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.

scholarly journals Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

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.

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>

scholarly journals The Rayleigh Problem for a Third Grade Electrically Conducting Fluid in a Magnetic Field

2008 ◽  
Vol 15 (sup1) ◽  
pp. 77-90 ◽  
Author(s):  
Tasawar Hayat ◽  
Herman Mambili-Mamboundou ◽  
Ebrahim Momoniat ◽  
Fazal M Mahomed
Keyword(s):  
Magnetic Field ◽  
Conducting Fluid ◽  
Third Grade ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Rayleigh Problem

Mechanisms for magnetic field reversals

2010 ◽  
Vol 368 (1916) ◽  
pp. 1595-1605 ◽  
Author(s):  
F. Pétrélis ◽  
S. Fauve
Keyword(s):  
Magnetic Field ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Large Scale ◽  
Conducting Fluid ◽  
Similar Model ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Simple Mechanism ◽  
The Magnetic Field

We present a review of the different models that have been proposed to explain reversals of the magnetic field generated by a turbulent flow of an electrically conducting fluid (fluid dynamos). We then describe a simple mechanism that explains several features observed in palaeomagnetic records of the Earth’s magnetic field, in numerical simulations and in a recent dynamo experiment. A similar model can also be used to understand reversals of large-scale flows that often develop on a turbulent background.

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