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Alex Lazarian Collaboration: Andrey Beresnyak

Imbalanced MHD Turbulence. Alex Lazarian Collaboration: Andrey Beresnyak Astronomy Department, University of Wisconsin-Madison and Center for Magnetic Self-Organization (CMSO). Based on Beresnyak & Lazarian 2008, ApJ, 682, 1070 Beresnyak & Lazarian 2009, ApJ, 701, 000.

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Alex Lazarian Collaboration: Andrey Beresnyak

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  1. Imbalanced MHD Turbulence Alex Lazarian Collaboration: Andrey Beresnyak Astronomy Department, University of Wisconsin-Madison and Center for Magnetic Self-Organization (CMSO) Based on Beresnyak & Lazarian 2008, ApJ, 682, 1070 Beresnyak & Lazarian 2009, ApJ, 701, 000

  2. Our model includes weak cascading for strong wave and strong cascading for weak wave. It is difficult for weak wave to strongly cascade strong wave

  3. B w- w+ We use Elsasser variables

  4. “Propagation balance” substitutes GS95 “critical balance” for imbalanced turbulence Anisotropic eddy GS95 critical balance: B Shearing rate = ~1 Propagation rate For the case of turbulence with more energy moving in one direction (imbalanced MHD turbulence) Beresnyak & Lazarian 08 proposed field wandering “propagation balance”. For balanced turbulence the angle of field wondering at perpendicular scale parallel scale corresponding to perpendicular scale is which coincides with GS95 critical balance.

  5. Application of the “propagation balance” allows to find the longitudinal scale of the strong wave Strong wave with perpendicular scale induces strong cascading of the weak wave at the scale . Weak wave cascades strong weakly and the cascading involves interactions of the waves with the same parallel scale, as this is the feature of weak turbulence. The rms angle of emerging eddies is . Thus Strong wave cascades from to

  6. A model of strong imbalanced turbulence includes “balances” and rates of cascading Old critical balance New “propagation balance” ; energy shear rate Strong cascading of weak wave Weak cascading of strong wave weakening factor Asymptotic power-law solutions:

  7. Numerical simulations show difference in anisotropies dominant subdominant W+ W-

  8. Numerical data roughly agrees with our model   different anisotropies!

  9. Our simulations require long times to achieve the steady state

  10. Energy spectra of w's 1 10 1 10 100 100 wavevector

  11. Energy spectra of w's 1 10 1 10 100 100 wavevector

  12. Imbalanced turbulence

  13. Our model correctly reproduce the following features of simulations: 1. the anisotropies are different and the strong wave anisotropy is smaller; 2. subdominant wave eddies are aligned with respect to the local field, while dominant wave eddies are aligned with respect to larger-scale field; 3. the energy imbalance is higher than in the case when both waves are cascaded strongly, which suggests that dominant wave is cascaded weakly 4. the inertial range of the dominant wave is shorter 5. there is no “pinning” on dissipation scale, which suggest nonlocal cascading

  14. Models with local cascading disagree with simulations

  15. balanced B0=1 B0=10

  16. Imbalanced cascade is different from GS cascade

  17. Anisotropy calculated from SF's (mapping) Balanced turbulence

  18. w- w+ w- w+ Coexisting of weak and strong cascading is not trivial GS95 model assumes for strong turbulence which parallel scale  is determined by uncertainty relation between cascading timescale and wave frequency: cas~1, i.e. ~vA/w. For weak interaction ~const with cascading (and only waves with equalinteract). Thus for strong wave~const, but for weak waveis decreasing, cascade stops. Is stationary imbalanced turbulence possible?

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