On the stability of a thermally stratified conducting fluid under the action of aligned magnetic field

1985 ◽  
Vol 42 (3) ◽  
pp. 277-302 ◽  
Author(s):  
N. Rudraiah ◽  
E. S. Shivaraya
Keyword(s):  
Magnetic Field ◽  
Conducting Fluid ◽  
The Stability ◽  
Aligned Magnetic Field

Hydromagnetic stability of a thin electrically conducting fluid film flowing down the outside surface of a long vertically aligned column

2009 ◽  
Vol 223 (2) ◽  
pp. 415-426 ◽  
Author(s):  
P-J Cheng
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Conducting Fluid ◽  
Fluid Film ◽  
Electrically Conducting ◽  
Free Film ◽  
Electrically Conducting Fluid ◽  
Non Linear ◽  
The Stability

This article considers the stability of a thin electrically conducting fluid film flowing down the outer surface of a long vertical cylinder in the presence of an applied magnetic field. Using the long-wave perturbation method to solve the generalized non-linear kinematic equations with free film interface, the normal mode approach is first used to compute the linear stability solution. The method of multiple scales is then used to obtain the weak non-linear dynamics. The results indicate that both subcritical instability and supercritical stability conditions are possible. The degree of instability in the film flow is intensified by the lateral curvature of the cylinder. The results also show that increasing the strength of the magnetic field tends to enhance the stability.

On the interaction between Tollmien-Schlichting and Rayleigh-Bénard instabilities in the presence of a longitudinal magnetic field

1983 ◽  
Vol 93 (2) ◽  
pp. 355-377
Author(s):  
N. Rudraiah ◽  
E. S. Shivaraya
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Magnetic Reynolds Number ◽  
Tollmien Schlichting ◽  
Stuart Number ◽  
The Stability ◽  
Rayleigh Benard ◽  
Stable Flow ◽  
Aligned Magnetic Field

AbstractThe method used by Gage and Reid(10) to investigate hydrodynamic stability of thermally stratified fluid is extended to hydromagnetic stability to study the effect of aligned magnetic field on the stability of unstable thermal stratification under the assumption of small magnetic Reynolds number. The interaction between the Tollmien–Schlichting–Stuart mechanism of instability due to shear and magnetic field and Rayleigh–Bénard–Thompson mechanism of instability due to thermally unstable stratification and magnetic field is brought out in detail. It is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, Squire's theorem is not valid. This conclusion follows from the fact that in our analysis the Richardson number Ri ( < 0) will not be greater than the value −0·92 × 10−6. In particular, it is shown that for the values of stratification parameter n ≤ 0·6 the effect of magnetic field for small values of Stuart number N is to augment instability and impose the restriction on the validity of our numerical procedure. However, for η = 0·8 a sharp transition from unstable to stable flow takes place at N = 0·3. A physical explanation for this based on eddies is given.

On magnetohydrodynamic flows with aligned magnetic fields

1964 ◽  
Vol 19 (1) ◽  
pp. 49-59 ◽  
Author(s):  
M. B. Glauert
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Magnetic Fields ◽  
Boundary Layers ◽  
Flow Patterns ◽  
Basic Flow ◽  
Conducting Fluid ◽  
Magnetic Diffusivity ◽  
Magnetohydrodynamic Flows ◽  
Aligned Magnetic Field

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.

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.

The stability of hydromagnetic Couette flow

1964 ◽  
Vol 60 (3) ◽  
pp. 635-651 ◽  
Author(s):  
P. H. Roberts
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Conducting Fluid ◽  
Theoretical Studies ◽  
Numerical Computations ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability ◽  
Gap Width

AbstractThe theoretical studies of Chandrasekhar on the stability of Couette flow in a viscous, electrically conducting, fluid in the presence of a uniform axial magnetic field are extended to include cases of finite gap width between the cylinders, and cases in which the conductivity of the walls of the containing cylinders is finite. In addition, the non-axisymmetric modes of instability are discussed, and the results of numerical computations are presented.

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