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.
In the dynamic model αΩ-dimensions are simulated reversions of the magnetic field with a varying intensity of the α-generator. The change of the α-generator intensity as a result of synchronization of higher modes of the velocity field and the magnetic field is regulated by a function Z(t) with a power kernel. Dynamo modes are obtained for two types of radial component in the scalar parameterization of the α-effect. The results were analyzed depending on the change in the exponent of the kernel of the function Z(t) and the type of the power kernel, also a comparative analysis with the results of the study [9], where the exponential kernel of the function Z(t) was used.
In the dynamic model aΩ-dynamo the change in the intensity of the a-generator under the action of external forces is considered as a result of synchroniza-tion of higher modes of the velocity field and the magnetic field and is regulated by the function Z(t) with an exponential-power kernel J(t). Depending on the choice of the exponent and the scale factor of the kernel determine its temporal characteristics: delay time and waiting time. The question of changing the modes of magnetic field generation depending on the temporal characteristics of the function’s kernel is investigating. In the dynamic model aΩ-dynamo the change of the a-generator intensity under the action of external forces is considered as a result of synchronization of higher modes of the velocity field and the magnetic field and is regulated by the function Z(t) with an exponential-power kernel J(t). Depending on the choice of the exponent and the scale factor of the kernel J(t) determine its temporal characteristics: delay time and waiting time. The question of changing the modes of magnetic field generation depending on the temporal characteristics of the function’s kernel is investigating.
The low-mode model αΩ-dynamo is used in this paper to simulate the modes of magnetic field generation with insignificant changes in the velocity field of a viscous fluid. In the framework of those model the α-effect intensity is regulated by the process that is included in the magnetohydrodynamic system (MHD-system) as an additive correction as a functional Z(t) depended on the magnetic field energy. Function that determines damped oscillations with variable damping frequency and constant damping coefficient, taken equal to one, is selected as kernel J(t) of functional Z(t). The research of the behavior of the magnetic field is carried out on large time scales, therefore, a rescaled and dimensionless MHD-system with the unit of time iquel the time of the magnetic field dissipation (104 years) for numerical calculations is used. The control parameters of the system are the Reynolds number and the amplitude of the α-effect, that include information about the large-scale and turbulent generators, respectively. Numerical simulation of the magnetic field generation modes was carried out for the values of the damping coefficient b = 1 and frequency a = 0.1, 0.5, 1, 5, 10. According to the results of numerical simulation, an increase in the values of the damping frequency, when the damping coefficient is equal to one, is characterized by a decrease in the inhibitory effect of the process Z(t) on the α-effect and an increase in the region of divergence of the magnetic field on the phase plane of the control parameters. In a comparative analysis with the results of the authors’ work, where the change of the α-effect intensity was determined by the function Z(t) with an exponential kernel and the same value of the damping coefficient, the following differences were noted: an increase in oscillations in both a magnetic and a velocity fields, the appearance of a chaotic regime of magnetic field generation at the value of the damping frequency equal to one, and also insignificant narrowing of the region of α-effect suppression at values of the damping frequency increasing to one.
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