Magnetic Convection in a Nonuniformly Rotating Electroconducting Medium

Kopp, M. I.; Tour, A. V.; Yanovsky, Vladimir

doi:10.1134/s106377611812018x

Cited by 18 publications

(46 citation statements)

References 26 publications

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“…where R T M = q α R α is a dimensionless parameter depending on the temperature gradient and gradient of the thermoelectromotive force coefficient. In the limiting case, when TM effects are absent, this equation coincides with the result of [39]:…”

Section: Stationary Convection Regimesupporting

confidence: 75%

“…where Ra (0) is the contribution to the dispersion equation without taking into account TM effects, obtained in [39]:…”

Section: Dispersion Equation For Tm Perturbationsmentioning

confidence: 99%

“…In the absence of thermal and thermomagnetic phenomena, the system of equations ( 58) was used to study the saturation mechanism of the standard MRI [45]. In the case when there are no TM effects, the system of equations (58) was used to study weakly nonlinear and chaotic convection regimes in a nonuniformly rotating plasma in an axial magnetic field [39].…”

Section: Equations Of Nonlinear Convection In Rotating Flows Of a Mag...mentioning

confidence: 99%

“…Here TMI is due to the collinear temperature gradient and the gradient of the thermoelectromotive force coefficient. This work is a continuation of the research begun in [39], where the problem of the stability of an electrically conducting fluid between two rotating cylinders (Couette flow) and the Rayleigh-Benard problem in an external constant magnetic field was considered. In contrast to [39], we studied the influence of TM effects on convective processes, as well as the weakly nonlinear evolution of the toroidal magnetic field generated by TMI.…”

Section: Introductionmentioning

confidence: 99%

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Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid

Kopp¹,

Kulik²,

Тур³

et al. 2021

Preprint

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In this paper, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient ∇T 0 and thermoelectromotive coefficient gradient ∇α. The influence of the generation of a toroidal magnetic field by TM instability on convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field B 0 OZ is established. As a result of applying the method of perturbation theory for the small parameter ǫ = (Ra − Ra c )/Ra c of supercriticality of the stationary Rayleigh number Ra c a nonlinear equation of the Ginzburg-Landau type was obtained. This equation describes the evolution of the finite amplitude of perturbations. Numerical solutions of this equation made it possible to determine the heat transfer in the fluid layer with and without TM effects. It is shown that the amplitude of the stationary toroidal magnetic field noticeably increases with allowance for TM effects.

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Section: Stationary Convection Regimesupporting

confidence: 75%

“…where Ra (0) is the contribution to the dispersion equation without taking into account TM effects, obtained in [39]:…”

Section: Dispersion Equation For Tm Perturbationsmentioning

confidence: 99%

Section: Equations Of Nonlinear Convection In Rotating Flows Of a Mag...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid

Kopp¹,

Kulik²,

Тур³

et al. 2021

Preprint

Self Cite

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show abstract

“…also rotate non-uniformly. This circumstance served as the motivation for a theoretical study of Rayleigh-Benard convection in a non-uniformly rotating electrically conductive fluid in the axial uniform magnetic field [11]- [13], as well as in an external spiral magnetic field [14] with the nontrivial topology B 0 rotB 0 = 0.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear magnetic convection in a nonuniformly rotating electrically conductive medium under the action of modulation of external fields

Kopp¹,

Тур²,

Yanovsky³

2019

Preprint

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In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear nonautonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

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Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid

Kopp

Yanovsky

2022

Physics of Fluids

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This study investigates the combined influence of the Hall current and the axial magnetic field on the criterion for the onset of convection in a nonuniformly rotating layer of electrically conductive nanofluids taking into account the effects of Brownian diffusion and thermophoresis. The analytical and numerical computations are presented for water-based nanofluids with alumina nanoparticles. In the absence of a temperature gradient, a new type of magnetorotational instability in an axial magnetic field in a thin layer of a nanofluid is considered. The growth rate and regions of development of this instability are numerically obtained depending on the angular velocity profile (the Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, the stationary regime of nonuniformly rotating magnetoconvection is studied. The exact analytical expression for critical Rayleigh number [Formula: see text] is obtained in terms of various nondimensional parameters. The results indicate that the increase in the Lewis number, the modified diffusivity ratio, and the concentration Rayleigh number is to accelerate the onset of convection. The increase in the Hall current parameter can delay or enhance the onset of convective instability. Rotation profiles with negative Rossby numbers lower the threshold for the development of thermal instability and stimulate the onset of convection. The conditions for stabilization and destabilization of stationary convection in an axial magnetic field are determined. The results are represented graphically and verified numerically.

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Magnetic Convection in a Nonuniformly Rotating Electroconducting Medium

Cited by 18 publications

References 26 publications

Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid

Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid

Weakly nonlinear magnetic convection in a nonuniformly rotating electrically conductive medium under the action of modulation of external fields

Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid

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