Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer

Abstract

We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the α-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer of incompressible electrically conducting fluid that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in the expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetries of the perturbed state are now missing. Numerical results for the amplitude equations show that a large-scale perturbation, periodic in slow horizontal variable, either converges to a small-scale neutral stability mode with amplitudes tending to constant values, or it blows up at a finite slow time.