G. Rudiger et Vv. Pipin, Viscosity-alpha and dynamo-alpha for magnetically driven compressible turbulence in Kepler disks, ASTRON ASTR, 362(2), 2000, pp. 756-761
For a given isotropic and homogeneous field of magnetic fluctuations both t
he viscosity-alpha as well as the dynamo-alpha have been computed for accre
tion disks on the basis of a quasilinear approximation with shear flow and
density fluctuations (i.e. magnetic buoyancy) included. The resulting visco
sity-alpha proves to be positive for sufficiently strong sheer (i.e. the an
gular momentum transport is outwards) while the sign of the dynamo-alpha de
pends on the hemisphere. Again, for sufficiently strong shear it changes it
s sign, it is no vv negative for the upper disk plane and positive for the
lower one.
The current helicity [j' . B'] also changes its si,on with increasing shear
. For a Kepler flow in the upper (lower) disk plane, the sign is positive (
negative). In our turbulence model the current helicity of the fluctuations
and the alpha -effect of dynamo theory are almost always out of phase: the
signs of all the quantities are in perfect correspondence to the numerical
simulations of Brandenburg (1998, 2000). The kinetic helicity has the same
sign as the alpha -effect - not, as often assumed, the opposite one.
The resulting ratio between the dynamo-alpha and the viscosity-alpha reveal
s the dynamo-alpha amplitude as rather small compared with the turbulence i
ntensity. This is in contrast to earlier results on the basis of a quantita
tive approximation but again is in agreement with recent results of numeric
al simulations.