scholarly journals Transverse Thermal Instability of Radiative Plasma with FLR Corrections for Star Formation in ISM

2021 ◽  
Author(s):  
Sachin Kaothekar
Keyword(s):  
Growth Rate ◽  
Thermal Instability ◽  
Rotation Axis ◽  
Normal Mode Analysis ◽  
Transverse Mode ◽  
Instability Criterion ◽  
Larmor Radius ◽  
Axis Parallel ◽  
General Dispersion ◽  
The Stability

Impact of porosity, rotation and finite ion Larmor radius (FLR) corrections on thermal instability of immeasurable homogeneous plasma has been discovered incorporating the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is carried out with the help of the normal mode analysis scheme taking the suitable linearized perturbation equations of the difficulty. This general dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field. Thermal instability criterion establishes the stability of the medium. Mathematical calculations have been performed to represent the impact of different limitations on the growth rate of thermal instability. It is found that rotation, FLR corrections and medium porosity stabilize the growth rate of the medium in the transverse mode of propagation. Our outcome of the problem explains that the rotation, porosity and FLR corrections affect the dens molecular clouds arrangement and star configuration in interstellar medium.

Effect of Finite Larmor Radius on the Rayleigh-Taylor Instability of Two Component Magnetized Rotating Plasma

1998 ◽  
Vol 53 (12) ◽  
pp. 937-944 ◽  
Author(s):  
P. K. Sharma ◽  
R. K. Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Larmor Radius ◽  
Horizontal Magnetic Field ◽  
Finite Larmor Radius ◽  
Neutral Particles ◽  
Rayleigh Taylor Instability ◽  
Superposed Fluids

Abstract The Rayleigh-Taylor (R-T) instability of two superposed plasmas, consisting of interacting ions and neutrals, in a horizontal magnetic field is investigated. The usual magnetohydrodynamic equations, including the permeability of the medium, are modified for finite Larmor radius (FLR) corrections. From the relevant linearized perturbation equations, using normal mode analysis, the dispersion relation for the two superposed fluids of different densities is derived. This relation shows that the growth rate unstability is reduced due to FLR corrections, rotation and the presence of neutrals. The horizontal magnetic field plays no role in the R-T instability. The R-T instability is discussed for various simplified configurations. It remains unaffected by the permeability of the porous medium, presence of neutral particles and rotation. The effect of different factors on the growth rate of R-T instability is investigated using numerical analysis. Corresponding graphs are plotted for showing the effect of these factors on the growth of the R-T instability.

Magneto Thermal Convection in a Compressible Couple-Stress Fluid

2010 ◽  
Vol 65 (3) ◽  
pp. 215-220 ◽  
Author(s):  
Mahinder Singh ◽  
Pardeep Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Thermal Instability ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Linearized Stability ◽  
The Stability ◽  
The Magnetic Field

The problem of thermal instability of compressible, electrically conducting couple-stress fluids in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress, and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values of the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.

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 Morphological instability in a directionally solidifying binary solution with an imposed shear flow

2001 ◽  
Vol 436 ◽  
pp. 85-106 ◽  
Author(s):  
C. A. CHUNG ◽  
FALIN CHEN
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Binary Solution ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Transverse Component ◽  
Layer Mode ◽  
Axis Parallel ◽  
Roll Axis ◽  
The Stability

The effect of an imposed shear flow on the stability of directionally solidifying binary alloys is investigated. It is shown that without the imposed shear flow the system is dominated by stationary boundary-layer-mode convection, a convection of salt-finger type confined to the solute boundary layer above the melt/mush interface. When the shear flow (no matter how small) is imposed, the boundary-layer mode becomes a longitudinal mode (roll-axis parallel to the imposed flow) propagating in the direction perpendicular to the shear flow, while the modes containing a transverse component are inhibited. As the shear flow becomes large enough, a transverse mode (roll-axis perpendicular to the imposed flow) of very unstable characteristics is induced. This mode, called the morphological mode, can exist even without buoyancy. It is triggered by the flow induced in the mushy layer through the Bernoulli force, a pressure variation resulting from the imposed flow passing along the corrugated melt/mush interface. It, nonetheless, has no relation to the boundary layer instability of the shear flow. The effect of imposed shear flow is so significant that the stability characteristics can be entirely different when the intensity of the imposed flow is larger than a critical value, which is calculated in the present paper.

scholarly journals Linear Vlasov theory of a magnetised, thermally stratified atmosphere

2016 ◽  
Vol 82 (5) ◽  
Author(s):  
Rui Xu ◽  
Matthew W. Kunz
Keyword(s):  
Growth Rate ◽  
Temperature Gradient ◽  
Physical Interpretation ◽  
Magnetic Confinement ◽  
Larmor Radius ◽  
Drift Waves ◽  
Finite Larmor Radius ◽  
Electron Temperature Gradient ◽  
Confinement Fusion ◽  
The Stability

