Self‐consistent cutoff wave number of the ablative Rayleigh–Taylor instability

Abstract The Rayleigh-Taylor instability of a partially ionized plasma in a porous medium is considered in the presence of a variable magnetic field perpendicular to gravity. The cases of two uniform partially ionized plasmas separated by a horizontal boundary and exponentially varying density, viscosity, magnetic field and neutral particle number density are considered. In each case, the magnetic field succeeds in stabilizing waves in a certain wave-number range which were unstable in the absence of the magnetic field, whereas the system is found to be stable for potentially stable configuration/stable stratifications. The growth rates both increase (for certain wave numbers) and decrease (for different wave numbers) with the increase in kinematic viscosity, medium permeability and collisional frequency. The medium permeability and collisions do not have any qualitative effect on the nature of stability or instability.

Download Full-text

Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

The Scientific World JOURNAL ◽

10.1155/2014/485807 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Mukesh Kumar Awasthi ◽

Vineet K. Srivastava

Keyword(s):

Heat Transfer ◽

Mass Transfer ◽

Electric Field ◽

Heat And Mass Transfer ◽

Taylor Instability ◽

Wave Number ◽

Physical Parameters ◽

Tangential Electric Field ◽

Rayleigh Taylor Instability ◽

The Stability

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

Download Full-text

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-1996-1-203 ◽

1996 ◽

Vol 51 (1-2) ◽

pp. 17-22 ◽

Cited By ~ 9

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.

Download Full-text

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

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2018-0033 ◽

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.

Download Full-text