scholarly journals Generalized function treatment of the Alfvén-gravity wave problem

1983 ◽  
Vol 6 (2) ◽  
pp. 395-402
Author(s):  
L. Debnath ◽  
K. Vajravelu
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Function Method ◽  
Radiation Condition ◽  
Physical Significance ◽  
Generalized Function ◽  
Wave Problem ◽  
Physical Interest ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.

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.

A general method for solving steady-state internal gravity wave problems

1972 ◽  
Vol 56 (4) ◽  
pp. 721-740 ◽  
Author(s):  
D. G. Hurley
Keyword(s):  
Steady State ◽  
Circular Cylinder ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Two Dimensional ◽  
Wave Problem ◽  
Wave Problems ◽  
General Method ◽  
Stratified Liquid

The paper describes a simple but general method for solving 'steady-state’ problems involving internal gravity waves in a stably stratified liquid. Under the assumption that the motion is two-dimensional and that the Brunt-Väisälä frequency is constant, the method is used to re-derive in a very simple way the solutions to problems where the boundary of the liquid is either a wedge or a circular cylinder. The method is then used to investigate the effect that a model of the continental shelf has on an incident train of internal gravity waves. The method involves analytic continuation in the frequency of the disturbance, and may well prove to be effective for other types of wave problem.

THE EFFECT OF FINITE CONDUCTIVITY ON GRAVITY WAVES IN A HORIZONTAL MAGNETIC FIELD

1965 ◽  
Vol 43 (4) ◽  
pp. 645-652 ◽  
Author(s):  
R. A. Wentzell ◽  
J. H. Blackwell
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Gravity Waves ◽  
Gravitational Force ◽  
Finite Conductivity ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Infinite Conductivity ◽  
Mode Solution

A study has been made of the behavior of the plane interface between a vacuum and an electrically conducting fluid subject to a normal gravitational force and a magnetic field parallel to the interface. The system is examined for perturbations which bend the lines of force, without restriction to the extensively used idealization of infinite electrical conductivity. The eigenvalue spectra obtained, which are surprisingly different from the simpler ones corresponding to infinite conductivity, are examined by approximate and numerical techniques over the complete range of electrical conductivity from infinity to zero. The disappearance of a normal mode solution above a critical value of conductivity is an interesting feature of the effect of finite conductivity on magnetohydrodynamic stability.

Evolution of Turbulent Magnetic Fields – Approach to a Steady State

1971 ◽  
Vol 43 ◽  
pp. 487-504
Author(s):  
S. Nagarajan
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Dynamical Evolution ◽  
Magnetic Excitation ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Turbulent Dynamo ◽  
Magnetic Spectrum

The dynamical evolution of a weak, random, magnetic excitation in a turbulent electrically-conducting fluid is examined under varying kinematic conditions. It is found that the results of an earlier paper (Kraichnan and Nagarajan, 1967) can be reliably extended to a stage of evolution wherein the magnetic spectrum has reached local equipartition with the velocity. The transfer of the magnetic energy to smaller wavenumbers (larger scales) is considerable and significant. This result is highly pertinent to the turbulent dynamo question, which has been variously investigated recently. The relevance of the coupling of the rms magnetic field to the magnetic modes of all scales in deciding the efficiency of this transfer is discussed.

Mixed convection flow of an electrically conducting fluid in a vertical channel with boundary conditions of the third kind

2014 ◽  
Vol 92 (11) ◽  
pp. 1387-1396 ◽  
Author(s):  
J.C. Umavathi ◽  
A.J. Chamkha
Keyword(s):  
Mixed Convection ◽  
Average Velocity ◽  
Vertical Channel ◽  
Perturbation Parameter ◽  
Conducting Fluid ◽  
Integration Scheme ◽  
Electrically Conducting ◽  
Nusselt Numbers ◽  
Electrically Conducting Fluid ◽  
External Fluid

In this study, the effects of viscous and Ohmic dissipation in steady, laminar, mixed, convection heat transfer for an electrically conducting fluid flowing through a vertical channel is investigated in both aiding and opposing buoyancy situations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed using a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. In the examined cases of velocity and temperature fields, the Nusselt numbers at both the walls and the average velocity are explored. It is found that the velocity profiles for an open circuit (E > 0 or E < 0) lie in between the short circuit (E = 0). The graphical results illustrating the effects of various parameters on the flow as well as the average velocity and Nusselt numbers are presented for open and short circuits. In the absence of electric field load parameter and Hartmann number, the results agree with Zanchini (Int. J. Heat Mass Transfer, 41, 3949 (1998)). Further, the analytical and numerical solutions agree very well for small values of the perturbation parameter.

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