scholarly journals Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation

2021 ◽  
Vol 39 (3) ◽  
pp. 775-786
Author(s):  
Avula Benerji Babu ◽  
Gundlapally Shiva Kumar Reddy ◽  
Nilam Venkata Koteswararao
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Normal Mode Analysis ◽  
Vertical Axis ◽  
Wave Number ◽  
Mode Analysis ◽  
Vertical Magnetic Field ◽  
Rotating Fluid ◽  
Axis Of Rotation

In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

Finite-Resistivity Effects on Rayleigh-Taylor Instability of a Stratified Plasma Including Suspended Particles

1985 ◽  
Vol 40 (8) ◽  
pp. 826-833
Author(s):  
Rajkamal Sanghvi ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Kinematic Viscosity ◽  
Normal Mode Analysis ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Suspended Particles ◽  
Wave Number ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Horizontal Magnetic Field

The Rayleigh-Taylor (RT) instability of a stratified and viscid magnetoplasma including the effects of "finite-resistivity and suspended particles is investigated using normal mode analysis. The horizontal magnetic field and the viscosity of the medium are assumed to be variable. The dispersion relation, which is obtained for the general case on employing boundary conditions appropriate to the case of two free boundaries, is then specialized for the longitudinal and transverse modes. It is found that the criterion of stable stratification remains essentially unchanged and that the unstable stratification for the longitudinal mode can be stabilized for a certain wave number band, whereas the transverse mode remains unstable or all wave numbers which can be stabilized by a suitable choice of the magnetic field for vanishing resistivity. Thus, resistivity is found to have a destabilizing influence on the RT configuration. The growth rates of the unstable RT modes with the kinematic viscosity and the relaxation frequency parameter of the suspended particles have been analytically evaluated. Dust (suspended particles) tends to stabilize the configuration when the medium is considered viscid with infinite conductivity. The kinematic viscosity has a stabilizing influence on the ideal plasma modes.

scholarly journals Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

2013 ◽  
Vol 35 (4) ◽  
pp. 75-88
Author(s):  
G.C. Rana ◽  
H.S. Jamwal
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Analysis Method ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
The Magnetic Field

Abstract In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

scholarly journals Hydromagnetic thermosolutal instability of Rivlin-Ericksen rotating fluid permeated with suspended particles and variable gravity field in porous medium

2014 ◽  
Vol 6 (1) ◽  
pp. 24-45
Author(s):  
G. C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Gravity Field ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
Variable Gravity ◽  
Solute Gradient

AbstractThe thermosolutal instability of Rivlin-Ericksen elasticoviscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, the rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically.

scholarly journals Effect of Magnetic Field on Thermal Instability of Oldroydian Viscoelastic Rotating Fluid in Porous Medium

2013 ◽  
Vol 18 (2) ◽  
pp. 555-569 ◽  
Author(s):  
R.C. Thakur ◽  
G.C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Rotating Fluid ◽  
Medium Permeability ◽  
Effects Of Rotation ◽  
The Magnetic Field

In this paper, we investigate the effect of a vertical magnetic field on thermal instability of an Oldroydian visco-elastic rotating fluid in a porous medium. By applying the normal mode analysis method, the dispersion relation governing the effects of rotation, magnetic field and medium permeability is derived and solved analytically and numerically. For the case of stationary convection, the Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has a stabilizing effect while the magnetic field and medium permeability have a stabilizing/destabilizing effect under certain conditions on thermal instability of the Oldroydian viscoelastic fluid in a porous medium. The oscillatory modes are introduced due to the presence of rotation, the magnetic field and gravity field. It is also observed that the ‘principle of exchange of stability’ is invalid in the presence of rotation and the magnetic field.

Magnetogravitational instability of a rotating anisotropic plasma with finite-ion-Larmor-radius corrections and generalized polytropic laws

1998 ◽  
Vol 60 (4) ◽  
pp. 673-694 ◽  
Author(s):  
G. D. SONI ◽  
R. K. CHHAJLANI
Keyword(s):  
Magnetic Field ◽  
Electrical Resistivity ◽  
Dispersion Relation ◽  
Normal Mode Analysis ◽  
Transverse Mode ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Anisotropic Pressure ◽  
Axis Of Rotation ◽  
The Magnetic Field

