Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics
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**Session 2 -- Software**
*Display presentation, Monday, June 12, 1995, 9:20am - 6:30pm*

## [2.09] Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics

*J. Zsarg\'o and K. Petrovay (ELTE, Univ. of Toledo)*

It is widely known that a sufficient condition for the
applicability of quasilinear-type approximations (e.g.\ the second-order
correlation approximation or SOCA) in mean-field electrodynamics
is that $U\tau\ll \mbox{min}
\,\{l, H\}$ where $l$, $H$, $U$ and $\tau$ are
characteristic horizontal and vertical scale lengths, velocity, and time,
respectively. A necessary condition for their validity is however not known.
In order to check the validity of the quasilinear results in cases where the
above condition is not satisfied, as well as to study qualitative and
quantitative differences between the quasilinear results and the actual
solutions, we numerically solve the MHD induction equation for the kinematical
case in a series of simplified ``toy'' model flows and then compare the results
with the corresponding quasilinear solutions. Our model flows are
two-dimensional two-component flows with simple (exponential or linear)
stratifications. For conceptual clarity, in each model only one independent
physical quantity (initial magnetic field, density, or velocity amplitude,
respectively) has an inhomogeneous distribution. Solutions are computed for
several widely differing values of the $l/H$ horizontal/vertical scale length
ratio. In all cases we find that the computed turbulent electromotive force
does not differ from the quasilinear value by more than an order-of-unity
factor, as long as $U\tau$ does not greatly exceed $\mbox{min}
\,\{l, H\}$.

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