On the stability of hydrostatic equilibrium in a uniform magnetic field with partial dissipation

2021 ◽  
Author(s):  
Xintong Ji ◽  
Dongfen Bian
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Hydrostatic Equilibrium ◽  
Partial Dissipation ◽  
The Stability

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

On the Hydromagnetic Kelvin-Helmholtz Instability between Compressible Fluids

1974 ◽  
Vol 29 (6) ◽  
pp. 888-892 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Compressible Fluids ◽  
Plane Interface ◽  
Helmholtz Instability ◽  
Solar Plasma ◽  
The Stability ◽  
Conducting Fluids ◽  
Equal Density

We have discussed the effect of gravity on the hydromagnetic Kelvin-Helmholtz instability of a plane interface between compressible, inviscid, infinitely conducting fluids. The stability of the interface is investigated including gravity. The solar plasma and the magnetospheric medium are supposed to be of equal density and to carry a uniform magnetic field (H ) in the direction of streaming. The cases (i) H1 ≠ H2 and x1 (x = cp/cv) not necessarily equal to x2 , (ii) H1= H2 x1 ≠ x2 and (iii) H1 = H2, x1=x2 are discussed for perturbations, transverse as well as parallel to the direction of streaming. It is concluded that the interface is unstable in all the cases except for transverse perturbations, the two media carrying the same magnetic field and being characterized by the same x, when it is found to be verlocity.

scholarly journals Estimating the chromospheric magnetic field from a revised NLTE modeling: the case of HR 7428

2016 ◽  
Vol 12 (S328) ◽  
pp. 38-45
Author(s):  
Innocenza Busá
Keyword(s):  
Magnetic Field ◽  
Magnetic Field Intensity ◽  
Primary Component ◽  
Atmospheric Modeling ◽  
Magnetic Pressure ◽  
Hydrostatic Equilibrium ◽  
Distribution Versus ◽  
Field Estimation ◽  
The Stability ◽  
Semi Empirical

AbstractSemi-empirical atmospheric modeling is here used to obtain the chromospheric magnetic field distribution versus height in the K2 primary component of the RS CVn binary system HR 7428. The chromospheric magnetic field estimation versus height comes from considering the possibility of not imposing hydrostatic equilibrium in the atmospheric modeling. The stability of the best Non-hydrostatic equilibrium model, implies the presence of and additive (toward the center of the star) pressure, that decrease in strength from the base of the chromosphere toward the outer layers. Interpreting the additive pressure as magnetic pressure and I derive a magnetic field intensity of about 500 Gauss at the base of the chromosphere.

The Mechanics of Ferroelastic Plates in a Uniform Magnetic Field

1970 ◽  
Vol 37 (1) ◽  
pp. 153-158 ◽  
Author(s):  
F. Moon
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Field Strength ◽  
Uniform Magnetic Field ◽  
Two Dimensional ◽  
Transverse Waves ◽  
Buckling Instability ◽  
Simply Supported ◽  
The Stability ◽  
Oblique Magnetic Field

The stability and vibration of two-dimensional ferroelastic plates in a uniform, static oblique magnetic field are investigated. It is shown that for either clamped or simply supported boundary conditions, the plate remains either undeformed or unstable. Buckling instability is found to occur only when the field is near normal to the plate. The buckling magnetic field and frequency field dispersion relation is found for a simply supported circular plate. At near-normal field incidence the lowest mode plate frequency decreases with magnetic field. Otherwise an increase in field strength is found to increase the natural frequency. The propagation of transverse waves down an infinite simply supported panel in a magnetic field is also studied.

scholarly journals Stability of the 3D incompressible MHD equations with horizontal dissipation in periodic domain

2021 ◽  
Vol 6 (11) ◽  
pp. 11837-11849
Author(s):  
Ruihong Ji ◽  
◽  
Ling Tian ◽  
Keyword(s):  
Magnetic Field ◽  
Stability Problem ◽  
Stability Result ◽  
Mhd Equations ◽  
Periodic Domain ◽  
Magnetic Diffusion ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
The Stability ◽  
Incompressible Mhd

<abstract><p>The stability problem on the magnetohydrodynamics (MHD) equations with partial or no dissipation is not well-understood. This paper focuses on the 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the stability of perturbations near the steady solution given by a background magnetic field in periodic domain. The new stability result presented here is among few stability conclusions currently available for ideal or partially dissipated MHD equations.</p></abstract>

