Stability of magnetohydrodynamic shock waves

1967 ◽  
Vol 1 (4) ◽  
pp. 463-472 ◽  
Author(s):  
Martin Lessen ◽  
Narayan V. Deshpande
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Shock Waves ◽  
Growth Rates ◽  
Acoustic Waves ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Magnetohydrodynamic Shock ◽  
The Stability ◽  
The Magnetic Field

The stability of oblique magnetohycirodynamic shock waves is studied with respect to a disturbance that excites magneto-acoustic waves. The problem is solved numerically by the normal mode analysis and it is shown that slow shocks are unstable in the sense that the disturbance grows exponentially with time. Growth rates are calculated for a particular Mach number and for different values of the magnetic field and obliqueness. The fast shock appears to be stable.

Stability of isothermal magnetohydrodynamic shock waves

1973 ◽  
Vol 10 (2) ◽  
pp. 301-316 ◽  
Author(s):  
Nicole Bel ◽  
Colette Laury-Micoulaut
Keyword(s):  
Shock Waves ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Magnetohydrodynamic Shock ◽  
The Stability

The stability of normal isothermal magnetohydrodynamic shock waves is studied with respect to isothermal as well as adiabatic perturbations. The problem is solved by the normal-mode analysis. The isothermal normal MHD shock appears to be stable.

Magneto Thermal Convection in a Compressible Couple-Stress Fluid

2010 ◽  
Vol 65 (3) ◽  
pp. 215-220 ◽  
Author(s):  
Mahinder Singh ◽  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Linearized Stability ◽  
The Stability ◽  
The Magnetic Field

The problem of thermal instability of compressible, electrically conducting couple-stress fluids in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress, and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values of the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.

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.

Magneto-gasdynamic flow over a wedge

1966 ◽  
Vol 25 (1) ◽  
pp. 165-178 ◽  
Author(s):  
D. C. Pack ◽  
G. W. Swan
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Wave Pattern ◽  
Ionized Gas ◽  
Current Sheets ◽  
Gasdynamic Flow ◽  
The Stability ◽  
The Magnetic Field ◽  
Insight Into

The solution for the flow of a fully ionized gas over a wedge of finite angle is known for the case when the applied magnetic field is aligned with the incident stream. In this flow there are current sheets on the surfaces of the wedge. When the magnetic field is allowed to deviate slightly from the stream, the current sheets may move into the gas and become shock waves. The magnetic fields adjacent to the wedge above and below it have to be matched. A perturbation method is introduced by means of which expressions for the unknown quantities in the different regions may be determined when there are four shocks attached to the wedge. The results give insight into the manner in which the shock-wave pattern develops as the obliquity of the magnetic field to the stream increases. The question of the stability of the shock waves is also examined.

Magnetohydrodynamic shock waves in non-aligned flow

1969 ◽  
Vol 3 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Shigeki Morioka ◽  
John R. Spreiter
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Shock Waves ◽  
Phase Plane ◽  
Physical Space ◽  
Cubic Equation ◽  
Simple Cubic ◽  
Special Cases ◽  
Magnetohydrodynamic Shock ◽  
Steady Shock

The steady shock dicontinuity in the flow of a perfectly conducting gas with anarbitrarily oriented magnetic field is considered by taking as the parameters the Mach number, the Alfvén Mach number, the magentic field direction, and the shock angle. The shock solutions satisfying the conservation laws as well as the entrophy and evolutionary conditions are given by the roots of a simple cubic equation and the associated formulas. Several special cases are discussed analytically and numerically. The possible types of magnetohydrodynamic shock waves are shown on the speed-deflexion phase plane, and the possible shock configurations in the physical space are discussed on the basis of them.

scholarly journals The effect of compressibility, rotation and magnetic field on thermal instability of Walters’ fluid permeated with suspended particles in porous medium

