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

Sheremetyeva, O.V.; Godomskaya, Anna

doi:10.14529/mmp210203

Cited by 5 publications

(12 citation statements)

References 7 publications

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“…This article generalizes research in one of the directions of the cycle of papers of the IKIR FEB RAS on the study of a low-mode model of Earth's dynamo [1][2][3][4][5][6][7][8]. Despite the progress made in geomagnetism theory, the problem of the origin of the Earth's magnetic field and that of space objects has not been fully resolved.…”

Section: Introductionmentioning

confidence: 92%

“…If the α-effect intensity α 0 is assumed to be constant, then the MHD-system admits three types of solutions [7] for a magnetic field in the range of changes of the control parameters, namely, damped (with or without oscillations), infinitely increasing (with or without oscillations) and steady oscillations. The intensity α 0 changes in time under the action of the Lorentz force.…”

Section: Statement Of a Problemmentioning

confidence: 99%

“…To investigate the nature of the magnetic field occurrence, its structure and possible changes, various approximate solutions of the geodynamo equations are used, because their exact solutions are unknown. The study is carried out using both direct number simulation [23,24], and based on simplified models [5,7,16]. Model studies of the MHDsystem behavior are limited by computational capabilities.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that a rescaled and dimensionless MHD-system is used in the paper. The timeline unit is equal to the damping time of the magnetic field [7].…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this study is to determine the values of the parameters in the model at which various dynamical regimes of the magnetic field can be obtained, including a chaotic regime on the background of the insignificantly varying velocity field, and to conduct a comparative analysis of the results of numerical simulation with previously obtained results at a constant intensity of the α-effect and using α-quenching with the kernel J(t) = e −bt [7].…”

Section: Introductionmentioning

confidence: 99%

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Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode αΩ-Dynamo Model with Hereditary α-Quenching by Field Energy

Sheremetyeva

2023

Mathematics

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The article considers a large-scale model of an αΩ-dynamo in the low-mode approximation. The intensity of the α-effect is regulated by a process that depends on the energy of the magnetic field and has hereditarity properties (finite “memory”). The regulation process is included in the MHD-system in the form of an additive correction. The action character of the process is defined by the alternating kernel with variable parameters: the damping frequency and the damping coefficient. The Reynolds number and the α-effect measure are the control parameters of the system. Information about the action of a large-scale generator is contained in the Reynolds number, and that about the action of a turbulent one is contained in the measure of the α-effect. The stability of the solution of the MHD-system is studied depending on the values of the control parameters and the parameters of the alternating kernel. Based on the results of numerical simulation of the dynamical regimes, limitations are determined for the values of the model parameters at which the regimes are reproduced against the background of small oscillations of the viscous liquid velocity field. The results of the study of the stability of solutions and numerical simulations of the dynamical regimes are represented on the phase plane of the control parameters. The paper investigates the question of changing the pattern on the phase plane depending on the values of the damping coefficient, the damping frequency, and the waiting time. A comparison is made with the results obtained earlier, when the α-effect intensity is a constant or is regulated by a process with an exponential kernel and the same values of the damping coefficient.

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Section: Introductionmentioning

confidence: 92%

Section: Statement Of a Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It should be noted that a rescaled and dimensionless MHD-system is used in the paper. The timeline unit is equal to the damping time of the magnetic field [7].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode αΩ-Dynamo Model with Hereditary α-Quenching by Field Energy

Sheremetyeva

2023

Mathematics

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Conditions for Generating a Chaotic Regime in a Low-Mode $$\alpha \Omega $$-Dynamo Model with Hereditary $$\alpha $$-Quenching by Field Energy

Sheremetyeva

2023

Springer Proceedings in Earth and Environmental Sciences

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

Cited by 5 publications

References 7 publications

Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode αΩ-Dynamo Model with Hereditary α-Quenching by Field Energy

Magnetic Field Dynamical Regimes in a Large-Scale Low-Mode αΩ-Dynamo Model with Hereditary α-Quenching by Field Energy

Conditions for Generating a Chaotic Regime in a Low-Mode $$\alpha \Omega $$-Dynamo Model with Hereditary $$\alpha $$-Quenching by Field Energy

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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