Diocotron instability in presence of a cold plasma

1969 ◽  
Vol 3 (2) ◽  
pp. 149-153
Author(s):  
Aldo Nocentini
Keyword(s):  
Magnetic Field ◽  
Dielectric Constant ◽  
Uniform Magnetic Field ◽  
Cold Plasma ◽  
Charged Particles ◽  
Cylindrical Layer ◽  
Low Density ◽  
Diocotron Instability ◽  
The Stability

The influence of the presence of a low density, cold plasma on the stability against electrostatic perturbations of a cylindrical layer of charged particles moving in a uniform magnetic field is considered. It is shown that the influence of the plasma is important when the thickness of the layer is small, and the effect is stabilizing or destabilizing whether the dielectric constant of the plasma is smaller or larger than 1. In particular it is shown that the plasma can cause an unstable precession of the layer.

Axialsymmetrische magnetohydrodynamische Gleichgewichtskonfigurationen

1957 ◽  
Vol 12 (10) ◽  
pp. 850-854 ◽  
Author(s):  
R. Lüst ◽  
A. Schlüter
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Axial Symmetry ◽  
Hydrostatic Equilibrium ◽  
Gas Pressure ◽  
The Stability ◽  
Special Case ◽  
The Magnetic Field ◽  
Lines Of Force

Es werden die Bedingungen für magnetohydrodynamische Gleichgewichtskonfigurationen mit axialer Symmetrie untersucht. Das Magnetfeld wird aufgeteilt in seine meridionalen und seine toroidalen Anteile, welche durch skalare Funktionen F bzw. T beschrieben werden. Es wird gezeigt, daß der Gasdruck p und die Funktionen F und T Funktionen voneinander sein müssen. Wenn man über die Funktionen p (F) und T (F) verfügt, bekommt man eine Differentialgleichung für F. Die Fälle, in denen diese Differentialgleichung linear ist, werden betrachtet und die Differentialgleichung explizit gelöst, wenn T (F) =const ist. In einem Spezialfall werden die magnetischen Feldlinien numerisch berechnet und in einer Abbildung angegeben. Schließlich werden noch einige Bemerkungen über die Stabilität solcher Felder angefügt.The conditions for magneto-hydrostatic equilibrium are studied in the case of axial symmetry. The magnetic field is divided into its meridional and its toroidal parts which are described by the scalar functions F and T respectively. It is shown that the gas pressure p and the functions F and T have to be functions of each other. Taking in particular p(F) and T (F) as known relations, a differential equation for F is derived. The cases in which this differential equation is linear are considered and explicitly solved if furthermore T(F) = const. In a special case, the magnetic lines of force are calculated numerically and shown in a figure. Some remarks on the stability are added.

scholarly journals Instabilities in a Non-Uniformly Rotating Medium with Stratification of the Temperature in an External Uniform Magnetic Field

2019 ◽  
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Uniform Magnetic Field ◽  
Landau Equation ◽  
Stationary Convection ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
The Stability

In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number subject to the profile of the inhomogeneous rotation (Rossby number) is obtained. It is shown that the negative values of the Rossby number have a destabilizing effect, since the critical Rayleigh number becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity and azimuthal shear with linear dependence on the coordinate. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid.

HYDROMAGNETIC KELVIN INSTABILITY IN THE PRESENCE OF NEUTRAL PARTICLES

1967 ◽  
Vol 45 (8) ◽  
pp. 2779-2785 ◽  
Author(s):  
S. S. Rao ◽  
G. L. Kalra
Keyword(s):  
Magnetic Field ◽  
Speed Of Sound ◽  
Uniform Magnetic Field ◽  
Collision Frequency ◽  
Wave Number ◽  
Tangential Discontinuity ◽  
Neutral Particles ◽  
The Stability

The stability of a tangential discontinuity in velocity in a plasma mixed with cold neutral particles is investigated in the presence of a uniform magnetic field. It is found that the effect of collisions between the plasma and the neutral particles is stabilizing or destabilizing according as ν, the collision frequency, is less than or greater than the parameter kc, where k is the wave number of the perturbation and c is the speed of sound for the plasma.

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