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 539-550 ◽  
Author(s):  
Kumar Aggarwal ◽  
Anushri Verma
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Elastic Parameter ◽  
Mode Analysis ◽  
Medium Permeability ◽  
Stabilizing Effect ◽  
Model Fluid ◽  
The Stability

The purpose of this paper is to study the effects of compressibility, rotation, magnetic field and suspended particles on thermal stability of a layer of visco-elastic Walters? (model) fluid in porous medium. Using linearized theory and normal mode analysis, dispersion relation has been obtained. In case of stationary convection, it is found that the rotation has stabilizing effect on the system. The magnetic field may have destabilizing effect on the system in the presence of rotation while in the absence of rotation it always has stabilizing effect. The medium permeability has destabilizing effect on the system in the absence of rotation while in the presence of rotation it may have stabilizing effect. The suspended particles and compressibility always have destabilizing effect. Due to vanishing of visco-elastic parameter, the compressible visco-elastic fluid behaves like Newtonian fluid. Graphs have also been plotted to depict the stability characteristics. The viscoelasticity, magnetic field and rotation are found to introduce oscillatory modes into the system which were non-existent in their absence.

Effect of Magnetic Field on Generalized Thermo-Viscoelastic Diffusion Medium with Voids

2016 ◽  
Vol 16 (07) ◽  
pp. 1550033 ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Montaser Fekry
Keyword(s):  
Magnetic Field ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Physical Domain ◽  
Specific Material ◽  
Analytical Expressions ◽  
And Diffusion ◽  
Physical Quantities ◽  
The Magnetic Field

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic, generalized thermo-viscoelastic diffusion material with voids under the influence of magnetic field. The formulation is applied to the generalized thermoelasticity theory under the Lord–Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord–Shulman and the coupled theories in the presence and absence of the magnetic field and diffusion.

scholarly journals Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

2013 ◽  
Vol 18 (3) ◽  
pp. 871-886
Author(s):  
M. Singh ◽  
R.K. Gupta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Rayleigh Numbers ◽  
The Magnetic Field

Abstract The effect of Hall currents and suspended dusty particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico viscous fluid in a porous medium is considered. Following the linearized stability theory and normal mode analysis the dispersion relation is obtained. For the case of stationary convection, Hall currents and suspended particles are found to have destabilizing effects whereas compressibility and magnetic field have stabilizing effects on the system. The medium permeability, however, has stabilizing and destabilizing effects on thermal instability in contrast to its destabilizing effect in the absence of the magnetic field. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers are depicted graphically. The magnetic field, Hall currents and viscoelasticity parameter are found to introduce oscillatory modes in the systems, which did not exist in the absence of these parameters

scholarly journals Normal Mode Analysis of Generalized Magneto-Thermoelastic Medium with Initial Stress Under Green-Naghdi Theory

2020 ◽  
Vol 35 (4) ◽  
pp. 313-325
Author(s):  
Alzaerah Ramadhan Mohammed Aldeeb
Keyword(s):  
Magnetic Field ◽  
Initial Stress ◽  
Normal Mode ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Energy Dispersion ◽  
Elasticity Equations ◽  
Physical Quantities ◽  
The Magnetic Field ◽  
Research Show

The normal mode analysis method was used to study the effect of both the initial stress and the magnetic field on a thermally elastic body. This method is used to obtain the exact expressions for the considered variables. Some particular cases are also discussed in the context of the problem. The generalized thermal elasticity equations were reviewed under the influence of the basic initial stress and the magnetic field using the theory (Green-Naghdi) of the second and third types (the second type with no energy dispersion and the third type with energy dispersion). The different physical quantities were illustrated in the presence and absence of both the initial stress and the magnetic field. The results of this research show the extent of difference between the second and third types of Green and Naghdi's theory. All results and figures were obtained using (MATLAB R2013a) program

scholarly journals Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

2013 ◽  
Vol 35 (4) ◽  
pp. 75-88
Author(s):  
G.C. Rana ◽  
H.S. Jamwal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Analysis Method ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
The Magnetic Field

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

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