scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

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 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.

scholarly journals Rayleigh Taylor instability in dusty magnetized fluids with surface tension flowing through porous medium

2016 ◽  
Vol 20 (1) ◽  
pp. 119-130
Author(s):  
Praveen Sharma ◽  
Anita Tiwari ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Porous Medium ◽  
Dispersion Relation ◽  
Dust Particles ◽  
Simultaneous Presence ◽  
Horizontal Magnetic Field ◽  
Stability And Instability ◽  
Suspended Dust

In this paper we investigate the effect of surface tension on hydromagnetic Rayleigh-Taylor (R-T) instability of two incompressible superimposed fluids in a porous medium with suspended dust particles immersed in a uniform horizontal magnetic field. The relevant linearized perturbation equations have been solved using normal mode technique and the dispersion relation is derived analytically for the considered system. The dispersion relation is influenced by the simultaneous presence of medium porosity, suspended dust particles, permeability, magnetic field and surface tension. The onset criteria of R-T stability and instability are obtained and discussed. The growth rate of R-T instability is calculated numerically and is affected by the simultaneous presence of surface tension and magnetic field. The effects of various parameters on the growth rate of the R-T instability are discussed.

scholarly journals The Effect of the Magnetic Field on the Rayleigh-Taylor Instability in a Couple-Stress Fluid

2018 ◽  
Vol 23 (3) ◽  
pp. 611-622
Author(s):  
K.B. Chavaraddi ◽  
V.B. Awati ◽  
M.M. Nandeppanavar ◽  
P.M. Gouder
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Boundary Conditions ◽  
Couple Stress ◽  
Taylor Instability ◽  
Wave Number ◽  
Special Cases ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

Abstract In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.

Nonlinear Rayleigh–Taylor instability in hydromagnetics

1976 ◽  
Vol 15 (2) ◽  
pp. 239-244 ◽  
Author(s):  
G. L. Kalra ◽  
S. N. Kathuria
Keyword(s):  
Magnetic Field ◽  
Power Generation ◽  
Growth Rate ◽  
Linear Theory ◽  
Nonlinear Theory ◽  
Taylor Instability ◽  
Rayleigh Taylor Instability ◽  
Image Position

Nonlinear theory of Rayleigh—Taylor instability in plasma supported by a vacuum magnetic field shows that the growth rate of the mode, unstable in the linear theory, increases if the wavelength of perturbation π lies betweenand 2πcrit. This might have an important bearing on the proposed thermonuclear MHD power generation experiments.

scholarly journals Effect of a magnetic field on the growth rate of the Rayleigh–Taylor instability of a laser-accelerated thin ablative surface

2004 ◽  
Vol 22 (1) ◽  
pp. 29-33 ◽  
Author(s):  
N. RUDRAIAH ◽  
B.S. KRISHNAMURTHY ◽  
A.S. JALAJA ◽  
TARA DESAI
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Transverse Magnetic Field ◽  
Plasma Layer ◽  
Fusion Energy ◽  
Transverse Magnetic ◽  
Taylor Instability ◽  
Electrically Conducting ◽  
Rayleigh Taylor Instability ◽  
Thin Plasma

The Rayleigh–Taylor instability (RTI) of a laser-accelerated ablative surface of a thin plasma layer in an inertial fusion energy (IFE) target with incompressible electrically conducting plasma in the presence of a transverse magnetic field is investigated using linear stability analysis. A simple theory based on Stokes-lubrication approximation is proposed. It is shown that the effect of a transverse magnetic field is to reduce the growth rate of RTI considerably over the value it would have in the absence of a magnetic field. This is useful in the extraction of IFE efficiently.

On the Stability of Two Superposed Viscous-Viscoelastic (Walters B′) Fluids

2006 ◽  
Vol 129 (1) ◽  
pp. 116-119 ◽  
Author(s):  
Pardeep Kumar ◽  
Roshan Lal
Keyword(s):  
Viscous Fluid ◽  
Viscoelastic Fluid ◽  
Kinematic Viscosity ◽  
Taylor Instability ◽  
Stable Configuration ◽  
Stabilizing Effect ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability ◽  
Newtonian Viscous Fluid ◽  
The Stability

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying Walters B′ viscoelastic fluid is considered. For the stable configuration, the system is found to be stable or unstable under certain conditions. However, the system is found to be unstable for the potentially unstable configuration. Further it is found numerically that kinematic viscosity has a destabilizing effect, whereas kinematic viscoelasticity has a stabilizing effect on the system.

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.

scholarly journals Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

2019 ◽  
Vol 867 ◽  
pp. 1012-1042 ◽  
Author(s):  
S. A. Piriz ◽  
A. R. Piriz ◽  
N. A. Tahir
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Ideal Fluid ◽  
Taylor Instability ◽  
Finite Width ◽  
Unexpected Result ◽  
Magnetic Field Effects ◽  
Linear Elastic ◽  
Rayleigh Taylor Instability ◽  
The Stability

We present the linear theory of two-dimensional incompressible magneto-Rayleigh–Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the stabilising effects of the elasticity. As a consequence, the layer can become more unstable than when only one of these stabilising mechanisms is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.

Zur Rayleigh-Taylor-Instabilität eines rotierenden Wasserstofflichtbogens im axialen Magnetfeld

1970 ◽  
Vol 25 (2) ◽  
pp. 273-282 ◽  
Author(s):  
H. F. Döbele
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Heat Conduction ◽  
Dispersion Relation ◽  
Electrical Conduction ◽  
Growth Rates ◽  
Plasma Column ◽  
Qualitative Agreement ◽  
Axial Magnetic Field ◽  
Rayleigh Taylor Instability

Abstract The Rayleigh-Taylor instability of a rotating hydrogen arc in an axial magnetic field is investigated with allowance for electrical conduction, heat conduction and viscosity. The r-depending part of the perturbation was assumed to be in the form of a half-period of a standing wave. The corresponding dispersion relation is derived in the WKB-approximation and is solved numerically. In contrast with the case without dissipation, the frequencies and growth rates of the different modes depend on the parameters of the unperturbed plasma column. The calculation shows, in qualitative agreement with the experiment, that with increasing magnetic field the highest growth rate passes successively to the next higher mode.

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