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.

Effect of a magnetic field and Coriolis forces on Rayleigh–Taylor's instability

1969 ◽  
Vol 47 (15) ◽  
pp. 1621-1635 ◽  
Author(s):  
J. M. Gandhi
Keyword(s):  
Magnetic Field ◽  
Variational Principles ◽  
Vertical Axis ◽  
Finite Depth ◽  
Conducting Fluid ◽  
Wave Number ◽  
Constant Growth Rate ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

We present variational principles which characterize the solution of the equilibrium of a plane horizontal layer of an incompressible, electrically conducting fluid of electrical conductivity σ e.m.u., of magnetic permeability K, having a variable density ρ(z) in the vertical z direction, which is also the direction of gravity having acceleration g, and of viscosity μ(z) and which is rotating at Ω radians per second about the vertical axis in the presence of a horizontal magnetic field for the two cases:(i) When the electrically conducting fluid is assumed to be nonrotating (Ω = 0), with the conductivity σ being finite and the horizontal magnetic field being uniform.(ii) When the electrically conducting fluid is assumed to be rotating (Ω ± 0), with the conductivity σ being infinite and the horizontal magnetic field being stratified.Based on the variational principles for these two cases, an approximate solution is obtained for the special case of a fluid of finite depth d stratified according to the law ρ0 = ρ1 exp βz (ρ1 and β are some constants), for which kinematic viscosity ν is assumed to be constant. Growth rate and total wave number of the disturbance are related by two cubic equations, and for simplified cases explicit solutions are obtained. The properties of hydromagnetic waves generated are discussed.

ON THE KELVIN–HELMHOLTZ PROBLEM IN MAGNETOHYDRODYNAMICS WITH FINITE CONDUCTIVITY

1965 ◽  
Vol 43 (7) ◽  
pp. 1342-1346
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Finite Conductivity ◽  
Type Problem ◽  
Horizontal Magnetic Field ◽  
Helmholtz Problem ◽  
Infinite Conductivity ◽  
The Magnetic Field

A study has been made of the effect of large but finite conductivity upon Kelvin–Helmholtz-type instabilities in the presence of a horizontal magnetic field. For finite conductivity, the selected Kelvin–Helmholtz-type problem which is stable at infinite conductivity is stable no matter how large the magnetic field. These instabilities grow aperiodically at a rate proportional to (resistivity)[Formula: see text].

Magnetogasdynamic Aligned Flows with Finite Electric Conductivity

1972 ◽  
Vol 50 (12) ◽  
pp. 1273-1276
Author(s):  
O. P. Chandna ◽  
R. W. Holmes
Keyword(s):  
Magnetic Field ◽  
Charge Density ◽  
Electric Conductivity ◽  
Conducting Fluid ◽  
Finite Conductivity ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Zero Charge

It is established that the steady, axially symmetric flow of a compressible, electrically conducting fluid with finite conductivity has either zero charge density or an irrotational magnetic field. Some properties and solutions of these flows are studied for plane and axially symmetric flows.

Convection of Electrically Conducting Fluid in a Rotating Magnetic System: Cross rolls

2020 ◽  
Author(s):  
Yadagiri Rameshwar ◽  
Gudukuntla Srinivas ◽  
Hari Ponnamma Rani ◽  
Jozef Brestensky ◽  
Enrico Filippi
Keyword(s):  
Magnetic Field ◽  
Flow Behavior ◽  
Linear Equations ◽  
Finite Amplitude ◽  
Conducting Fluid ◽  
Energy Potential ◽  
Onset Of Convection ◽  
Horizontal Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

<p>We have studied theoretically the weakly nonlinear analysis in a rotating Rayleigh-Benard system of electrically conducting fluid in the presence of applied horizontal magnetic field with free-free boundary conditions [1]. This theoretical approach is carried near the onset of convection to study the flow behavior at the occurrence of cross rolls, which are perpendicular to the applied magnetic field. The nonlinear problem is solved by using the Fourier analysis of perturbations up to the O(ε<sup>8</sup>) to study the cross rolls visualization [2,3]. The dependence of the Nusselt number on the Rayleigh number, Ekman number, Elsasser number is extensively examined. The fluid flow is visualized in terms of kinetic energy, potential energy, streamlines, isotherms, and heatlines.</p><p> </p><p>References :</p><p>[1] P. H. Roberts and C. A. Jones , The Onset of Magnetoconvection at Large Prandtl Number in a Rotating Layer I. Finite Magnetic Diffusion, Geophysical and Astrophysical Fluid Dynamics, Vol. 92, pp. 289-325 (2000).</p><p>[2] H.L. Kuo, Solution of the non-linear equations of the cellular convection and heat transport,  Journal of Fluid Mechanics,  Vol.10, pp.611-630 (1961).</p><p>[3] Y. Rameshwar, M. A. Rawoof Sayeed, H. P. Rani, D. Laroze, Finite amplitude cellular convection under the influence of a vertical magnetic field, International Journal of Heat and Mass Transfer, Vol. 114, pp.  559-577 (2017).</p>

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Average Nusselt Number ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Square Cavity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Double Diffusive

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

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.

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