Sufficient Conditions for Stability of Rotating Flows

1978 ◽  
Vol 45 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Cheng-I Yang
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Sufficient Conditions ◽  
Swirling Flows ◽  
Rotating Flows ◽  
Conducting Fluid ◽  
Stability And Instability ◽  
Swirl Velocity ◽  
Circular Magnetic Field ◽  
The Stability

This is a study of sufficient conditions for the stability of rotating flows and swirling flows of perfect conducting fluid with circular magnetic fields. Miles’ theorem [1] and Howard’s semicircle theorem [2] on the stability of stratified shear flows are extended to rotating flows with discontinuous swirl velocity. Some stronger sufficient conditions for stability are established. Some sufficient conditions for the stability and instability of the perfect conductive fluids subjected to a transverse circular magnetic field are also studied.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

scholarly journals Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

scholarly journals On the stability of a general magnetic field topology in stellar radiative zones

2019 ◽  
Vol 82 ◽  
pp. 365-371
Author(s):  
K. Augustson ◽  
S. Mathis ◽  
A. Strugarek
Keyword(s):  
Magnetic Field ◽  
Global Change ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Massive Stars ◽  
Spherical Geometry ◽  
Stable Region ◽  
Magnetic Field Topology ◽  
The Stability ◽  
The Magnetic Field

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.

scholarly journals Are the photospheric sunspots magnetically force-free in nature?

2010 ◽  
Vol 6 (S273) ◽  
pp. 333-337 ◽  
Author(s):  
Sanjiv Kumar Tiwari
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Sufficient Conditions ◽  
Field Measurements ◽  
Magnetic Behaviour ◽  
Optical Telescope ◽  
Energy Gradient ◽  
Necessary And Sufficient

AbstractIn a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter α), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by Metcalf et al. (1995) and Moon et al. (2002) ending with inconsistent results. Metcalf et al. (1995) concluded that the photospheric magnetic fields are far from the force-free nature whereas Moon et al. (2002) found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.

scholarly journals Distortion of magnetic fields in the pre-stellar core Barnard 68

2008 ◽  
Vol 4 (S259) ◽  
pp. 107-108 ◽  
Author(s):  
Ryo Kandori ◽  
Motohide Tamura ◽  
Ken-ichi Tatematsu ◽  
Nobuhiko Kusakabe ◽  
Yasushi Nakajima ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Near Infrared ◽  
Flux Ratio ◽  
Field Structure ◽  
Wide Field ◽  
Stellar Core ◽  
The Core ◽  
Cloud Cores ◽  
The Stability

AbstractMagnetic fields are believed to play an important role in controlling the stability and contraction of molecular cloud cores. In the present study, magnetic fields of a cold pre-stellar core, Barnard 68, have been mapped based on wide-field near-infrared polarimetric observations of background stars. A distinct “hourglass-shaped” magnetic field is identified toward the core, as the observational evidence of magnetic field structure distorted by mass accumulation in a pre-stellar core. Our findings on the geometry of magnetic fields as well as the mass-to-magnetic flux ratio are presented.

Hydromagnetic stability of a compressible jet

1975 ◽  
Vol 14 (3) ◽  
pp. 443-448 ◽  
Author(s):  
B. B. Chakraborty ◽  
H. K. S. Iyengar
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Magnetic Fields ◽  
Axial Direction ◽  
Vortex Sheet ◽  
Fluid Velocities ◽  
The Stability ◽  
Axisymmetric Disturbances ◽  
Jet Velocities ◽  
The Magnetic Field

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems

1995 ◽  
Vol 117 (B) ◽  
pp. 145-153 ◽  
Author(s):  
D. S. Bernstein ◽  
S. P. Bhat
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Viscous Damping ◽  
Stability And Instability ◽  
The Stability ◽  
Second Order Systems ◽  
Necessary And Sufficient

Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

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