Dynamics of Axisymmetric Truncated Dynamo Models (original) (raw)

In-out intermittency in PDE and ODE models of axisymmetric mean-field dynamos

1998

Employing some recent results in dynamics of systems with invariant subspaces we find evidence in both truncated and full axisymmetric mean-field dynamo models of a recently discovered type of intermittency, referred to as in-out intermittency. This is a generalised form of on-off intermittency that can occur in systems that are not skew products. As far as we are aware this

Axisymmetric mean field dynamos with dynamic and algebraic alpha\alphaalpha--quenchings

1997

We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic alpha\alphaalpha--quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere models is

Axisymmetric mean eld dynamos with dynamic and algebraic -quenchings

1998

We study axisymmetric mean eld spherical and spherical shell dynamo models, with both dynamic and alge- braic -quenchings. Our results show that there are qualita- tive as well as quantitative differences and similarities between thesemodels.Regardingsimilarities,bothgroupsofmodelsex- hibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere modelsistheoccurrenceofchaoticbehaviourinthealgebraic- quenching models. For the spherical shell models with dynamic the main features include the possibility of multi-attractor regimeswithnalstatesensitivitywithrespecttosmallchanges in the magnitude of and the initial parity. We nd the effect of introducing a dynamic is likely to be complicated and depend on the region of the parameter space considered, rather than a uniform change towards simplicity or complexity.

The influence of geometry and topology on axisymmetric mean-field dynamos

1998

We study the changes in the dynamical behaviour of axisymmetric spherical mean-field dynamo models produced by changes in their geometry and topology, by considering a two parameter family of models, ranging from a full sphere to spherical shell, torus and disc-like configurations, within a unified framework. We find that the two parameter space of the family of models considered here separates into at least three different regions with distinct characteristics for the onset of dynamo action. In two of these regions, the most easily excited fields are oscillatory, in one case with dipolar symmetry, and in the other with quadrupolar, whereas in the third region the most easily excited field is steady and quadrupolar. In the nonlinear regime, we find that topological changes can alter significantly the dynamical behaviour, whilst modest changes in geometry can produce qualitative changes, particularly for thin disc-like configurations. This is of potential importance, since the exact shapes of astrophysical bodies, especially accretion discs and galaxies, are usually not precisely known.

Non-normal parameter blowout bifurcation: An example in a truncated mean-field dynamo model

Physical Review E, 1997

We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I intermittency and blowout bifurcations to transient on-off intermittency, involving laminar phases in the invariant submanifold. In particular, our model provides examples of blowout bifurcations that occur on varying a non-normal parameter; that is, the parameter varies the dynamics within the invariant subspace at the same time as the dynamics normal to it. As a consequence of this we find that the Lyapunov exponents do not vary smoothly and the blowout bifurcation occurs over a range of parameter values rather than a point in the parameter space. *

Intermittent Behaviour in Axisymmetric Mean-Field Dynamo Models in Spherical Shells

Monthly Notices of the Royal Astronomical Society, 1998

Axisymmetric mean eld dynamo models in spherical shells are shown to be capable of producing temporally intermittent behaviour. This is of potential importance since (i) it is, as far as we are aware, the rst time such a behaviour has been produced internally by a mean eld dynamo model in a spherical shell, without requiring any additional assumptions or truncations, and (ii) it may be characteristic of the type of behaviour observed in the long term record of the solar activity, such as Maunder minima. We also show that these types of behaviour persist when the functional form of the alpha quenching is altered and also occur over intervals of the shell thickness and the dynamo number.

Mean Field Dynamos with Algebraic and Dynamic a-Quenchings

Stud Geophys Geod, 1998

S u m m a r y : Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic a-quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples.

Crisis-induced intermittency in truncated mean field dynamos

Physical Review E, 1997

We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonstrate that this merging is accompanied by a crisis-induced intermittency. We also find a range of parameter values over which the system has a fractal parameter dependence for fixed initial conditions. This is the first time this type of intermittency has been observed in a dynamo model and it could be of potential importance in accounting for some forms of intermittency in the solar and stellar output.

Mean Field Dynamos with Algebraic and Dynamic alpha-Quenchings

1998

Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic alpha\alphaalpha--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic alpha\alphaalpha appears to be complicated and is affected by the region of parameter space examined.