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.

On the motion of a rigid cylinder in a rotating electrically conducting fluid

1994 ◽  
Vol 260 ◽  
pp. 299-314 ◽  
Author(s):  
David E. Loper
Keyword(s):  
Magnetic Field ◽  
Force Balance ◽  
Conducting Fluid ◽  
Flow Structures ◽  
Coriolis Forces ◽  
Rigid Cylinder ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Magnetic Field ◽  
Lines Of Force

The flow structures generated and drag experienced by a rigid cylinder moving in an arbitrary direction through a rotating electrically conducting fluid in the presence of an applied magnetic field are investigated, with he aim of understanding better the nature of the small-scale flow in the core of the Earth which may be responsible for maintaining the geomagnetic field through dynamo action. Three cases are considered in the limit of small Rossby and magnetic Reynolds numbers. In the case of very weak rotation, the possible flow structures consist of a thin Hartmann layer and a long wake extending in the direction of the magnetic field, in which Lorentz and viscous forces balance, but only the long wake plays a dynamical role. The dominant drag force is experienced for motion that cuts magnetic lines of force. Motion of the cylinder parallel to its axis induces a much weaker drag, while that in the direction of the magnetic field induces none to dominant order. The cylinder also experiences weak lateral forces due to the Coriolis effect. In the case of weak rotation, the balance in the long wake is now magnetostrophic: between Lorentz and Coriolis forces. The drag is qualitatively identical to that in the first case, but the drag induced by motion parallel to the axis of the cylinder is increased, though still smaller than that for motions cutting magnetic lines of force. In the case of strong rotation, the flow structures consist of a thin Ekman layer and a foreshortened Taylor column extending in the direction of the rotation axis. In this column, the force balance is again magnetostrophic. Again only the large-scale structure plays a dynamical role. Motion of the cylinder perpendicular to its axis induces a larger drag than does motion parallel to its axis. The cylinder also experiences large lateral Coriolis forces.

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.

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.

Plane MHD Steady Flows with Constantly Inclined Magnetic and Velocity Fields

1975 ◽  
Vol 53 (23) ◽  
pp. 2613-2616 ◽  
Author(s):  
O. P. Chandna ◽  
H. Toews ◽  
V. I. Nath
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Velocity Field ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Steady Flows ◽  
Physical Conditions ◽  
Zero Current ◽  
Necessary And Sufficient ◽  
The Magnetic Field

Plane steady state viscous fluid flows, in which the magnetic field and velocity field are constantly inclined to one another, are considered. Necessary and sufficient physical conditions have been derived for flows with zero current density and the general solutions for these flows are obtained. Irrotational flows and flows with straight streamlines are also studied.

The magnetohydrodynamic flow past a flat plate

1959 ◽  
Vol 6 (1) ◽  
pp. 77-96 ◽  
Author(s):  
H. P. Greenspan ◽  
G. F. Carrier
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Flat Plate ◽  
Steady Flow ◽  
Full Range ◽  
Ambient Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Two Parameters

The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters ε = ωμν and β = μH2/ρv2. This description of the fields is approximated in three different ways and essentially covers the full range of ε and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

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.

Erklärung stellarer und planetarer Magnetfelder durch einen turbulenzbedingten Dynamomechanismus

1966 ◽  
Vol 21 (8) ◽  
pp. 1285-1296 ◽  
Author(s):  
M. Steenbeck ◽  
F. Krause
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Magnetic Fields ◽  
Cross Product ◽  
Skin Depth ◽  
Electrically Conducting ◽  
Magnetic Stars ◽  
The Magnetic Field ◽  
Component Parallel ◽  
Good Agreement

In a foregoing paper 1 the effects of a turbulent motion on magnetic fields were investigated. Especially turbulence was treated under the influence of CORIOLiS-forces and gradients of density and/or turbulence intensity. It was shown that on these conditions the average cross-product of velocity and magnetic field has a non-vanishing component parallel to the average magnetic field. Here we give the consequences of this effect for rotating, electrically conducting spheres.At first a sphere rotating with constant angular velocity is investigated. The quadratic effect provides for dynamo maintainance of the magnetic fields. A field of dipol-type has the weakest condition for maintainance. Applications to the magnetic field of the earth show a good agreement with the conceptions of the physical state of the earth’s core.For a second model differential rotation is included. We have also dynamo maintainance. Since we have to assume that generally the angular velocity is a function decreasing with the distance from the centre of the sphere, the calculations show that we have a preferred self-excited build-up of a quadrupol-type field. This model may be applicable to magnetic stars.Finally we look for dynamo maintainance of alternating fields. We consider the skin-depth to be small compared with the radius of the sphere, then we have plane geometry. The existence of periodical solutions is proved. Applications to the general magnetic field of the sun, which has a period of 22 years, are discussed.

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.  

scholarly journals Unsteady MHD Flow Due to Non-Coaxial Rotations of a Porous Disk and a Fluid at Infinity Subjected to a Periodic Suction

2018 ◽  
Vol 23 (3) ◽  
pp. 623-633
Author(s):  
M. Guria
Keyword(s):  
Magnetic Field ◽  
Fixed Point ◽  
Velocity Field ◽  
Unsteady Flow ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Shear Stresses ◽  
Porous Disk ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

Abstract The unsteady flow of a viscous incompressible electrically conducting fluid due to non-coaxial rotations of a porous disk subjected to a periodic suction and the fluid at infinity in the presence of applied transverse magnetic field has been studied. The fluid at infinity passes through a fixed point. The velocity field, shear stresses are obtained in a closed form.

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