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

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.

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“…1). Substituting in the system (6) decompositions 7, (8) and the function (9). After applying the Galerkin method, we get the system…”

Section: The Numerical Simulationmentioning

confidence: 99%

Temporal regularities of changing magnetic field generation modes in the model of the αΩ-dynamo

Sheremetyeva

Godomskaya²

2020

E3S Web Conf.

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Modelling the Magnetic Field Generation Modes in the Low-Mode Model of the αΩ-Dynamo with Varying Intensity of the α-Effect

Sheremetyeva¹,

Godomskaya²

2021

Bulletin SUSU MMP

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Modes of magnetic field generation in the low-mode αΩ-dynamo model with dynamic regulation of the α-effect by the field energy

Sheremetyeva¹

2021

Вестник КРАУНЦ. Физико-Математические Науки

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В работе используется маломодовая модель αΩ-динамо для моделирования режимов генерации магнитного поля при незначительных изменениях поля скорости вязкой жидкости. В рамках этой модели интенсивность α-эффекта регулируется процессом с памятью, который вводится в магнитогидродинамическую систему (МГД-система) как аддитивная поправка в виде функционала Z(t) от энергии поля. В качестве ядра J(t) функционала Z(t) выбрана функция, определяющая затухающие колебания с варьируемым коэффициентом затухания и постоянной частотой затухания, принятой равной единице. Исследование поведения магнитного поля проводится на больших временных масштабах, поэтому для численных расчётов используется перемасштабированная и обезразмеренная МГД-система, где в качестве единицы времени принято время диссипации магнитного поля (104 лет). Управляющими параметрами системы выступают число Рейнольдса и амплитуда α-эффекта, в которых заложена информация о крупномасштабном и турбулентном генераторах. Результаты численного моделирования режимов генерации магнитного поля при различных значениях коэффициента затухания и постоянной частоте затухания отражены на фазовой плоскости управляющих параметров. В работе исследуется вопрос о динамике изменения картины на фазовой плоскости в зависимости от значения коэффициента затухания. Проводится сравнение с результатами, полученными ранее при постоянной интенсивности α-эффекта и при изменении интенсивности α — эффекта, которое определялось функционалом Z(t) с показательным ядром и аналогичными значениями коэффициента затухания. In this paper, we use a low-mode αΩ-dynamo model to simulate the modes of magnetic field generation with insignificant changes in the velocity field of a viscous fluid. Within the framework of this model, an additive correction is introduced into the magnetohydrodynamic system to control the intensity of the α-effect in the form of a function Z(t) from the field energy. As the kernel J(t) of the function Z(t) is chosen the function that determines damped oscillations with the different values of the damping coefficient and a constant damping frequency taken equal to one. The study of the magnetic field behavior is carried out on a large time scales, therefore, for numerical calculations, a rescaled and dimensionless MHD-system is used, where the time of the magnetic field dissipation (104 years) is accepted as the unit of time. The main parameters of the system are the Reynolds number and the amplitude of the α-effect, which contains information about the large-scale and turbulent generators, respectively. According to the results of numerical simulation, an increase in the values of the damping coefficient is characterized an increase in the inhibition effect of the process Z(t) on the α-effect and decrease of the magnetic field divergence region on the plane of the main parameters.

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

Cited by 3 publications

References 4 publications

Temporal regularities of changing magnetic field generation modes in the model of the αΩ-dynamo

Temporal regularities of changing magnetic field generation modes in the model of the αΩ-dynamo

Modelling the Magnetic Field Generation Modes in the Low-Mode Model of the αΩ-Dynamo with Varying Intensity of the α-Effect

Modes of magnetic field generation in the low-mode αΩ-dynamo model with dynamic regulation of the α-effect by the field energy

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