Stability Of Rotating Gravitating Streams

2005 ◽  
Vol 60 (7) ◽  
pp. 484-488 ◽  
Author(s):  
P. K. Bhatia ◽  
R. P. Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Critical Wave Number ◽  
Horizontal Magnetic Field ◽  
Axis Of Rotation ◽  
Streaming Velocity ◽  
The Stability ◽  
The Magnetic Field

This paper treats the stability of two superposed gravitating streams rotating about the axis transverse to the horizontal magnetic field. The critical wave number for instability is found to be affected by rotation for propagation perpendicular to the axis about which the system rotates. The critical wave number for instability is not affected by rotation when waves propagate along the axis of rotation. The critical wave number is affected by both the magnetic field and the streaming velocity in both cases. Both the magnetic field and the rotation are stabilizing, while the streaming velocity is destabilizing.

Hydromagnetic Stability of Two Rivlin-Ericksen Elastico-Viscous Superposed Conducting Fluids

1997 ◽  
Vol 52 (6-7) ◽  
pp. 528-532
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Unstable Configuration ◽  
The Stability ◽  
Superposed Fluids ◽  
The Magnetic Field ◽  
Conducting Fluids

Abstract The stability of the plane interface separating two Rivlin-Ericksen elastico-viscous superposed fluids of uniform densities when the whole system is immersed in a uniform horizontal magnetic field has been studied. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities and equal kinematic viscoelasticities. It is found that the stability criterion is independent of the effects of viscosity and viscoelasticity and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave-number range of the unstable configuration. The behaviour of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically.

scholarly journals Instability through porous medium of two viscous superposed conducting fluids

1982 ◽  
Vol 5 (2) ◽  
pp. 365-375 ◽  
Author(s):  
R. C. Sharma ◽  
K. P. Thakur
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Wave Number ◽  
Horizontal Magnetic Field ◽  
Number Range ◽  
Wave Number Range ◽  
Medium Permeability ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids

The stability of the plane interface separating two viscous superposed conducting fluids through porous medium is studied when the whole system is immersed in a uniform horizontal magnetic field. The stability analysis is carried out for two highly viscous fluids of equal kinematic viscosities, for mathematical simplicity. It is found that the stability criterion is independent of the effects of viscosity and porosity of the medium and is dependent on the orientation and magnitude of the magnetic field. The magnetic field is found to stabilize a certain wave number range of the unstable configuration. The behaviour of growth rates with respect to viscosity, porosity and medium permeability are examined analytically.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Magnetic stabilization of transverse plasma instabilitiest

1971 ◽  
Vol 5 (3) ◽  
pp. 467-474 ◽  
Author(s):  
B. Buti ◽  
G. S. Lakhina
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Cyclotron Frequency ◽  
Plasma Frequency ◽  
Electron Plasma ◽  
Wave Number ◽  
Uniform External Magnetic Field ◽  
Magnetic Stabilization ◽  
Streaming Velocity ◽  
The Magnetic Field

Waves, propagating transverse to the direction of the streaming of a plasma in the presence of a uniform external magnetic field, are unstable if the streaming exceeds a certain minimum value. The magnetic field reduces the growth rate of this instability, and also increases the value of the minimum streaming velocity, above which the system is unstable. The thermal motions in the plasma, however, tend to stabilize the system if the magnetic field is weak (i.e. , Ω being the electron cyclotron frequency, k the characteristic wave-number, and Vt the thermal velocity); but, in case of strong magnetic field (i.e. ), they increase the growth rate, provided (ωp being the electron plasma frequency).

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

Rayleigh-Taylor Instability of a Stratified Magnetized Medium in the Presence of Suspended Particles

1984 ◽  
Vol 39 (10) ◽  
pp. 939-944 ◽  
Author(s):  
R. K. Chhajlani ◽  
R. K. Sanghvi ◽  
P. Purohit
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Suspended Particles ◽  
Frequency Parameter ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Horizontal Magnetic Field ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
The Magnetic Field

Abstract The hydromagnetric Rayleigh-Taylor instability of a composite medium has been studied in the presence of suspended particles for an exponentially varying density distribution. The prevalent horizontal magnetic field and viscosity of the medium are assumed to be variable. The dispersion relation is derived for such a medium. It is found that the stability criterion is independent of both viscosity and suspended particles. The system can be stabilized for an appropriate value of the magnetic field. It is found that the suspended particles can suppress as well as enhance the growth rate of the instability in certain regions. The growth rates are obtained for a viscid medium with the inclusion of suspended particles and without it. It has been shown analytically that the growth rate is modified by the inclusion of the relaxation frequency parameter of the suspended particles.

