Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics

Previous abstract Next abstract

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 $\mbox{min} \,\{l, H\}$.

Monday program listing