Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region

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

doi:10.1134/s0965542510110114

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…Therefore, two-dimensional dynamics within the framework of Lagrangian equations has become a subject of special attention. Here, certain progress has been achieved in the analysis of relatively simple models, such as the dynamics of a finite number of point vortices [32,51,52].…”

Section: Historical Overviewmentioning

confidence: 99%

“…In Ref. [52], the equations of the three-dimensional dynamics of an ideal electrically conducting stratified rotating fluid were studied. The magnetic and density fields were represented as a superposition of unperturbed fields corresponding to the stationary state of the medium and induced fields due to wave motion.…”

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

confidence: 99%

“…The approach is similar to that in Ref. [52], with representation of fields in the form of a superposition of unperturbed and induced fields and reduction to a scalar form. The purpose is to reduce a nonlinear system of partial differential equations that simulates disturbances in an ideal electrically conducting rotating fluid, taking into account inertial forces, gravity forces and Coriolis, Lorentz and existing density inhomogeneities.…”

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

confidence: 99%

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

confidence: 99%

Section: Vortex Motion Of Conducting Ideal Liquids In the Presence Of...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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“…The governing magnetohydrodynamic equations for the problem under consideration are written in projections onto the coordinate axes [1], [2]:…”

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Waves in a rotating layer of an ideal electrically conducting incompressible fluid with allowance effects of diffusion of magnetic field

Peregudin

Kholodova

2014

2014 20th International Workshop on Beam Dynamics and Optimization (BDO)

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A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces and diffusion of magnetic field. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation. Solutions to the scalar equation are constructed that describe small-amplitude wave propagation in an infinite horizontal layer and a long narrow channel.The system of nonlinear partial differential equations describing the dynamics of a rotating layer of an ideal conducting incompressible fluid is difficult to investigate because of its vector character. Therefore, it is natural to try to reduce it to equivalent scalar equations for auxiliary functions.We consider the nonlinear system of partial differential equations that model perturbations in a layer of an ideal conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces and diffusions of magnetic field. The purpose of this study is to reduce this system to a scalar equation and to construct analytical solutions to the corresponding boundary value problems.The accounting of diffusive members is necessary when studying dynamics of waves of more local character, i.e., when the horizontal scale of change of hydromagnetic sizes much less than a radius of a considered layer, and also at very great time scales. It would be desirable to see influence of diffusion of a magnetic field on its generation. Whether there will be able to be a magnetic field as much as long time and whether it will exist at shutdown of an inoculating field.The motion of a conducting fluid in a magnetic field causes electric currents. These currents change the magnetic field. At the same time, the forces acting on the currents in the magnetic field can change the character of the fluid motion. Hence, hydrodynamic motion and electromagnetic phenomena are interrelated. This relation is described by the joint system of field equations and the equations of motion of a fluid. According to the works by the well-known Swedish physicist and astrophysicist G. Alfven, the interrelation between electromagnetic and hydrodynamic phenomena strengthens as the linear scale of a phenomenon increases. For large-scale phenomena, this interrelation can be rather strong. For example, this is true of star interiors and the Earth's liquid core.Large-scale motions of an electrically conducting fluid have been intensively studied. In particular, we note, which investigate a model constructed in the approximation of fast rotation. Within the framework of this theory, the inertial force is ignored in the equation of motion. As a result, the inertial, Alfven, and Rossby waves are filtered out. Furthermore, in the limit of fast rotation, the velocity v is not determined uniquely but rather up to a...

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Impact of waves to the bottom rheology

Peregudin

Kholodova

2015

2015 International Conference on Mechanics - Seventh Polyakhov's Reading

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Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region

Cited by 7 publications

References 8 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

Waves in a rotating layer of an ideal electrically conducting incompressible fluid with allowance effects of diffusion of magnetic field

Impact of waves to the bottom rheology

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