Steady-Flow Dynamos

Abstract

AbstractIn this chapter we study large-scale magnetic modes generated by short-scale steady space-periodic parity-invariant flows of conducting fluid. We construct complete asymptotic expansions of the modes and their growth rates in power series in the scale ratio, and derive a closed set of equations for their leading terms. Computations show that a significant part of such flows can generate magnetic field by the mechanism of negative magnetic eddy diffusivity for magnetic Reynolds numbers below the critical value R m c for the onset of generation of the short-scale magnetic field. We present examples of flows exhibiting an anomalously large (in absolute value) negative magnetic eddy diffusivity and demonstrate that this phenomenon occurs when the magnetic Reynolds number is close to R m c.Finally, we show by direct simulations that even a modest scale separation, with the large scale twice larger than the small one, is beneficial for magnetic field generation (the concept of eddy diffusion is not yet applicable in this case—such a weak scale separation is outside the region of asymptotic behaviour of magnetic modes).KeywordsInvariant SubspaceMagnetic ModeSlow VariableAuxiliary ProblemMagnetic Reynolds NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.