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.

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.

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.

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.

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.

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.

The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field

1955 ◽  
Vol 233 (1192) ◽  
pp. 105-125 ◽  
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Conducting Fluid ◽  
Wave Number ◽  
Neutral Stability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Stability

The stability under small disturbances is investigated of the two-dimensional laminar motion of an electrically conducting fluid under a transverse magnetic field. It is found that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number M . Curves of wave number against Reynolds number for neutral stability are calculated for a range of values of M ; for large values of M the calculations are similar to those which determine the stability of ordinary boundary-layer flow. The critical Reynolds number is found to rise very rapidly with increasing M , so that a transverse magnetic field has a powerful stabilizing influence on this type of flow.

The stability of a homopolar dynamo

1955 ◽  
Vol 51 (4) ◽  
pp. 744-760 ◽  
Author(s):  
Edward Bullard
Keyword(s):  
Magnetic Field ◽  
Steady Motion ◽  
The Self ◽  
Electrical Load ◽  
Constant Amplitude ◽  
Electrically Conducting ◽  
Viscous Forces ◽  
Electrically Conducting Fluid ◽  
The Stability ◽  
Disk Dynamo

ABSTRACTThe stability of the self-exciting disk dynamo is considered. If there is no electrical load in parallel with the field coil and no friction at the axle, the dynamo can perform oscillations of constant amplitude about its state of steady motion. Viscous forces on the axle cause the dynamo to settle to a steady motion. A parallel load may have an effect similar to that of viscous forces or may cause the oscillations to grow without limit. With both a parallel load and viscous forces the amplitude of the oscillations is bounded.Possible analogies between these results and the motion of a body of electrically conducting fluid in a magnetic field are discussed. The main applications are astronomical and geophysical.

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.

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