Corrections to first order smoothing in mean-field electrodynamics
Abstract
We employ the method of ordered cumulants to calculate corrections to the first order smoothing approximations of the transport coefficients and appearing in the mean-field dynamo equation. Special results are derived for the case of stationary, isotropic Gaussian turbulence, and explicit formulae are given for (4) and (4), the terms arising when fourth order correlations are involved. The order of these terms, relative to the usual second order correlation terms, is S2, where S=uc/λc, is the Strouhal number. Two particular examples demonstrate that the corrections can dominate the original terms, and even change the sign of α and (or) β. The coefficient β(4) strongly depends on the helicity of the turbulent flow.
- Publication:
-
Geophysical and Astrophysical Fluid Dynamics
- Pub Date:
- 1988
- DOI:
- 10.1080/03091928808213623
- Bibcode:
- 1988GApFD..43..149N
- Keywords:
-
- Transport coefficients;
- helicity;
- homogeneous isotropic turbulence