Hereditary Oscillator Associated with the Model of a Large-Scale αω-Dynamo

Gleb Vodinchar

doi:10.3390/math8112065

Abstract

Cosmic magnetic fields possess complex time dynamics. They are characterized by abrupt polarity changes (reversals), fluctuations of fixed polarity, bursts and attenuations. These dynamic conditions can replace each other, including both regular and chaotic components. Memory in dynamo systems manifests itself in a feedback mechanism when a strong magnetic field begins to change the properties of turbulent flows. A hereditary oscillator can be the simplest model of such complex oscillatory systems with memory. The article suggests the construction of such oscillator by means of two-mode approximation of magnetic field components in the αω-dynamo model. The hereditary member describes the suppression of a field turbulent generator by magnetic helicity and determines the shape of oscillator potential. The article describes the implicit difference scheme for numerical research of oscillator. It also describes the results of numerical simulation for two cases—instantaneous feedback and delay in feedback. The results of simulation are interpreted in terms of oscillator theory. It is shown that the observed dynamic regimes in the model go well with the change of potential shape.

Highlights

The existence of large-scale magnetic fields of planets, stars and galaxies is usually associated with the action of hydromagnetic dynamo [1]
The productivity of modern computing systems does not allow for the conduction of the direct numerical simulation of the three-dimensional tasks of planetary and stellar dynamo on the time scales of celestial bodies existence
Let us look at some results of numerical simulation of the oscillator (14)

Summary

Introduction

The existence of large-scale magnetic fields of planets, stars and galaxies is usually associated with the action of hydromagnetic dynamo [1]. The productivity of modern computing systems does not allow for the conduction of the direct numerical simulation of the three-dimensional tasks of planetary and stellar dynamo on the time scales of celestial bodies existence In this respect, the numerical models either reproduce convective movements and magnetic fields on fairly shallow spatial grid on small time scales (∼105 years) or allow for the calculation of a long evolution (∼109 years) of only large-scale spatial structures. The equations of magnetic hydrodynamics are symmetrical in relation to the change of magnetic field sign This makes the existence of reversals possible—rapid shifts in magnetic field polarity without convection structure restructuring. These reversals are observed in real cosmic dynamo systems [7,8]. The work bears purely theoretical character and does not involve the comparison of model dynamic regimes with the real regimes of stars or planets dynamo

Hereditary Two-Modes αω-Dynamo Model

Hereditary Oscillator

Difference Scheme and Software for Numeric Simulation

Simulation Results

Discussion