Effect of rotation and a general oblique magnetic field on Kelvin–Helmholtz instability

1969 ◽  
Vol 47 (9) ◽  
pp. 975-978
Author(s):  
R. C. Sharma ◽  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Helmholtz Instability ◽  
Stabilizing Effect ◽  
The Magnetic Field ◽  
Oblique Magnetic Field

In the present paper, we study the effect of rotation and of an oblique magnetic field on Kelvin–Helmholtz instability. The dispersion relation has been derived for the case of equal densities and different velocities. It is found that the magnetic field has a stabilizing effect, even in the presence of rotation.

Kelvin–Helmholtz instability of a plasma with anisotropic and polytropic pressure laws

1998 ◽  
Vol 60 (2) ◽  
pp. 229-241 ◽  
Author(s):  
P. K. SHARMA ◽  
R. K. CHHAJLANI
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Equations Of State ◽  
Anisotropic Pressure ◽  
Magnetohydrodynamic Equations ◽  
Helmholtz Instability ◽  
Instability Condition ◽  
Two Fluids ◽  
The Magnetic Field

The Kelvin–Helmholtz (K–H) instability of two fluids of plasma streaming in opposite directions with the same velocity and in the presence of an external magnetic field is investigated. The usual magnetohydrodynamic equations with anisotropic pressure are considered. In the present problem, the two pressures parallel and perpendicular to the direction of the magnetic field are defined by polytropic pressure laws. The generalized pressure relations are used, and two equations of state for two pressures are assumed. The equations are linearized, and initially two different flow velocities are taken for the system. The flow is assumed to be in the direction perpendicular to the magnetic field. The problem is solved and a dispersion relation is obtained. From the dispersion relation, the K–H instability condition is obtained. It is found that the instability condition depends upon the polytropic indices of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low systems. It is also found that the growth rate of the instability depends upon various polytropic indices.

scholarly journals Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

scholarly journals Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Contact Discontinuity ◽  
Homogeneous Magnetic Field ◽  
Taylor Instability ◽  
Wide Range ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field ◽  
Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid

1973 ◽  
Vol 61 (3) ◽  
pp. 609-624 ◽  
Author(s):  
D. J. Acheson
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Growth Rates ◽  
Homogeneous Model ◽  
Stratified Fluid ◽  
Generation Mechanism ◽  
Helmholtz Instability ◽  
Coaxial Cylinders ◽  
The Magnetic Field ◽  
Rotating Stratified Fluid

We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfvén frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.

Oblique whistler-mode propagation in a hot anisotropic plasma

1982 ◽  
Vol 27 (2) ◽  
pp. 199-204 ◽  
Author(s):  
S. S. Sazhin ◽  
E. M. Sazhina
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Plasma Temperature ◽  
Anisotropic Plasma ◽  
Mode Propagation ◽  
Whistler Mode ◽  
Energy Focusing ◽  
Wave Normal ◽  
The Magnetic Field ◽  
Normal Angle

An approximate dispersion relation is obtained for quasi-longitudinal whistler mode propagation in the hot anisotropic plasma. The influence of plasma temperature and anisotropy on whistler energy focusing along the magnetic field and whistler trapping in the magnetospheric ducts are considered for the case when the whistler wave normal angle is not equal to zero.

Finite-frequency surface waves on current sheets

1991 ◽  
Vol 45 (3) ◽  
pp. 389-406 ◽  
Author(s):  
K. P. Wessen ◽  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Dielectric Tensor ◽  
Magnetic Field Direction ◽  
Field Reversal ◽  
Ion Cyclotron ◽  
The Magnetic Field

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.

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.

Stability of anisotropic plasmas to almost-perpendicular magnetosonic waves

1971 ◽  
Vol 6 (3) ◽  
pp. 495-512 ◽  
Author(s):  
R. W. Landau† ◽  
S. Cuperman
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Simple Form ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Ion Plasma ◽  
The Stability ◽  
The Magnetic Field

The stability of anisotropic plasmas to the magnetosonic (or right-hand compressional Alfvén) wave, near the ion cyclotron frequency, propagating almost perpendicular to the magnetic field, is investigated. For this case, and for wavelengths larger than the ion Larmor radius and for large ion plasma frequency (w2p+ ≫ Ωp+) the dispersion relation is obtained in a simple form. It is shown that for T # T' (even T ≫ T) no instabifity occurs. The resonant ters are also included, and it is shown that there is no resonant instabifity, only damping.

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