arXiv subjects

M. I. Kopp

Publications and source records attributed to M. I. Kopp.

14 recordsLinked to original sources

arXiv2025

Magnetorotational and convective instabilities in a thin layer of electrically conductive nanofluid under an external helical magnetic field

This review summarizes recent advances in the theoretical analysis of the stability of magnetized flows in a non-uniformly rotating layer of electrically conductive nanofluid, incorporating the effects of Brownian diffusion and thermophoresis. In the absence of temperature gradients, different forms of magnetorotational instability (MRI): standard (SMRI), azimuthal (AMRI), and helical (HMRI) are investigated for nanofluid layers subjected to axial, azimuthal, and helical magnetic fields. The corresponding growth rates and instability regions are analyzed in relation to the rotation profile (quantified by the Rossby number $\textrm{Ro}$) and the radial wave number $k$. When temperature gradients and nanoparticle concentration effects are present, stationary convective modes in both axial and helical magnetic fields are examined under conditions of non-uniform rotation. Analytical expressions for the critical Rayleigh number $\textrm{Ra}_{st}$ are derived, and neutral stability curves are constructed as functions of the angular velocity profile, the azimuthal magnetic field inhomogeneity (magnetic Rossby number $\textrm{Rb}$), and the wave number $k$. The study identifies and discusses key mechanisms responsible for the stabilization or destabilization of stationary convection in axial and spiral magnetic field configurations, highlighting the role of nanoparticle-driven effects in modifying classical magnetoconvective behavior.

physics.flu-dyn↗

arXiv2022

Diffusion evolution of a pore in bounded particle in a hydrogen atmosphere

The problem of the diffusion evolution of a pore filled with molecular hydrogen in a spherical granule in a hydrogen medium is solved. The initial position of the pore is displaced relative to the center of the granule. A nonlinear system of equations is obtained, which describes the behavior of the size of the gas-filled pore, the amount of gas in it and its position relative to the center of the bounded particle with time. Numerical calculations have shown the existence of two stages of evolution. The first (fast) stage is associated with the equalization of pressure in the pore with the external. The second is the slow diffusion "healing" of the pore, when the amount of gas adjusts to its size and the gas pressure is approximately equal to the external.

cond-mat.mes-hall↗

arXiv2021

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

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 $\nabla T_0$ and thermoelectromotive coefficient gradient $\nablaα$. 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 ${\bf{B}}_0 \| {\rm OZ}$ is established. As a result of applying the method of perturbation theory for the small parameter $ ε= \sqrt {(\textrm {Ra}-\textrm {Ra}_c) / \textrm {Ra}_c} $ of supercriticality of the stationary Rayleigh number $\textrm {Ra}_c$ 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.

physics.flu-dyn↗

arXiv2019

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

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 non-autonomous 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.

physics.plasm-ph↗

arXiv2019

Gas-filled pore in bounded particle

The diffusive evolution has been studied of gas-filled pore has in a bounded particle in gas media. The nonlinear equation set, describing the behaviour of gas-filled pore on bounded particle is obtained. Asymptotic modes are considered for evolution of small and large pores. Analytical solutions are obtained in asymptotic modes. The comparison is conducted of these solutions with results of numerical solution of complete equation set. The characteristic regularities of gas-filled pore behavior are found at arbitrary pore position relative to matrix particle center.

cond-mat.soft↗

arXiv2019

Rayleigh-Benard convection in a nonuniformly rotating electrically conductive medium in an external spiral magnetic field

The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number $\textrm{Ro}$) and on the profile of the external azimuthal magnetic field (magnetic Rossby number $\textrm{Rb}$). The nonlinear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of convective flows. The criteria of the occurrence of chaotic movements are found. It depends on the parameters of convection: dimensionless numbers of Rayleigh $\textrm{Ra}$, Chandrasekhar $\textrm{Q}$, Taylor $\textrm{Ta}$, and external azimuthal magnetic field with the Rossby magnetic number $\textrm{Rb}=-1$ for Rayleigh $(\textrm{Ro}=-1)$ and Kepler $(\textrm{Ro}=-3/4)$ profiles of the angular rotation velocity of the medium.

