scholarly journals Effects of Couple Stress on the Growth Rate of Rayleigh- Taylor Instability at the Interface in a Finite Thickness Couple Stress Fluid

2010 ◽  
Vol 3 (01) ◽  
Keyword(s):  
Growth Rate ◽  
Couple Stress ◽  
Finite Thickness ◽  
Taylor Instability ◽  
Couple Stress Fluid ◽  
Rayleigh Taylor Instability

scholarly journals Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid

2019 ◽  
Vol 8 (1) ◽  
pp. 39-45
Author(s):  
Vishwanath B. Awati ◽  
Krishna B. Chavaraddi ◽  
Priya M. Gouder
Keyword(s):  
Surface Tension ◽  
Couple Stress ◽  
Numerical Technique ◽  
Taylor Instability ◽  
Couple Stress Fluid ◽  
Nonlinear Saturation ◽  
Roughness Effects ◽  
Two Fluids ◽  
Rayleigh Taylor Instability ◽  
Boundary Roughness

Abstract The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.

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.

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.

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.

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 Influence of ablation-to-critical surface distance upon Rayleigh–Taylor instability

1991 ◽  
Vol 9 (2) ◽  
pp. 273-281 ◽  
Author(s):  
J. Sanz ◽  
A. Estevez
Keyword(s):  
Growth Rate ◽  
Taylor Instability ◽  
Slab Thickness ◽  
Critical Surface ◽  
Slab Model ◽  
Surface Distance ◽  
Wave Numbers ◽  
Instability Growth ◽  
Rayleigh Taylor Instability ◽  
Ablation Front

The Rayleigh—Taylor instability is studied by means of a slab model and when slab thickness D is comparable to the ablation-to-critical surface distance. Under these conditions the perturbations originating at the ablation front reach the critical surface, and in order to determine the instability growth rate, we must impose boundary conditions at the corona. Stabilization occurs for perturbation wave numbers such that kD ˜ 10.

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