Mathematical and numerical analysis of the waves motion in electrically conducting incompressible fluid

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

doi:10.1063/1.4912670

Cited by 4 publications

(3 citation statements)

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“…All the above mentioned studies, as well as Refs. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], date back to the second half of the 20th century and were motivated by the rapid development of rocket and space technology and increased interest in the problems of geophysics, oceanology, atmospheric physics, as well as problems in the study and protection of the environment. These studies are included here to show what approaches and methods can be used to obtain precise analytical solutions to problems in the dynamics of rotating fluids.…”

Section: Historical Overviewmentioning

confidence: 99%

“…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 study in Ref. [32] presents solutions to several nonlinear problems in the theory of a rotating fluid, namely an analysis of currents and waves of a finite amplitude in a rotating spherical layer as well as quasi-geostrophic movements in a rotating ocean. This can be viewed as the processes of wave propagation in cylindrical pools with a smooth change in the depth of the liquid.…”

Section: Dynamics Of Ideal Rotating Incompressible and Stratified Non...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: Historical Overviewmentioning

confidence: 99%

Section: Dynamics Of Ideal Rotating Incompressible and Stratified Non...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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Dynamic Processes at the Boundary of the Earth's Liquid Core

Peregudin,

Kholodova

2024

Springer Proceedings in Earth and Environmental Sciences

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Simple universal Kelvin equation valid in critical point vicinity, external-internal state correction, and their application in understanding of normal pentane capillary evaporation and condensation in mesoporous silica MCM-41

Валеев

Morozova

2019

J. Phys.: Conf. Ser.

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A new simple universal form of the Kelvin equation, which can be used near the gas-liquid phase transition critical point, and the correction of the pressure and density for gas phase fluid outside the porous medium are used for the normal pentane meniscus effective curvature radius calculation at the phase equilibrium in mesoporous silica MCM-41, on the basis of the capillary evaporation and condensation experimental data. Normal pentane is suggested as a promising fluid for characterizing the porosity that can be used even at room temperature.

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Mathematical and numerical analysis of the waves motion in electrically conducting incompressible fluid

Cited by 4 publications

References 0 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

Dynamic Processes at the Boundary of the Earth's Liquid Core

Simple universal Kelvin equation valid in critical point vicinity, external-internal state correction, and their application in understanding of normal pentane capillary evaporation and condensation in mesoporous silica MCM-41

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