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.

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.

scholarly journals Effect of Horizontal and Vertical Magnetic Fields on Rayleigh?Taylor Instability

1968 ◽  
Vol 21 (6) ◽  
pp. 923 ◽  
Author(s):  
RC Sharma ◽  
KM Srivastava
Keyword(s):  
Magnetic Fields ◽  
General Equation ◽  
Taylor Instability ◽  
Combined Effect ◽  
Physical Situation ◽  
Stable Case ◽  
Unstable Case ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Superposed Fluids

A general equation studying the combined effect of horizontal and vertical magnetic fields on the stability of two superposed fluids has been obtained. The unstable and stable cases at the interface (z = 0) between two uniform fluids, with both the possibilities of real and complex n, have been. separately dealt with. Some new results are obtained. In the unstable case with real n, the perturbations are damped or unstable according as 2(k'-k~L2)_(<X2-<Xl)k is> or < 0 under the physical situation (35). In the stable case, the perturbations are stable or unstable according as 2(k2_k~L2)+(<Xl-<X2)k is > or < 0 under the same physical situation (35). The perturbations become unstable if HIlIH 1- (= L) is large. Both the cases are also discussed with imaginary n.

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.

Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field

1994 ◽  
Vol 51 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Yusry O. El-Dib
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Magnetic Fluids ◽  
Taylor Instability ◽  
Stable Region ◽  
Solvability Conditions ◽  
System A ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Complex Coefficients

The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

scholarly journals Magnetic fields generated by the Rayleigh-Taylor instability

1986 ◽  
Vol 4 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
R. G. Evans
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Magnetic Fields ◽  
Taylor Instability ◽  
The Self ◽  
Magnetic Diffusion ◽  
Rayleigh Taylor Instability

In the absence of magnetic diffusion the self-generated magnetic field in a plasma is proportional to the fluid vorticity. The ratio of magnetic to fluid energy then shows that self-generated magnetic fields can only affect the Rayleigh Taylor growth rate for large k (wavelengths less then a few microns).

scholarly journals Magnetic-field generation by the ablative nonlinear Rayleigh–Taylor instability

2014 ◽  
Vol 81 (2) ◽  
Author(s):  
Philip M. Nilson ◽  
L. Gao ◽  
I. V. Igumenshchev ◽  
G. Fiksel ◽  
R. Yan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Atmospheric Pressure ◽  
Large Scale ◽  
Taylor Instability ◽  
Magnetic Field Generation ◽  
Field Generation ◽  
Rayleigh Taylor Instability ◽  
Astrophysical Flows ◽  
Rt Instability

Experiments reporting magnetic-field generation by the ablative nonlinear Rayleigh–Taylor (RT) instability are reviewed. The experiments show how large-scale magnetic fields can, under certain circumstances, emerge and persist in strongly driven laboratory and astrophysical flows at drive pressures exceeding one million times atmospheric pressure.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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