPI (across countries!) • Maintained/developed by ~25 people (CVS!) • Automatic validation (over night or any time) • Max resolution so far 10243 , 256 procs • Isotropic turbulence • MHD, passive scl, CR • Stratified layers • Convection, radiation • Shearing box • MRI, dust, interstellar • Sphere embedded in box • Fully convective stars • geodynamo • Other applications • Homochirality • Spherical coordinates

  5. (i) Higher order – less viscosity

  6. (ii) High-order temporal schemes Main advantage: low amplitude errors 2N-RK3 scheme (Williamson 1980) 2nd order 3rd order 1st order

  7. Cartesian box MHD equations Magn. Vector potential Induction Equation: Momentum and Continuity eqns Viscous force forcing function (eigenfunction of curl)

  8. Wallclock time versus processor # nearly linear Scaling 100 Mb/s shows limitations 1 - 10 Gb/s no limitation

  9. Wallclock time versus processor # nearly linear Scaling 100 Mb/s shows limitations 1 - 10 Gb/s no limitation

  10. Pre-processed data for animations

  11. 1. Bottleneck: surprise at higher res.

  12. Bottleneck effect in hydro at 10243 (Porter, Pouquet,& Woodward 1998)

  13. She-Jackson spectra

  14. Bottleneck effect: 1D vs 3D spectra

  15. Relation to ‘laboratory’ 1D spectra Parseval used:

  16. Longitudinal spectra

  17. Hyperviscous, Smagorinsky, normal height of bottleneck increased with hyper Haugen & Brandenburg (Phys. Fluids, astro-ph/041266) onset of bottleneck at same position CS=0.20 Inertial range unaffected by artificial diffusion

  18. Hyperdiffusion bottleneck Biskamp & Müller (2000)

  19. Structure function exponents agrees with She-Leveque third moment

  20. 2. Allow for B: small scale dynamo action non-helically forced turbulence PrM=n/h=1 PrM=n/h=50

  21. Looks like k-3/2 at 10243 Spectra not on top of each other??  Different from case with imposed field! Still not large enough?!

  22. Integral quantities converged “Only” 30% of energy is magnetic But 70% of dissipation is Ohmic!

  23. Maybe no small scale “surface” dynamo? Small PrM=n/h: stars and discs around NSs and YSOs Schekochihin Haugen Brandenburg et al (2005) k Here: non-helically forced turbulence When should we think of extrapolating to the sun? Implications for global models (w/strong SS field)

  24. Scale separation: inverse cascade Position of the peak compatible with Decomposition in terms of Chandrasekhar-Kendall-Waleffe functions No inverse cascade in kinematic regime LS field: force-free Beltrami

  25. 3. Passive scalar diffusion

  26. System of mean field equations mean concentration flux equation Damped wave equation, wave speed (causality!)

  27. MTA - the minimal tau approximation (remains to be justified!) 1) replace triple correlation by quadradatic 2) keep triple correlation 3) instead of now: 4) instead of diffusion eqn: damped wave equation i) any support for this proposal?? ii) what is tau??

  28. Wave equation: consequences • late time behavior unaffected (ordinary diffusion) • early times: ballistic advection (superdiffusive) Illustration of wave-like behavior: small tau intermediate tau large tau >>1 (!)

  29. Test 1: finite initial flux experiment but with Initial state: black: closure model red: turbulence sim. kf/k1St=tukf 1.5 1.8 5.1 2.4 Dispersion Relation: Oscillatory for k1/kf<3  direct evidence for oscillatory behavior!

  30. Test 2: imposed mean C gradient Convergence to St=3 for different Re >>1 (!)

  31. Conclusions • Turbulence increasingly important in astrophysics • Bottleneck: asymptotically unimportant • In practice: simulations not asymptotic: • hence important • Dynamo action: details affected by bottleneck 1046 Mx2/cycle

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