Overstable hydromagnetic convection in a rotating fluid layer

1975 ◽  
Vol 71 (1) ◽  
pp. 161-179 ◽  
Author(s):  
I. A. Eltayeb
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Fluid Layer ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Simultaneous Action ◽  
Marginal Stability ◽  
Leading Order ◽  
Coriolis Forces ◽  
Lorentz Forces

The effect of the simultaneous action of a uniform magnetic field and a uniform angular velocity on the linear stability of the Bénard layer to time-dependent convective motions is examined in the Boussinesq approximation. Four models, characterized by the relative directions of the magnetic field, angular velocity and gravitational force, are discussed under a variety of boundary conditions. Apart from a few cases, the treatment applies when the Taylor number T and the Chandrasekhar number Q (the square of the Hartmann number) are large. (These parameters are dimensionless measures of angular velocity and magnetic field, respectively.)It is shown that the motions at the onset of instability can be of three types. If the Coriolis forces dominate the Lorentz forces, the results for the rotating non-magnetic case are retained to leading order. If the Coriolis and Lorentz forces are comparable, the minimum temperature gradient required for instability is greatly reduced. Also, in this case, the motions that ensue at marginal stability are necessarily three-dimensional and the Taylor-Proudman theorem and its analogue in hydromagnetics are no longer valid. When the Lorentz forces dominate the Coriolis forces, the results obtained are similar to those for the magnetic non-rotating case at leading order.The most unstable mode is identified for all relations T = KQα, where K and α are positive constants, taking into account both time-dependent and time-independent motionsVarious types of boundary layers developing on different boundaries are also examined.

Hydromagnetic convection in a rapidly rotating fluid layer

1972 ◽  
Vol 326 (1565) ◽  
pp. 229-254 ◽  
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Acute Angle ◽  
Marginal Stability ◽  
Rotation Axes ◽  
Thermally Driven ◽  
The Magnetic Field

The linear stability of a rotating, electrically conducting viscous layer, heated from below and cooled from above, and lying in a uniform magnetic field is examined, using the Boussinesq approximation. Several orientations of the magnetic field and rotation axes are considered under a variety of different surface conditions. The analysis is, however, limited to large Taylor numbers, T , and large Hartmann numbers, M . (These are non-dimensional measures of the rotation rate and magnetic field strength, respectively.) Except when field and rotation are both vertical, the most unstable mode at marginal stability has the form of a horizontal roll whose orientation depends in a complex way on the directions and strengths of the field and angular velocity. For example, when the field is horizontal and the rotation is vertical, the roll is directed parallel to the field, provided that the field is sufficiently weak. In this case, the Rayleigh number, R (the non-dimensional measure of the applied temperature contrast) must reach a critical value, R c , which is O ( T 2/5 ) before convection will occur. If, however, the field is sufficiently strong [ T = O ( M 4 )], the roll makes an acute angle with the direction of the field, and R c = O ( T 1/2 ), i.e. the critical Rayleigh number is much smaller than when the magnetic field is absent. Also, in this case the mean applied temperature gradient and the wavelength of the tesselated convection pattern are both independent of viscosity when the layer is marginally stable. Furthermore, the Taylor-Proudman theorem and its extension to the hydromagnetic case are no longer applicable even qualitatively. Over the interior of the layer, however, the Coriolis forces to which the convective motions are subjected are, to leading order, balanced by the Lorentz forces. The results obtained in this paper have a bearing on the possibility of a thermally driven steady hydromagnetic dynamo.

OBSERVATION OF THE TRANSVERSE STERN–GERLACH EFFECT IN NEUTRAL POTASSIUM

1967 ◽  
Vol 45 (4) ◽  
pp. 1481-1495 ◽  
Author(s):  
Myer Bloom ◽  
Eric Enga ◽  
Hin Lew
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Reference Frame ◽  
Inhomogeneous Magnetic Field ◽  
Time Dependent ◽  
Effective Magnetic Field ◽  
Classical Analysis ◽  
At Resonance ◽  
Rotating Reference Frame

A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH0) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.

Experiments on the instability of a layer of mercury heated from below and subject to the simultaneous action of a magnetic field and rotation. II

1959 ◽  
Vol 249 (1256) ◽  
pp. 138-145 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Field Strength ◽  
Wave Number ◽  
Simultaneous Action ◽  
Marginal Stability ◽  
Discontinuous Change ◽  
Theoretical Predictions

Experiments are described which are devoted to the determination of the sizes of the convection cells which appear at marginal stability in a layer of mercury heated from below and subject to the action of a magnetic field either alone or in the presence of rotation. The experiments confirm the theoretical predictions of Chandrasekhar regarding the wave number of the disturbance which is manifested at marginal stability. In particular, under the simultaneous action of magnetic fields and rotation, the present experiments fully confirm the predicted discontinuous change in the wave number at the point where, for increasing field strength (for given rotation), the transition from cellular convection to overstable convection takes place.