The gravitational instability of an infinite homogeneous, finitely conducting, rotating, collisionless, anisotropic-pressure plasma in the presence of a uniform magnetic field with finite-ion-Larmor-radius (FLR) corrections and generalized polytropic laws is investigated. The polytropic laws are considered for the pressure components in directions parallel and perpendicular to the magnetic field. The method of normal-mode analysis is applied to derive the dispersion relation. Wave propagation is considered for both parallel and perpendicular axes of rotation. Longitudinal and transverse modes of propagation are discussed separately. The effects of rotation, finite electrical resistivity, FLR corrections and polytropic indices on the gravitational, firehose and mirror instabilities are discussed. The stability of the system is discussed by applying the Routh–Hurwitz criterion. Extensive numerical treatment of the dispersion relation leads to several interesting results. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, it is observed that rotation stabilizes the system by decreasing the critical Jeans wavenumber. It is also seen that the region of instability and the value of the critical Jeans wavenumber are larger for the Chew–Goldberger–Low (CGL) set of equations in comparison with the magnetohydrodynamic (MHD) set of equations. It is found that the effect of FLR corrections is significant only in the low-wavelength range, and produces a stabilizing influence. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the finite electrical resistivity removes the polytropic index [nu] from the condition for instability. The inclusion of rotation alone or FLR corrections alone or both together does not affect the condition for mirror instability. The growth rate of the mirror instability is modified owing to uniform rotation or FLR corrections or both together. We note that the condition of mirror instability depends upon the polytropic indices. We also note that neither the mirror instability nor the firehose instability can be observed for the isotropic MHD set of equations.

scholarly journals Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

2019 ◽  
pp. 1-13
Author(s):  
C. Israel-Cookey ◽  
L. Ebiwareme ◽  
E. Amos
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Internal Heat ◽  
Lewis Number ◽  
Mode Analysis ◽  
Internal Heating ◽  
Vadasz Number ◽  
The Stability ◽  
Solutal Rayleigh Number

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter,  and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number,  and solutal Rayleigh number,  delay the onset of instability.

scholarly journals Impacts of the Horizontal and Vertical Grids on the Numerical Solutions of the Dynamical Equations. Part I: Nonhydrostatic Inertia-Gravity Modes

2017 ◽  
Author(s):  
Celal S Konor ◽  
David A. Randall
Keyword(s):  
Normal Mode ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Normal Mode Analysis ◽  
Companion Paper ◽  
Wave Number ◽  
Mode Analysis ◽  
Dynamical Equations ◽  
Anelastic Equations ◽  
Vertical Grids

Abstract. We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia-gravity modes on a midlatitude f-plane. The dispersion equations are derived from the linearized anelastic equations that are discretized on the Z, C, D, CD, (DC), A, E, and B horizontal grids, and on the L and CP vertical grids. The effects of both horizontal grid spacing and vertical wave number are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined. Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone resolving scales (with low horizontal wavenumbers). We conclude that for cloud-resolving resolutions (with high horizontal wavenumbers) the Z and C grids become overall more accurate than for the cyclone-resolving scales, aided by nonhydrostatic effects. A companion paper, Part II, discusses the impacts of the discretization on the Rossby modes on a midlatitude β-plane.

scholarly journals TRIPLE-DIFFUSIVE CONVECTION IN WALTERS’ (MODEL B’) FLUID WITH VARYING GRAVITY FIELD SATURATING A POROUS MEDIUM

2013 ◽  
Vol 35 (3) ◽  
pp. 45-56 ◽  
Author(s):  
S.K. Kango ◽  
G.C. Rana ◽  
Ramesh Chand
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Gravity Field ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Analysis Theory ◽  
Diffusive Convection ◽  
Medium Permeability

Abstract The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.

Effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation

2014 ◽  
Vol 92 (11) ◽  
pp. 1359-1371 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
Magda E.M. Zidan ◽  
Mohamed I.M. Hilal
Keyword(s):  
Magnetic Field ◽  
Laser Pulse ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Plane Surface ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Gaussian Laser Beam ◽  
Thermoelastic Solid ◽  
Non Gaussian

This investigation deals with the rotation of magneto-thermoelastic solid with voids subjected to thermal loading due to laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam. The entire porous medium is rotated with a uniform angular velocity. The problem is studied in the context of Green–Naghdi (GN) theory of types II and III, with the effect of rotation, magnetic field, thermal loading and voids. Normal mode analysis is used to solve the physical problem to obtain the exact expressions for the displacement components, stresses, temperature distribution, and change in the volume fraction field, which have been shown graphically by comparison between two types of GN theory (types II and III) in the presence and the absence of rotation and magnetic field and for two values of time on thermoelastic material with voids.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

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