scholarly journals Hydromagnetic Instability of Two Viscoelastic Dusty-Fluids in Porous Medium

2021 ◽  
Vol 16 ◽  
pp. 137-144
Author(s):  
Pardeep Kumar ◽  
Sumit Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Suspended Particles ◽  
Stable Configuration ◽  
Number Density ◽  
Horizontal Magnetic Field ◽  
Two Fluids ◽  
Medium Permeability ◽  
The Stability ◽  
The Magnetic Field

An attempt has been made to investigate the instability of the plane interface between two viscoelastic superposed conducting fluids in the presence of suspended particles and variable horizontal magnetic field through porous medium is studied. The cases of two fluids of uniform densities, viscosities, magnetic fields, and suspended particles number densities separated by a horizontal boundary; and of exponentially varying density, viscosity, suspended particles number density, and magnetic field are considered. It is found that the stability criterion is independent of the effects of viscoelasticity, medium porosity, and suspended particles but is dependent on the orientation and magnitude of the magnetic field. The magnetic field succeeds in stabilizing a certain range of wavenumbers which were unstable in the absence of the magnetic field. The system is found to be stable for potentially stable configuration/stratification. The growth rates are found to increase (for certain wavenumbers) and decrease (for other wavenumbers) with the increase in kinematic viscosity, suspended particles number density, magnetic field, medium permeability and stress relaxation time.

On the stability of the screw pinch in the CGL model

1976 ◽  
Vol 16 (3) ◽  
pp. 261-283 ◽  
Author(s):  
Krishna M. Srivastava ◽  
F. Waelbroeck
Keyword(s):  
Magnetic Field ◽  
Wave Number ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Finite Larmor Radius ◽  
Main Column ◽  
First Order Correction ◽  
The Stability ◽  
The Magnetic Field ◽  
Ideal Plasma

We have investigated the stability of the screw pinch with the help of the double adiabatic (CGL) equations including the finite Larmor radius effects through the anisotropic pressure tensor. The calculations are approximate, with FLR treated as a first-order correction to the ideal plasma equations. The dispersion relation has been solved for various values of R2 = p∥/p⊥ and α for the rale and imaginary part of the frequency (ω = ωR ± iωI) in three particular cases: (a) μ = 0, the θ-pinch, (b) μ = ∞, the Z-pinch, (c) μ = -α/m, field distubances parallel to the equilibrium field. Here μ is the pitch of the magnetic field in the pressureless plasma surrounding the main column, α is the wave number, m is the azimuthal number, p∥ and p⊥ are plasma pressures along and perpendicular to the magnetic field.

Stability of Viscous Rotating Gravitating Streams in a Magnetic Field

2006 ◽  
Vol 61 (5-6) ◽  
pp. 258-262
Author(s):  
Prem Kumar Bhatia ◽  
Ravi Prakash Mathur
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Horizontal Magnetic Field ◽  
The Stability ◽  
The Magnetic Field ◽  
Perturbation Equations

We have studied the stability of two superposed viscous compressible gravitating streams rotating about an axis perpendicular to the direction of a horizontal magnetic field. For wave propagation parallel to the direction of the magnetic field the dispersion relation is derived by solving the linearized perturbation equations. Both the viscosity and rotation are found to suppress the instability of the system

On the stability of viscous flow between parallel planes in the presence of a co-planar magnetic field

1954 ◽  
Vol 221 (1145) ◽  
pp. 189-206 ◽  
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Wave Number ◽  
Neutral Stability ◽  
Energy Relation ◽  
Geometrical Properties ◽  
Electrically Conducting ◽  
Neutral Curves ◽  
The Stability ◽  
The Magnetic Field

Linearized equations are derived which govern the stability of a viscous, electrically conducting fluid in motion between two parallel planes in the presence of a co-planar magnetic field. With one suitable approximation, which restricts the valid range of Reynolds number of the theory, the problem of stability is reduced to the solution of a fourth-order ordinary differential equation. The disturbances considered are neither amplified nor damped, but are neutral. Curves of wave number against Reynolds number for neutral stability are calculated for a range of values of a certain parameter, q , which represents the magnetic effects. For given physical and geometrical properties, the critical Reynolds number above which the flow is unstable rises with the strength of the magnetic field. These results are completely within the range of the approximation mentioned. In addition, an energy relation is derived which illustrates the balance between energy transferred from the basic flow to the disturbances, and that dissipated by viscosity and by the magnetic field perturbations.

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