Generation of magnetic fields by convection

1973 ◽  
Vol 57 (3) ◽  
pp. 529-544 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Magnetic Field ◽  
Longitudinal Direction ◽  
Two Dimensional ◽  
Mean Flow ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Magnetic Prandtl Number ◽  
Hydromagnetic Dynamo ◽  
Convection Rolls ◽  
The Magnetic Field

The nonlinear hydromagnetic dynamo problem is investigated for the case of convection in a layer of an electrically conducting fluid heated from below. It is shown that two-dimensional convection rolls in conjunction with a longitudinal mean flow are capable of amplifying a magnetic field in the form of a wave propagating in the longitudinal direction. The action of the Lorentz forces causes a reduction of the amplitude of convection with the consequence that the energy of the magnetic field cannot grow beyond an equilibrium value which is determined as a function of the parameters of the problem. The analysis is based on an expansion in powers of the longitudinal wavenumber β of the magnetic field and applies in the case of large values of the magnetic Prandtl number.

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.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

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.

scholarly journals Effect of Perpendicular Magnetic Field on Free Convection in a Rectangular Cavity

2015 ◽  
Vol 20 (2) ◽  
pp. 49 ◽  
Author(s):  
Anand Kumar ◽  
Ashok K. Singh ◽  
Pallath Chandran ◽  
Nirmal C. Sacheti
Keyword(s):  
Magnetic Field ◽  
Stream Function ◽  
Governing Equations ◽  
Free Convective Flow ◽  
Alternating Direction Implicit ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Alternating Direction ◽  
Vertical Walls ◽  
The Magnetic Field

The steady free convective flow of a viscous incompressible and electrically conducting fluid in a two-dimensional cavity in the presence of a magnetic field applied normal to the plane of the cavity is investigated. The side vertical walls of the cavity are heated differentially while the horizontal walls are assumed to be insulated. The governing equations are re-formulated in terms of vorticity and stream function. The resulting boundary value problem is solved numerically using an alternating direction implicit (ADI) method. A number of plots illustrating the influence of Hartmann number and Rayleigh number on the streamlines and isotherms as well as the velocity and temperature profiles are shown. Furthermore, results for the average Nusselt number and the maximum absolute stream function have been obtained, and these are compared with the corresponding results in the literature when the magnetic field is applied along the cavity in the horizontal direction.  

Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung

1966 ◽  
Vol 21 (4) ◽  
pp. 369-376 ◽  
Author(s):  
M. Steenbeck ◽  
F. Krause ◽  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Fields ◽  
Rotating Stars ◽  
Correlation Tensor ◽  
Coriolis Forces ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Magnetic Field ◽  
Component Parallel

A turbulent, electrically conducting fluid containing a magnetic field with non-vanishing meanvalue is investigated. The magnetic field strength and the conductivity may be so small that the turbulence is not influenced by the action of the LORENTZ force.The average of the crossproduct of velocity and magnetic field is calculated in a second approximation. It contains the averages of the products of two components of the velocity field, i. e. the components of the correlation tensor.Here the structure of the correlation tensor is determined for a medium with gradients of density and/or turbulence intensity, furthermore the turbulent motion is influenced by CORIOLIS forces.As the main result is shown that in those turbulent velocity fields the average crossproduct of velocity and magnetic field generally has a non-vanishing component parallel to the average magnetic field.Such a turbulence may be present in rotating stars. Consequences concerning the selfexcited build up of steller magnetic fields are discussed in a following paper.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

Unsteady Hydromagnetic Flow Near a Moving Porous Plate

1981 ◽  
Vol 48 (2) ◽  
pp. 255-258 ◽  
Author(s):  
J. N. Tokis ◽  
G. C. Pande
Keyword(s):  
Porous Plate ◽  
Transverse Magnetic ◽  
Two Dimensional ◽  
Hydromagnetic Flow ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Magnetic Prandtl Number ◽  
Laplace Transform Technique ◽  
Infinite Extent ◽  
Two Dimensional Flow

Unsteady two-dimensional flow of a viscous incompressible and electrically conducting fluid near a moving porous plate of infinite extent in presence of a transverse magnetic field is investigated. Solution of the problem in closed form is obtained with the help of Laplace transform technique, when the plate is moving with a velocity which is an arbitrary function of time and the magnetic Prandtl number is unity. Three particular cases of physical interest are also discussed.

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