HELMHOLTZ INSTABILITY OF A VISCOUS COMPRESSIBLE PLASMA

1965 ◽  
Vol 43 (10) ◽  
pp. 1891-1903
Author(s):  
O. P. Bhutani ◽  
A. K. Sundaram
Keyword(s):  
Uniform Magnetic Field ◽  
Plane Boundary ◽  
Electrical Conductor ◽  
Helmholtz Instability ◽  
Compressible Plasma ◽  
Viscosity Parameter ◽  
Perfect Electrical Conductor ◽  
The Stability ◽  
Exchange Of Stability ◽  
Mode Technique

An attempt has been made to discuss the Helmholtz instability of a viscous compressible plasma considered to be a perfect electrical conductor. Initially, the plasma is assumed to be in contact with a uniform magnetic field along a plane boundary that is parallel to the field and is assumed to flow with uniform velocity V0 perpendicular to the field. By using the normal mode technique, the amplitudes of the perturbed quantities are obtained. The conditions for the validity of the principle of exchange of stability and overstability are obtained also. Finally, the growth-rate curves for different values of the viscosity parameter λ′ have been drawn and it has been found that the effect of viscosity adds to the stability of the system.

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

On the Hydromagnetic Kelvin-Helmholtz Instability between Compressible Fluids

1974 ◽  
Vol 29 (6) ◽  
pp. 888-892 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Compressible Fluids ◽  
Plane Interface ◽  
Helmholtz Instability ◽  
Solar Plasma ◽  
The Stability ◽  
Conducting Fluids ◽  
Equal Density

We have discussed the effect of gravity on the hydromagnetic Kelvin-Helmholtz instability of a plane interface between compressible, inviscid, infinitely conducting fluids. The stability of the interface is investigated including gravity. The solar plasma and the magnetospheric medium are supposed to be of equal density and to carry a uniform magnetic field (H ) in the direction of streaming. The cases (i) H1 ≠ H2 and x1 (x = cp/cv) not necessarily equal to x2 , (ii) H1= H2 x1 ≠ x2 and (iii) H1 = H2, x1=x2 are discussed for perturbations, transverse as well as parallel to the direction of streaming. It is concluded that the interface is unstable in all the cases except for transverse perturbations, the two media carrying the same magnetic field and being characterized by the same x, when it is found to be verlocity.

Effect of finite ion Larmor radius on the Kelvin–Helmholtz instability

1978 ◽  
Vol 20 (2) ◽  
pp. 149-160 ◽  
Author(s):  
Hirosh Nagano
Keyword(s):  
Magnetic Field ◽  
Flow Velocity ◽  
Wave Vector ◽  
Uniform Magnetic Field ◽  
Critical Value ◽  
Larmor Radius ◽  
Helmholtz Instability ◽  
Finite Larmor Radius ◽  
Compressible Plasma ◽  
The Difference

The effect of finite ion Larmor radius on the Kelvin–Helmholtz instability is investigated in the cases of an incompressible and a compressible plasma. When a wave vector is perpendicular to a uniform magnetic field, the effect of finite Larmor radius (FLR) stabilizes perturbations with a wavenumber exceeding a critical value, while there exists another case that the FLR effect destabilizes still more than the usual MHD approximation. The difference between these cases is decided from the configuration of flow velocity and magnetic field. When a wave vector is parallel to a magnetic field, the FLR effect tends to stabilize perturbations with a larger wavenumber.

Low Buckling Loads of Axially Compressed Conical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 384-392 ◽  
Author(s):  
M. Baruch ◽  
O. Harari ◽  
J. Singer
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Plane Boundary ◽  
Essential Difference ◽  
Physical Reason ◽  
Buckling Loads ◽  
Conical Shells ◽  
Simple Supports ◽  
Interaction Curves ◽  
The Stability

The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell-type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expression for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the “classical” ones are obtained for all but the stiffest simple supports SS4 (v = u = 0). Except for short shells, the effects do not depend on the length of the shell. The physical reason for the low buckling loads in the SS3 case is explained and the essential difference between cylinder and cone in this case is discussed. Buckling under combined axial compression and external or internal pressure is studied and interaction curves have been calculated for the 4 sets of in-plane boundary conditions.

Stability of Hydromagnetic Thermoconvective Flow Through Porous Medium

1973 ◽  
Vol 40 (4) ◽  
pp. 879-884 ◽  
Author(s):  
Prabhamani R. Patil ◽  
N. Rudraiah
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Normal Mode ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Thermal Convection ◽  
Stability Region ◽  
Flow Through ◽  
The Stability ◽  
Mode Technique

The stability of the onset of thermal convection of a conducting viscous fluid in a porous medium has been investigated using the linear (normal mode technique) and the non-linear (energy) stability theories. Both the theories show that the stability region is increased to the maximum extent when the usual viscous dissipation is also present in addition to the dissipation due to Darcy’s resistance and Joule heating.

A study for steady nanofluid flow between parallel plates

2017 ◽  
Vol 34 (8) ◽  
pp. 2514-2527 ◽  
Author(s):  
Syed Tauseef Mohyud-din ◽  
Muhammad Asad Iqbal ◽  
Muhammad Shakeel
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Uniform Magnetic Field ◽  
Design Methodology ◽  
Magnetic Parameter ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Content Type ◽  
Viscosity Parameter ◽  
Variation Of Parameters

Purpose In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed. Design/methodology/approach The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid. Findings An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter. Originality/value The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

Kelvin-Helmholtz instability of a dusty gas

1965 ◽  
Vol 61 (2) ◽  
pp. 569-571 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Small Volume ◽  
Volume Concentration ◽  
Dusty Gas ◽  
Number Density ◽  
Plane Poiseuille Flow ◽  
Small Particles ◽  
Helmholtz Instability ◽  
Parallel Flows ◽  
The Stability ◽  
Small Disturbances

In a recent paper ((2)) Saffman gave a representation of the flow of a dusty gas in which the dust was described in terms of a number density of small particles with very small volume concentration but appreciable mass concentration. In the same paper the problem of the stability of plane parallel flows to small disturbances was formulated, and subsequently the author ((1)) gave some approximate results for the stability of plane Poiseuille flow.

scholarly journals ON THE STABILITY OF A COMPRESSIBLE PLASMA COLUMN

1964 ◽  
Vol 20 (8) ◽  
pp. 785
Author(s):  
SHI BING-REN
Keyword(s):  
Plasma Column ◽  
Compressible Plasma ◽  
The Stability
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