Chaotic behaviour in low-order models of planetary and stellar dynamos

Abstract

The behaviour of the geodynamo and the solar cycle can be modelled by low-order systems of coupled nonlinear differential equations. The Earth's magnetic field reverses aperiodically, and similar behaviour is exhibited by disc dynamos that are described by the Lorenz equations. Chaotic behaviour is also a characteristic feature of coupled disc dynamos. In stars like the Sun, magnetic activity varies cyclically, with regular reversals of magnetic fields, but the cyclic activity is modulated on longer timescales. This behaviour can be described by normal form equations that account for symmetry-breaking as well as for variations in amplitude. The Von Ka´rma´n Sodium (VKS) experiment has successfully demonstrated magnetic reversals in the laboratory, and these results can be represented by evolution equations also.

Bistability and chaos in the Taylor-Green dynamo

“…[17]. Dynamo transition and subsequent dynamo states have also been studied using low-dimensional models of dynamo [18].…”

Convective dynamo action in a spherical shell: symmetries and modulation

“…The precise modulational effects important in the system are sometimes model-dependent. For this reason, progress can also be made by considering low-order systems based on symmetry considerations (Knobloch & Landsberg 1996;Knobloch et al 1998;Weiss 2011). These models demonstrate that the dynamics found in the ad hoc mean-field models is robust and may be expected in simulations of the full three-dimensional dynamo system.…”

Supercriticality to subcriticality in dynamo transitions

“…Krstulovic et al [8] also briefly discused a model containing two nonlinear equations to explain the Pm dependence of the supercritical and subcritical dynamo transitions. Weiss [26] provides a detailed review of the important low-order dynamo models which have been used to understand planetary and solar dynamos.…”