Moffatt-drift-driven large-scale dynamo due to a fluctuations with non-zero correlation times
Number of Authors: 1
2016 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 798, 696-716 p.Article in journal (Refereed) Published
We present a theory of large-scale dynamo action in a turbulent flow that has stochastic, zero-mean fluctuations of the a parameter. Particularly interesting is the possibility of the growth of the mean magnetic field due to Moffatt drift, which is expected to he finite in a statistically anisotropic turbulence. We extend the Kraichnan Moffatt model to explore effects of finite memory of a fluctuations, in a spirit similar to that of Sridhar & Singh (Mon. Not. R. Astron. Soc., vol. 445, 2014, pp. 3770-3787). Using the first-order smoothing approximation, we derive a linear integro-differential equation governing the dynamics of the large-scale magnetic field, which is non-perturbative in the alpha-correlation time tau(alpha), We recover earlier results in the exactly solvable white-noise limit where the Moffatt drift does not contribute to the dynamo growth/decay. To study finite-memory effects, we reduce the integro-differential equation to a partial differential equation by assuming that tau(alpha). be small but non-zero and the large-scale magnetic field is slowly varying. We derive the dispersion relation and provide an explicit expression for the growth rate as a function of four independent parameters. When tau(alpha) not equal 0, we find that: (i) in the absence of the Moffatt drift, but with finite Kraichnan diffusivity, only strong a fluctuations can enable alpha mean-field dynamo (this is qualitatively similar to the white-noise case); (ii) in the general case when also the Moffatt drift is non-zero, both weak and strong a fluctuations can lead to a large-scale dynamo; and (iii) there always exists a wavenumber (k) cutoff at sonic large k beyond which the growth rate turns negative, irrespective of weak or strong a fluctuations. Thus we show that a finite Moffatt drift can always facilitate large-scale dynamo action if sufficiently strong, even in the case of weak alpha fluctuations, and the maximum growth occurs at intermediate wavenumbers.
Place, publisher, year, edition, pages
2016. Vol. 798, 696-716 p.
dynamo theory, magnetohydrodynamics, turbulence theory
IdentifiersURN: urn:nbn:se:su:diva-131908DOI: 10.1017/jfm.2016.284ISI: 000377447400031OAI: oai:DiVA.org:su-131908DiVA: diva2:947222