THE STAEILITY OF COUETTE FLOW IN AN AXIAL MAGNETIC FIELD

1958 ◽  
Vol 36 (11) ◽  
pp. 1509-1525 ◽  
Author(s):  
E. R. Niblett
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Theoretical Prediction ◽  
Viscous Flow ◽  
Rotation Speed ◽  
Axial Magnetic Field ◽  
Radioactive Isotopes ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

Chandrasekhar's theory of the stability of viscous flow of an electrically conducting fluid between coaxial rotating cylinders with perfectly conducting walls is extended to include the case of non-conducting walls, and it is found that their effect is to reduce the critical Taylor numbers and increase the wavelength of the instability patterns by considerable amounts. An experiment designed to measure the values of magnetic field and rotation speed at the onset of instability in mercury between perspex cylinders is described. The radioactive isotopes Hg197 and Hg203 were used to trace the flow. The results support the theoretical prediction that the boundary conditions can have a large effect on the motion.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

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.

Stability of the Base Flow to Axisymmetric and Plane-Polar Disturbances in an Electrically Driven Flow Between Infinitely-Long, Concentric Cylinders

2000 ◽  
Vol 123 (1) ◽  
pp. 31-42
Author(s):  
J. Liu ◽  
G. Talmage ◽  
J. S. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Axial Magnetic Field ◽  
Normal Modes ◽  
Azimuthal Velocity ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Electrically Conducting ◽  
Concentric Cylinders ◽  
The Stability

The method of normal modes is used to examine the stability of an azimuthal base flow to both axisymmetric and plane-polar disturbances for an electrically conducting fluid confined between stationary, concentric, infinitely-long cylinders. An electric potential difference exists between the two cylinder walls and drives a radial electric current. Without a magnetic field, this flow remains stationary. However, if an axial magnetic field is applied, then the interaction between the radial electric current and the magnetic field gives rise to an azimuthal electromagnetic body force which drives an azimuthal velocity. Infinitesimal axisymmetric disturbances lead to an instability in the base flow. Infinitesimal plane-polar disturbances do not appear to destabilize the base flow until shear-flow transition to turbulence.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

1998 ◽  
Vol 60 (3) ◽  
pp. 529-539 ◽  
Author(s):  
RENU BAJAJ ◽  
S. K. MALIK
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Thermal Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
The Magnetic Field

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.

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.

Hydromagnetic spin-up of a fluid confined by two flat electrically conducting boundaries

1971 ◽  
Vol 50 (3) ◽  
pp. 609-623 ◽  
Author(s):  
David E. Loper
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Arbitrary Field ◽  
Plate Interface ◽  
Magnetic Diffusion ◽  
Electrically Conducting ◽  
Single Plate ◽  
Electrically Conducting Fluid ◽  
Special Cases ◽  
Plate Analysis

The prototype linear spin-up problem consisting of a homogeneous viscous electrically conducting fluid confined between two infinite flat rotating electrically conducting plates in the presence of an applied axial magnetic field is studied in an effort to understand better the strength and nature of the coupling between a fluid and its rotating conducting container. It is assumed that the response time of the bounding plates to a magnetic perturbation is much less than the fluid spin-up time and that the plate conductivity is an arbitrary function of distance from the fluid-plate interface. The general Laplace transform solution is inverted and discussed for three special cases: magnetic diffusion regions thick compared with fluid depth during spin-up, arbitrary magnetic field strength and boundary conductance; magnetic diffusion regions thin, weak conductance, arbitrary field; magnetic diffusion regions thin, strong conductance, arbitrary field. In each case conductance of the boundary strengthens the coupling between fluid and boundary, thereby decreasing the spin-up time. The corresponding single plate analysis of Loper (1970a) is found to predict spin-up accurately only if the boundary conductance is much smaller than that of the fluid. The fluid possesses an oscillatory mode of spin-up if the magnetic diffusion regions are thin and boundary conductance is large. That is, the inviscid current-free core of fluid rotates significantly faster than the boundaries during a portion of the spin-up process.

Evolution of wave packets in magnetohydrodynamics

1995 ◽  
Vol 53 (2) ◽  
pp. 145-167 ◽  
Author(s):  
Anju Pusri ◽  
S. K. Malik
Keyword(s):  
Magnetic Field ◽  
Wave Packets ◽  
Stability Diagram ◽  
Envelope Soliton ◽  
Electrically Conducting ◽  
Self Focusing ◽  
Electrically Conducting Fluid ◽  
Regions Of Stability ◽  
Taylor Problem ◽  
The Stability

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

scholarly journals Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field

2018 ◽  
Author(s):  
Dhananjay Yadav
Keyword(s):  
Magnetic Field ◽  
Convective Instability ◽  
Fluid Layer ◽  
Analytical Investigation ◽  
Linear Stability Theory ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Through Flow ◽  
The Stability ◽  
Hele Shaw Cell

In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory. The Galarkin method is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability of the system is examined analytically as well as graphically. It is observed that the through flow and magnetic field have both stabilizing effects, while the Hele-Shaw number has destabilizing effect on the stability of system. It is also found that the oscillatory mode of convection possible only when the magnetic Prandtl number takes the values less than unity.

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