The Influence of the Magnetic Boundary Conditions on the Nature of Astrophysical Convection

1983 ◽  
Vol 5 (2) ◽  
pp. 172-173
Author(s):  
J. M. Lopez ◽  
J. O. Murphy
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Fluid Layer ◽  
Heat Energy ◽  
Time Dependent ◽  
Linear Partial Differential Equations ◽  
Convective Motions ◽  
Convective State ◽  
Field Disturbance ◽  
The Magnetic Field

The relevance of the results for the total heat energy transported across a fluid layer by convective motions, obtained from the time integrations of the set of non-linear partial differential equations for hydromagnetic convection, has already been designated in a previous contribution (Lopez and Murphy 1982). Some differences in the form of the boundary conditions adopted for the magnetic field disturbance, H, have been noted in other publications where the interaction of convection and a magnetic field has also been considered. The solutions of the time-dependent equations, referenced above, illustrate that the magnetic boundary conditions have a determining role in the resultant convective state for some ranges of values in parameter space.

EFFECT OF AN APPLIED MAGNETIC FIELD AND GRAVITY MODULATION ON THE TIME DEPENDENT HYDRO-MAGNETIC INSTABILITY

2021 ◽  
Vol 10 (1) ◽  
pp. 391-401
Author(s):  
T. N. Vishalakshi ◽  
G. Chandra Shekara
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Fluid Layer ◽  
Time Dependent ◽  
Gravity Modulation ◽  
Magnetic Instability ◽  
Long Run ◽  
Time Variations ◽  
Short Time ◽  
The Magnetic Field

In this present study a linear hydro-magnetic instability of time-dependent convection is designed and analyzed by using extended Stuart-Davis technique. The time variations are applied by fluctuating the fluid layer in the direction perpendicular to the flow and also the gravity modulation is introduced as sine and exponential function of time is considered to be one of the important effect. The extended Stuart-Davis technique is applied in tackling the time-dependency. To understand the effect of applied magnetic field and gravity modulation on the convection is analyzed with respect to different values of Chandrasekhar's number. The results shows that the magnetic field is having stabilizing impact in case of sinusoidal variation gravity field on the contrast it as destabilizing impact in case of exponential variation of gravity for short time but in long run it is having stabilizing effect.

Experiments on the instability of a layer of mercury heated from below and subject to the simultaneous action of a magnetic field and rotation

1957 ◽  
Vol 242 (1228) ◽  
pp. 81-88 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Rayleigh Number ◽  
Angular Velocity ◽  
Kinematic Viscosity ◽  
Critical Rayleigh Number ◽  
Simultaneous Action ◽  
A Value ◽  
Theoretical Predictions ◽  
The Magnetic Field

Experiments on the onset of thermal convection in a rotating layer of mercury heated from below and subject to an impressed magnetic field are described. Experiments have been performed for values of the parameter Q 1 ( = σH 2 d 2 / π 2 pv , where H denotes the strength of the magnetic field, ρ the density of fluid and σ the coefficient of electrical conductivity) varying between 9·85 and 2·01 x 10 4 and a value approximately 10 6 for the parameter T1 ( = 4Ω 2 d 4 / π 4 v 2 , where Ω is the angular velocity of rotation, d the depth of the layer and v the coefficient of kinematic viscosity). The critical Rayleigh number R c for the onset of instability as well as the manner of its occurrence—overstability or cellular convection—have been determined for fourteen different values of Q 1 . In agreement with Chandrasekhar’s theoretical predictions, the experiments confirm that the transition between overstability and convection occurs discontinuously at a critical field strength (when the angular velocity is maintained constant). The nature of the dependence of R c and Q 1 (for given T 1 ) is also in agreement with theory.

scholarly journals Moving Pearl Vortices in Thin-Film Superconductors

2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Vladimir Kogan ◽  
Norio Nakagawa
Keyword(s):  
Magnetic Field ◽  
Thin Film ◽  
Time Dependent ◽  
Superconducting Thin Film ◽  
Self Energy ◽  
London Equation ◽  
The Magnetic Field

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

scholarly journals Measurements of the time-dependent cosmic-ray Sun shadow with seven years of IceCube data: Comparison with the Solar cycle and magnetic field models

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
M. G. Aartsen ◽  
R. Abbasi ◽  
M. Ackermann ◽  
J. Adams ◽  
J. A. Aguilar ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Cosmic Ray ◽  
Time Dependent ◽  
Data Comparison
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