Mathematical Modeling of the Dynamics of a Rotating Layer of an Electrically Conducting Fluid with Magnetic Field Diffusion Effects

Peregudin, S. I.; Peregudina, Elena; Kholodova, S. E.

doi:10.1007/978-3-030-53521-6_41

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…In Refs. [96][97][98], large-scale nonlinear oscillations of an electrically conducting ideal fluid in a layer of variable depth were considered, taking into account magnetic, Archimedean and Coriolis forces and magnetic field diffusion. For the posed spatial problem, the assumption of a linear distribution of hydromagnetic pressure with a depth was acceptable.…”

Section: Vortex Motion Of Conducting Ideal Liquids In the Presence Of...mentioning

confidence: 99%

“…The study in Ref. [97] takes into account the diffusion of the magnetic field. For the posed spatial problem, the assumption of a linear distribution of hydromagnetic pressure with depth is acceptable.…”

Section: Vortex Motion Of Conducting Viscous Fluids In the Presence O...mentioning

confidence: 99%

“…The goal of Ref. [105] was to reduce a system of partial differential equations that simulates a disturbance in a layer of an ideal electrically conducting rotating fluid, taking into account the diffusion of a magnetic field, and limited by surfaces varying in space and time, taking into account inertial forces. For the equations obtained as a result of reduction, solutions were constructed that described the propagation of small amplitude waves in an infinitely horizontal layer and in a narrow, long channel.…”

Section: Vortex Motion Of Conducting Viscous Fluids In the Presence O...mentioning

confidence: 99%

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Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Gurchenkov,

Matveev

2024

Physics

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Since the middle of the 20th century, an understanding of the diversity of the natural magnetohydrodynamic phenomena surrounding us has begun to emerge. Magnetohydrodynamic nature manifests itself in such seemingly heterogeneous processes as the flow of water in the world’s oceans, the movements of Earth’s liquid core, the dynamics of the solar magnetosphere and galactic electromagnetic fields. Their close relationship and multifaceted influence on human life are becoming more and more clearly revealed. The study of these phenomena requires the development of theory both fundamental and analytical, unifying a wide range of phenomena, and specialized areas that describe specific processes. The theory of translational fluid motion is well developed, but for most natural phenomena, this condition leads to a rather limited model. The fluid motion in the cavity of a rotating body such that the Coriolis forces are significant has been studied much less. A distinctive feature of the problems under consideration is their significant nonlinearity, (i.e., the absence of a linear approximation that allows one to obtain nontrivial useful results). From this point of view, the studies presented here were selected. This review presents studies on the movements of ideal and viscous fluids without taking into account electromagnetic phenomena (non-conducting, non-magnetic fluid) and while taking them into account (conducting fluid). Much attention is payed to the macroscopic movements of sea water (conducting liquid) located in Earth’s magnetic field, which spawns electric currents and, as a result, an induced magnetic field. Exploring the processes of generating magnetic fields in the moving turbulent flows of conducting fluid in the frame of dynamic systems with distributed parameters allows better understanding of the origin of cosmic magnetic fields (those of planets, stars, and galaxies). Various approaches are presented for rotational and librational movements. In particular, an analytical solution of three-dimensional unsteady magnetohydrodynamic equations for problems in a plane-parallel configuration is presented.

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Section: Vortex Motion Of Conducting Ideal Liquids In the Presence Of...mentioning

confidence: 99%

Section: Vortex Motion Of Conducting Viscous Fluids In the Presence O...mentioning

confidence: 99%

Section: Vortex Motion Of Conducting Viscous Fluids In the Presence O...mentioning

confidence: 99%

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Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Gurchenkov,

Matveev

2024

Physics

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Numerical Simulation in Wave Dynamics Problems

Peregudin

Kholodova²

2023

Springer Geology

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Mathematical Modeling of Geophysical Processes in a Layer of Electrically Conductive Liquid of Variable Depth

2023

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Mathematical Modeling of the Dynamics of a Rotating Layer of an Electrically Conducting Fluid with Magnetic Field Diffusion Effects

Cited by 7 publications

References 18 publications

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Dynamics of Fluids in the Cavity of a Rotating Body: A Review of Analytical Solutions

Numerical Simulation in Wave Dynamics Problems

Mathematical Modeling of Geophysical Processes in a Layer of Electrically Conductive Liquid of Variable Depth

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