Rayleigh-Taylor instability of compressible fluids in the presence of a vertical magnetic field

1971 ◽  
Vol 24 (1) ◽  
pp. 294-304 ◽  
Author(s):  
P. D. Ariel
Keyword(s):  
Magnetic Field ◽  
Taylor Instability ◽  
Compressible Fluids ◽  
Vertical Magnetic Field ◽  
Rayleigh Taylor Instability

The effect of a general oblique magnetic field on Rayleigh–Taylor instability

1979 ◽  
Vol 57 (8) ◽  
pp. 1094-1102 ◽  
Author(s):  
P. D. Ariel ◽  
B. D. Aggarwala
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Exact Solution ◽  
Variational Principle ◽  
Taylor Instability ◽  
Vertical Magnetic Field ◽  
Mode Solution ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids ◽  
Oblique Magnetic Field

The effect of a general oblique magnetic field on the development of Rayleigh–Taylor instability has been investigated. It has been demonstrated that n2 is purely real, where n is the growth rate of disturbance. Also in this case, the solution is characterized by a variational principle. The exact solution for the case of two superposed fluids has been derived when the oblique magnetic field is constant. It is shown that when the lighter fluid is topped by the heavier fluid a mode of maximum instability exists if the ratio of horizontal to vertical magnetic field is sufficiently large. No normal mode solution is possible if the lighter fluid lies atop the heavier fluid. Use has been made of variational principle to obtain the approximate solution of a fluid having exponentially varying density. It is found that for some disturbances, the oblique magnetic field has a greater stabilizing influence compared to a horizontal or vertical magnetic field of the same strength.

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.

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