The stability of dissipative magnetohydrodynamic shear flow in a parallel magnetic field

1985 ◽  
Vol 33 (1-4) ◽  
pp. 295-314 ◽  
Author(s):  
J. Lerner ◽  
E. Knobloch
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Parallel Magnetic Field ◽  
The Stability

Shear flow instability in a conducting viscous fluid

1973 ◽  
Vol 57 (3) ◽  
pp. 481-490
Author(s):  
B. Roberts
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Flow Instability ◽  
Approximate Solutions ◽  
Viscous Fluids ◽  
Neutral Stability ◽  
Parallel Magnetic Field ◽  
The Stability ◽  
Shear Flow Instability

The effect of a parallel magnetic field upon the stability of the plane interface between two conducting viscous fluids in uniform relative motion is considered. A parameter reduction, which has not previously been noted, is employed to facilitate the solution of the problem. Neutral stability curves for unrestricted ranges of the governing parameters are found, and the approximate solutions of other authors are examined in this light.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

Stability of aligned magnetoatmospheric flow

1978 ◽  
Vol 19 (1) ◽  
pp. 77-86 ◽  
Author(s):  
J. A. Adam
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Atmospheric Model ◽  
Stratified Fluid ◽  
Sufficient Condition ◽  
Stationary Equilibrium ◽  
Horizontal Magnetic Field ◽  
Energy Principle ◽  
Simple Generalization ◽  
The Stability

Using the stationary equilibrium energy principle a sufficient condition is obtained for the stability of a compressible stratified fluid with a non-uniform horizontal magnetic field, with an aligned shear flow. The condition is used to provide a simple generalization of a known result for a specific atmospheric model.

On the hydromagnetic stability of an unsteady Kelvin-Helmholtz flow

1973 ◽  
Vol 59 (1) ◽  
pp. 65-76 ◽  
Author(s):  
B. Roberts
Keyword(s):  
Magnetic Field ◽  
Basic Flow ◽  
Conducting Fluid ◽  
Helmholtz Instability ◽  
Parallel Magnetic Field ◽  
Oscillatory Component ◽  
The Stability ◽  
The Hill ◽  
The Magnetic Field

An analysis is made of the stability of an unsteady basic flow of a conducting fluid in the presence of a parallel magnetic field. The particular profile investigated is the classical Kelvin–Helmholtz profile modified by the addition of an oscillatory component. Two cases are considered in detail: that of a perfectly conducting fluid and that of a poorly conducting fluid. The investigation leads, in both cases, to an equation of the Hill type. It is concluded that the magnetic field has a stabilizing influence but is nevertheless unable to suppress the Kelvin–Helmholtz instability in an unsteady (basic) flow.

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