Dynamics of a rotating layer of an ideal electrically conducting incompressible fluid

Kholodova, S. E.

doi:10.1134/s0965542508050114

Cited by 11 publications

(3 citation statements)

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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%

“…The problems of the theory of surface and internal waves in the ocean were considered in Ref. [51]. Internal waves are often called waves whose amplitudes in the water column are greater (much greater) than on its surface.…”

Section: Dynamics Of Ideal Rotating Incompressible and Stratified Non...mentioning

confidence: 99%

“…In Ref. [51], the disturbances in a layer of an ideal electrically conductive rotating fluid bounded by surfaces that varied in space and time in the presence of inertial forces were studied. The behavior was modeled by a system of nonlinear partial differential equations, which was then reduced.…”

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: Dynamics Of Ideal Rotating Incompressible and Stratified Non...mentioning

confidence: 99%

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

confidence: 99%

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