Reversals of the Magnetic Field in one low-dimensionalαΩ-dynamo model

Abstract

Abstract. Described low-dimensional model, that implements the various known regimes of cosmic dynamo systems, in particular, the various regimes of reversals. The source of regular reversals in the model is its internal dynamics. Violation of this cyclicality, failures in the a dynamo, the occurrence regime irregularity reversals caused by chaotic fluctuations in the parameters. This fluctuations are interpreted as the result of spontaneous coherent addition of the higher modes. The simplicity of the model allows you to easily modify it for various celestial bodies.

Symbolic Computations in Simulations of Hydromagnetic Dynamo

“…It was implemented by the authors in the Maple12 package and was successfully used to develop and study some models of geodynamo, for example [8][9][10][11]. The technology allows them to automate the routine operations for calculating the coefficients of Galerkin approximations in hydrodynamic problems and significantly increases the reliability and speed of computations.…”

“…Then, we need to determine the specific type of basis modes. For example, if the modes of free dissipation are used for them, then all radial functions do not depend on index m, and are some linear combinations of power functions and spherical Bessel functions [8]. Expressions for such functions are also easily obtained from known recurrence relations [7].…”

Modes of magnetic field generation in models of a αΩ-dynamo with a power type α-generator

“…The authors, using the large-scale dynamo model developed by [1] for several years, have been investigating the possibility of the occurrence of inversions in a magnetic field provided that the velocity field is constant. In the study [2] used the small-mode approximation, which includes the minimum number of modes for which dynamo can work, namely, one hydrodynamic and two magnetic poloidal B 1 (t) and toroidal B 2 (t). As a result of the computational experiment for the model were obtained inversions both in a magnetic field and in a viscous fluid velocity field, and there are not only cases of field attenuation, but also their undamped mutual generation.…”

“…The next stage of the work was the study of the system, into which α− and Ω−generators were algebraically introduced, that are responsible for the turbulent and laminar components of the velocity field of the magnetohydrodynamic system (MHD-system) [3]. The numerical calculations showed that inversions in a magnetic field occur, however, both the velocity field and the magnetic field decay quickly, and the periods of oscillations in the fields under consideration are almost identical.…”

“…The numerical calculations showed that inversions in a magnetic field occur, however, both the velocity field and the magnetic field decay quickly, and the periods of oscillations in the fields under consideration are almost identical. In the time subsequent work, fluctuations were introduced, which made it possible to understand their influence on the nature of inversions [4,5]. As a result the following modes of dynamo were obtained: quasi-periodic with reversed fault and with missing reversed fault, the magnetic field with damped and without oscillations.…”