Turbulent Transport of Magnetic Fields - Part Two - the Role of Fluctuations in Kinematic Theory

Details Turbulent Transport of Magnetic Fields - Part Two - the Role of Fluctuations in Kinematic Theory Turbulent Transport of Magnetic Fields - Part Two - the Role of Fluctuations in Kinematic Theory

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...171..357h&link_type=abstract

Astronomy and Astrophysics, Vol.171, NO. 1/2/JANI, P. 357, 1987

Astronomy and Astrophysics

Astrophysics

39

Scientific paper

It is argued that due to fluctuations in the turbulent convection, the ensemble averaged field < B > of a dynamo must damp out to zero if , in particular < B2 >, is to remain finite. This idea is supported by two case studies: a simple α2 dynamo and the αΩ dynamo in the local approximation. Apart from the well-known constants α and β, the equation for < BB > contains the parameter γ ≡ < ∣ V × u1∣2 > τc/3, that also occurred in the model analysed the preceding paper. These results lead to a new statistical formulation of kinematic dynamo theory, which must eventually be extended to nonlinear theory. New aspects are: 1) Turbulent transport of B is a stochastic process and fluctuations have a large influence; 2) B in the dynamo fluctuates on all spatial scales and bears only a statistical relation to < B >; 3) The frequency stability δω/ω of αΩ dynamos and the average time between spontaneous reversals in α2 dynamos are determined by kinematic theory; for the solar dynamo δω/ω is estimated to be larger than observed, but nonlinear effects may cure this; 4) The average magnetic stress tensor (i. e. energy density, Lorentz force and field cross-correlation coefficients) as well as γ are determinable quantities (for the Sun γ ≍ 10-10 s-1); 5) In principle, helical turbulence (α ≠ 0) is not necessary for dynamo action; 6) The global resonances found by Stenflo and Vogel, and the appearance of coronal holes may correspond to stochastic excitations of overtones of the dynamo equation. The meaning of the ensemble average, the energy balance of the dynamo and the physics of turbulent mixing are discussed in detail. The limitations are: zero resistivity, and homogeneous, isotropic turbulence with a short correlation time.

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