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.

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 Effects of Surface Tension and General Rotation on the Rayleigh-Taylor Instability of Three-Layer Flow

2013 ◽  
Vol 3 (1) ◽  
pp. 87
Author(s):  
G. A. Hoshoudy
Keyword(s):  
Surface Tension ◽  
Taylor Instability ◽  
Constant Density ◽  
Stable Case ◽  
General Rotation ◽  
Special Cases ◽  
General Dispersion ◽  
Rayleigh Taylor Instability ◽  
Layer Flow ◽  
The Stability

The stability of two interfaces separating three fluids, where the fluids are assumed to be incompressible, inviscid, and of constant density, has been investigated for a system that is acted upon by a general rotation. The effect of surface tension at the two interfaces is taken into account. A general dispersion relation for the system is obtained analytically by formulating the problem in terms of complex variables. Numerical calculations were performed for a hexane-NaCl-CCl4 system to investigate stable case, and special cases that isolate the effect of various parameters on the growth rate of the Rayleigh-Taylor instability are discussed. It is found that the two cutoff wave numbers for the system with surface tension are unchanged by the addition of a general rotation, and that for the system considered, all growth rates are reduced in the presence of a general rotation.

scholarly journals Effect of Horizontal and Vertical Magnetic Fields on Kelvin?Helmholtz Instability

1968 ◽  
Vol 21 (6) ◽  
pp. 917 ◽  
Author(s):  
RC Sharma ◽  
KM Srivastava
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Combined Effect ◽  
Horizontal Motion ◽  
Helmholtz Instability ◽  
The Stability ◽  
Superposed Fluids ◽  
Oblique Magnetic Field

This paper discusses the effect of a general oblique magnetic field on the stability of two superposed fluids in relative horizontal motion. The stable and unstable cases at the interface (z = 0) between two uniform fluids with constant denRities and velocities of streaming are separately discussed. The combined effect of horizontal and vertical magnetic fields is to increase the wavelength at which the Kelvin-Helmholtz instability sets in.

Rayleigh-Taylor Instability of Viscous-Viscoelastic Fluids in Presence of Suspended Particles Through Porous Medium

1996 ◽  
Vol 51 (1-2) ◽  
pp. 17-22 ◽  
Author(s):  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Suspended Particles ◽  
Taylor Instability ◽  
Viscous Fluids ◽  
Wave Number ◽  
Uniform Rotation ◽  
Stable Case ◽  
Unstable Case ◽  
Rayleigh Taylor Instability

Abstract The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying an Oldroydian viscoelastic fluid containing suspended particles in a porous medium is considered. As in both Newtonian viscous-viscous fluids the system is stable in the potentially stable case and unstable in the potentially unstable case, this holds for the present problem also. The effects of a variable horizontal magnetic field and a uniform rotation are also considered. The presence of magnetic field stabilizes a certain wave-number band, whereas the system is unstable for all wave-numbers in the absence of the magnetic field for the potentially unstable configuration. However, the system is stable in the potentially stable case and unstable in the potentially unstable case for highly viscous fluids in the presence of a uniform rotation.

scholarly journals Hydrodynamic and Hydromagnetic Stability of Viscous-Viscoelastic Superposed Fluids in Presence of Suspended Particles

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Pardeep Kumar ◽  
Mahinder Singh
Keyword(s):  
Magnetic Field ◽  
Suspended Particles ◽  
Viscous Fluids ◽  
Horizontal Magnetic Field ◽  
Stable Case ◽  
Unstable Case ◽  
Rayleigh Taylor Instability ◽  
Newtonian Viscous Fluid ◽  
Superposed Fluids ◽  
The Magnetic Field

The Rayleigh‐Taylor instability of a Newtonian viscous fluid overlying an Oldroydian viscoelastic fluid containing suspended particles is considered. As in both Newtonian viscous-viscous fluids, the system is stable in the potentially stable case and unstable in the potentially unstable case, this holds for the present problem also. The effect of a variable horizontal magnetic field is also considered. The presence of magnetic field stabilizes a certain wavenumber band, whereas the system is unstable for all wavenumbers in the absence of the magnetic field for the potentially unstable arrangement.

The effects of surface tension and viscosity on the stability of two superposed fluids

1961 ◽  
Vol 57 (2) ◽  
pp. 415-425 ◽  
Author(s):  
W. H. Reid
Keyword(s):  
Surface Tension ◽  
Gravity Waves ◽  
Relative Importance ◽  
Quartic Equation ◽  
Stable Case ◽  
Unstable Case ◽  
Lower Fluid ◽  
The Stability ◽  
Superposed Fluids ◽  
Effect Of Surface

ABSTRACTThe effect of surface tension on the stability of two superposed fluids can be described in a universal way by a non-dimensional ‘surface tension number’ S which provides a measure of the relative importance of surface tension and viscosity. When both fluids extend to infinity, the problem can be reduced to the finding of the roots of a quartic equation. The character of these roots is first analysed so as to obtain all possible modes of stability or instability. Two illustrative cases are then considered in further detail: an unstable case for which the density of the lower fluid is zero and a stable case for which the density of the upper fluid is zero, the latter case corresponding to gravity waves. Finally, the variational principle derived by Chandrasekhar for problems of this type is critically discussed and it is shown to be of less usefulness than had been thought, especially in those cases where periodic modes exist.

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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