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"Stellar magnetism"

International Conference Proceedings,

1992 , 11-29 .

TH E CALCULATIO N O F TH E TURBULEN T DIFFUSIVITIE S O F MAGNETI C FIELD S AN D PARTICLE S USIN G TH E NON-LINEA R EQUATION S FO R TH E GREE N FUNCTIO N

N . A . SILANT'E V Centra l Astronomica l Observator y o f the Russia n AS , Pulkovo , 196140 , St. - Petersburg , Russi a

ABSTRACT .

The hierarchy is derived of non-linear equations for the averaged the process of in the transport at ion of an admixturbulent medium. For non-

Green function which describes ture magnetic field and

particles

compressible medium the simplest non-linearity which

non-linear equation with the

the second order

can be easily solved numerically by

iterative procedure solu-

is analogous to chain fraction iterations.

The exact numerical

tions of this equation and also for calculating

the approximate analytic formulae are used types of turbulence E (p) ~ p -5/3

turbulent diffusivities for some E (p) is

the and

spectrum of turbulence E (p) ~ (p p ).
0

of Kolmogoroff's type

It is shown that this method allows us to calculate the values of the paramelife-

turbulent diffusivities with a good accuracy for all ter --

/R ,
0

where

-

,

-

and R are the characteristic velocity,
0

time and spatial scale of the turbulent pulsations of basic gas.