Moffatt-drift-driven large-scale dynamo due to a fluctuations with non-zero correlation times

• 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.

Subject headings

NATURVETENSKAP  -- Fysik -- Fusion, plasma och rymdfysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Fusion, Plasma and Space Physics (hsv//eng)

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

dynamo theory

magnetohydrodynamics

turbulence theory

Publication and Content Type

ref (subject category)

art (subject category)