The stability of a collisionless, magnetised plasma to local convective disturbances is examined, with a focus on kinetic and finite-Larmor-radius effects. Specific application is made to the outskirts of galaxy clusters, which contain hot and tenuous plasma whose temperature increases in the direction of gravity. At long wavelengths (the ‘drift-kinetic’ limit), we obtain the kinetic version of the magnetothermal instability (MTI) and its Alfvénic counterpart (Alfvénic MTI), which were previously discovered and analysed using a magnetofluid (i.e. Braginskii) description. At sub-ion-Larmor scales, we discover an overstability driven by the electron-temperature gradient of kinetic-Alfvén drift waves – the electron MTI (eMTI) – whose growth rate is even larger than the standard MTI. At intermediate scales, we find that ion finite-Larmor-radius effects tend to stabilise the plasma. We discuss the physical interpretation of these instabilities in detail, and compare them both with previous work on magnetised convection in a collisional plasma and with temperature-gradient-driven drift-wave instabilities well known to the magnetic-confinement-fusion community. The implications of having both fluid and kinetic scales simultaneously driven unstable by the same temperature gradient are briefly discussed.

Thermal Instability of Rivlin–Ericksen Elastico-Viscous Nanofluid Saturated by a Porous Medium

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Mode Analysis ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
The Stability

Thermal instability in a horizontal layer of Rivlin–Ericksen elastico-viscous nanofluid in a porous medium is considered. A linear stability analysis based upon normal mode analysis is used to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphs have been plotted by giving numerical values to various parameters to depict the stability characteristics. The effects of the concentration Rayleigh number, Vadasz number, capacity ratio, Lewis number, and kinematics viscoelasticity parameter on the stability of the system are investigated. Regimes of oscillatory and nonoscillatory convection for various parameters are derived and discussed in detail. The sufficient conditions for the nonexistence of oscillatory convection have also been obtained.

The Stability of Swirling Jets

1989 ◽  
Vol 8 (1) ◽  
pp. 38-40 ◽  
Author(s):  
Colin S. Coleman
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Normal Mode Analysis ◽  
Axial Flow ◽  
Mode Analysis ◽  
Small Component ◽  
Swirling Jets ◽  
Axisymmetric Mode ◽  
Negative Helicity ◽  
The Stability

AbstractThe stability of a swirling cylindrical jet of compressible fluid is examined by performing a normal mode analysis and numerically solving the eigenvalue problem. Perturbations of the form f(r)exp[i(ωt-mϕ-kz)] are considered, where f is any fluid variable. Instabilities which are characteristic of both a non-swirling (top-hat) jet and a Rankine vortex are investigated for a particular axial wavenumber.The vortex instabilities are weak, and are found to remain weak when axial flow is present. The jet instabilities are much stronger, but axial flow is a stabilizing influence. The positive helicity (km > 0) non-axisymmetric modes (m ≠ 0) are stabilized by a small component of azimuthal flow. The axisymmetric mode (m = 0) and the negative helicity non-axisymmetric modes persist in rapidly swirling jets, but with a greatly reduced growth rate.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

scholarly journals Crystal structures and conformations of two Diels–Alder adduct derivatives: 1,8-bis(thiophen-2-yl)-14-oxatetracyclo[6.5.1.02,7.09,13]tetradeca-2(7),3,5-trien-10-one and 1,8-diphenyl-14-oxatetracyclo[6.5.1.02,7.09,13] tetradeca-2,4,6-trien-10-one

2015 ◽  
Vol 71 (2) ◽  
pp. 213-216
Author(s):  
S. Gopinath ◽  
P. Narayanan ◽  
K. Sethusankar ◽  
Meganathan Nandakumar ◽  
Arasambattu K. Mohanakrishnan
Keyword(s):  
Crystal Packing ◽  
Rotation Axis ◽  
Alder Reaction ◽  
Ring System ◽  
Diels Alder ◽  
Compound I ◽  
Diels Alder Reaction ◽  
Phenyl Rings ◽  
Axis Parallel ◽  
Alder Adduct

The title compounds, C21H16O2S2(I) and C25H20O2(II), are products of a tandem `pincer' Diels–Alder reaction consisting of [2 + 2] cycloadditions between benzo[c]furan and cyclopentanone. Each comprises a fused tetracyclic ring system containing two five-membered rings (inenvelopeconformations with the O atom as the flap) and six-membered rings (inboatconformations). In addition, two thiophene rings in (I) and two phenyl rings in (II) are attached to the tetracyclic ring system. The cyclopentanone ring adopts atwistedconformation in (I) and anenvelopeconformation in (II). In (I), the thiophene rings are positionally disordered over two sets of sites, with occupancy ratios of 0.901 (2):0.099 (2) and 0.666 (2):0.334 (2). In (II), the oxygen atom of the cyclopentanone ring is rotationally disordered over two sites with an occupancy ratio of 0.579 (4):0.421 (4). The molecular structure of (I) is stabilized by an intramolecular C—H...O hydrogen bond, which generates anS(7) ring motif. In the crystal, the molecules are linkedviaweak C—H...O hydrogen bonds, which generateR22(16) ring motifs in (I) andC(8) chains in (II). In both structures, the crystal packing also features C—H...π interactions. The crystal studied of compound (I) was twinned by non-merohedry. The twin component is related by the twin law [−1 0 0 −0.101 1 −0.484 0 0 −1] operated by a twofold rotation axis parallel to thebaxis. The structure of (I) was refined with a twin scale factor of 0.275 (2).

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

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