1 Forced – decaying Helical – nonhelical

2 Points of the talk Resistive effects during inverse transfer B-field does not care about irrotational part Magnetic helicity from 1-D data sets

3 (i)Small scale dynamo (i)Exponential growth (ii)Growth rate proportional to Rm1/2 (iii)Kazantsev spectrum

4 (ii) Large-scale dynamo Similar to SS dynamo at early times Inverse cascade/transfer behavior Resistively slow saturation (!)

5 (iii) Non-helical decay Fast decay at small scales Slight increase for small k and strong B

6 (iv) Helical decay Inverse cascade on large scales Christensson et al. (2001, PRE 64, ) Initial slope E~k 4

7 Revised helical decay law H not exactly constant Assume power law, not const H follows power law iff r=1/2; then M. Christensson, M. Hindmarsh, A. Brandenburg: 2005, AN 326, 393

8 Dynamos: small-scale vs large-scale B-scale larger than U-scale B-scale smaller than U-scale Wavenumber =1/scale energy injection scale

9 SS and LS dynamos

10 Small-scale vs large-scale dynamo

11 Inverse cascade

12 Resistive effects on inverse transfer

13 Application to phase transitions Forcing purely potential No vorticity production?

14 Gaussian expansion waves

15 No dynamo from potential flows No dynamo action in nearly potential flows (at least not fo far)

16 No vorticity either

17 Vorticity production if 2 W /u rms k f > 1 if Ma > 0

18 B field ignores irrotational part

19 Helicity from 1-D data sets Matthaeus et al. (1982) Measure correlation function In Fourier space, calculate magnetic energy and helicity spectra  Should be done with Ulysses data away from equatorial plane

20 Bi-helical fields from Ulysses Taylor hypothesis Broad k bins Southern latitude with opposite sign Small/large distances Positive H at large k Break point with distance to larger k

21 Conclusions Resistive effects during inverse transfer B-field does not care about irrotational part Magnetic helicity from 1-D data sets