Mean field electrodynamics (MFE) facilitates practical modeling of secular, large scale properties of magnetohydrodynamic or plasma systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (1) what are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (2) how precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a contribution from the difference in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can identify an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.
H. Zhou, E. Blackman and L. Chamandy
Thu, 12 Oct 17
Comments: 27 pages, 7 figures. Submitted to Journal of Plasma Physics