physics.plasm-ph↗

arXiv2018

Evolution of gas-filled pore in bounded particles

In the present work, evolution of gas-filled pore inside spherical nanoshells is considered. On the supposition that diffusion fluxes are quasistationary, the nonlinear equation system is obtained analytically, that describes completely the behaviour of gas-filled pore and matrix shell. Two limiting cases are considered: the case when the pore is small as compared to the matrix shell and the case of the pore close to the matrix shell boundary. The characteristic regularities of pore behaviour are established.

cond-mat.mes-hall↗

arXiv2018

Evolution of vacancy pores in bounded particles

In the present work, the behavior of vacancy pore inside of spherical particle is investigated. On the assumption of quasistationarity of diffusion fluxes, the nonlinear equation set was obtained analytically, that describes completely pore behavior inside of spherical particle. Limiting cases of small and large pores are considered. The comparison of numerical results with asymptotic behavior of considered limiting cases of small and large pores is discussed.

cond-mat.mes-hall↗

arXiv2018

Nonlinear dynamo in obliquely rotating stratified electroconductive fluid in an uniformly magnetic field

We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to small-scale oscillations of the velocity with a small Reynolds number. Using the method of multi-scale asymptotic expansions there are obtained nonlinear equations for vortex and magnetic perturbations in the third order in Reynolds number. Studied is the linear stage of magneto-vortex dynamo caused by instabilities of $α$-effect type. Stationary solutions for the equations of nonlinear magneto-vortex dynamo are found by numerical methods in the form of localized chaotic structures.

physics.flu-dyn↗

arXiv2018

Chaotic magnetoconvection in a non-uniformly rotating electroconductive fluids

We study a new type of magnetoconvection in a nonuniform rotating plasma layer under a constant vertical magnetic field. To describe the weakly nonlinear stage of convection we apply Galerkin-truncated approximation and we obtain the system of equations of Lorentz type. A numerical analysis of these equations shows the presence of chaotic behavior of convective flows. Criteria for the appearance of chaotic motions are found depending on the convection parameters (Rayleigh number $\textrm{Ra}$), magnetic field (Chandrasekhar number $\textrm{Q}$), rotation (Taylor number $\textrm{Ta}$) for the Keplerian angular velocity profile $(\textrm{Ro}=-3/4)$ of the medium.

astro-ph.EP↗

arXiv2017

Nonlinear dynamo in obliquely rotating electroconductive fluids

In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. We used the method of multiscale asymptotic expansions. The nonlinear equations for vortex and magnetic perturbations motions are obtained up to third order in Reynolds number. The linear stage of the magneto-vortex dynamo, arising as a result of instabilities of the type of hydrodynamic and magnetohydrodynamic $α$ - effects, is investigated. Stationary solutions of nonlinear equations of magneto-vortex dynamo in the form of localized chaotic structures are found numerically.

physics.plasm-ph↗

arXiv2017

Nonlinear vortex structures in obliquely rotating stratified fluids driven by small scale non helical forces

In this paper, we study a new type of large-scale instability in obliquely rotating stratified fluids with small scale non-helical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic developments. The nonlinear equations for large scale motions are obtained in the third order of the perturbation theory. In this paper, we consider the linear instability and the stationary nonlinear modes. We obtain solutions in the form of nonlinear Beltrami waves and localized vortex structures as kinks of new type.

physics.flu-dyn↗

arXiv2016

Nonlinear Dynamo

In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of the velocity field and magnetic fields. These small-scale stationary oscillations are maintained by small external sources at low Reynolds numbers. We obtain a nonlinear system of equations describing the evolution of large-scale structures of the velocity field and magnetic fields. The linear stage of evolution leads to the known instability. In this article we consider the stationary large-scale structures of a magnetic field arising at stabilization of linear instability.

astro-ph.EP↗

arXiv2015

The Large scale instability in rotating fluid with small scale force

In this paper, we find a new large scale instability displayed by a rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the nonlinear stage of the instability and generation vortex kinks.

physics.flu-dyn↗