Coupling of Buoyant Convections in Boron Oxide and a Molten Semiconductor in a Vertical Magnetic Field

2002 ◽  
Vol 124 (4) ◽  
pp. 643-649 ◽  
Author(s):  
Martin V. Farrell ◽  
Nancy Ma
Keyword(s):  
Magnetic Field ◽  
Boron Oxide ◽  
Maximum Velocity ◽  
Horizontal Velocity ◽  
Vertical Magnetic Field ◽  
Electrical Conductor ◽  
Interfacial Velocity ◽  
Rectangular Container ◽  
Vertical Walls ◽  
The Magnetic Field

This paper treats the buoyant convection in a layer of boron oxide, called a liquid encapsulant, which lies above a layer of a molten compound semiconductor (melt) between cold and hot vertical walls in a rectangular container with a steady vertical magnetic field B. The magnetic field provides an electromagnetic (EM) damping of the molten semiconductor which is an excellent electrical conductor but has no direct effect on the motion of the liquid encapsulant. The temperature gradient drives counter clockwise circulations in both the melt and encapsulant. These circulations alone would lead to positive and negative values of the horizontal velocity in the encapsulant and melt, respectively, near the interface. The competition between the two buoyant convections determines the direction of the horizontal velocity of the interface. For B=5 T, there is significant EM damping of the melt motion and the encapsulant drives a positive interfacial velocity and a small clockwise circulation in the melt. For a much weaker field B=0.1 T, the maximum velocity in the melt is hundreds of times larger than that of the encapsulant, thus causing nearly all the encapsulant to circulate in the clockwise direction.

Effect of magnetic field on parametrically driven surface waves

2006 ◽  
Vol 463 (2079) ◽  
pp. 711-722 ◽  
Author(s):  
Supriyo Paul ◽  
Krishna Kumar
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Liquid Metals ◽  
Tricritical Point ◽  
Thin Layers ◽  
Vertical Magnetic Field ◽  
Harmonic Solution ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

scholarly journals Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

2018 ◽  
Vol 620 ◽  
pp. A191 ◽  
Author(s):  
M. Benko ◽  
S. J. González Manrique ◽  
H. Balthasar ◽  
P. Gömöry ◽  
C. Kuckein ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Temporal Evolution ◽  
Vertical Component ◽  
Field Vector ◽  
Linear Increase ◽  
Vertical Magnetic Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field ◽  
Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

Instability and transition of a vertical ascension or fall of a free sphere affected by a vertical magnetic field

2018 ◽  
Vol 859 ◽  
pp. 33-48 ◽  
Author(s):  
Jun-Hua Pan ◽  
Nian-Mei Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Magnetic Field ◽  
Interaction Parameter ◽  
Scaling Law ◽  
Density Ratio ◽  
Vertical Magnetic Field ◽  
Streamwise Vorticity ◽  
Close Relationship ◽  
Wake Patterns ◽  
The Magnetic Field ◽  
Solid System

When the Galileo number is below the first bifurcation, the instability and transition of a vertical ascension or the fall of a free sphere affected by a vertical magnetic field are investigated numerically. A compact model is used to explain that the magnetic field can destabilize the fluid–solid system. When the interaction parameter exceeds a critical value, the sphere trajectory is transitioned from a steady vertical trajectory to a steady oblique one. Furthermore, the trajectory will remain vertical at a sufficiently large magnetic field because of a double effect of the magnetic field on the fluid–solid system. Under the influence of an external vertical magnetic field, four wake patterns at the rear of the sphere are found and the physical behaviour of the free sphere is independent of the density ratio. The wake or trajectory of the free sphere is only determined by the Galileo number $G$ and the interaction parameter $N$. A close relationship between the streamwise vorticity and the sphere motion is found. An interesting ‘agglomeration phenomenon’ is also found, which shows that the vertical velocities are agglomerated into a point for a certain magnetic field regardless of the Galileo number and satisfy a scaling law $V_{z}\sim N^{-1/4}$, when $N>1$. The principal results of the present work are summarized in a map of regimes in the $\{G,N\}$ plane.

The stability of viscous flow in a curved channel in the presence of a magnetic field

1961 ◽  
Vol 264 (1317) ◽  
pp. 155-164 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Uniform Magnetic Field ◽  
Axial Direction ◽  
Electrical Conductor ◽  
Curved Channel ◽  
Coaxial Cylinders ◽  
Transverse Pressure ◽  
The Stability ◽  
The Magnetic Field

The stability of viscous flow between two coaxial cylinders maintained by a constant transverse pressure gradient is considered when the fluid is an electrical conductor and a uniform magnetic field is impressed in the axial direction. The problem is solved and the dependence of the critical number for the onset of instability on the strength of the magnetic field and the coefficient of electrical conductivity of the fluid is determined.

Electromagnetic damping of elastic waves: Experimental results

1968 ◽  
Vol 5 (4) ◽  
pp. 825-829 ◽  
Author(s):  
F. E. M. Lilley ◽  
C. M. Carmichael
Keyword(s):  
Magnetic Field ◽  
Elastic Wave ◽  
Applied Magnetic Field ◽  
Elastic Waves ◽  
Applied Field ◽  
Eddy Currents ◽  
Electrical Conductor ◽  
Electromagnetic Damping ◽  
The Waves ◽  
The Magnetic Field

The passage of an elastic wave causes straining and translation in the transmitting material. If a magnetic field is applied, and the medium is an electrical conductor, some of the energy of the wave is dissipated by the flow of electrical eddy currents. Usually the amount of energy lost is very small, but it may be greatly increased if the applied field is strongly non-uniform.Laboratory experiments are described which demonstrate this effect for standing elastic waves in a metal bar. The applied magnetic field changes from almost zero to its full strength over a distance which is short compared to the length of the standing wave. The result of this strong non-uniformity is that the energy lost due to the translation of the bar in the field greatly exceeds the energy lost due to the straining of the bar in the field.The dependence of the attenuation of the waves by the magnetic field is investigated for variation in frequency of vibration, bar thickness, and field gradient.

The invariant theory of isotropic turbulence in magneto-hydrodynamics

1951 ◽  
Vol 204 (1079) ◽  
pp. 435-449 ◽  
Keyword(s):  
Magnetic Field ◽  
Invariant Theory ◽  
Isotropic Turbulence ◽  
Equations Of Motion ◽  
Stationary Condition ◽  
Electrical Conductor ◽  
Large Wave ◽  
Triple Correlation ◽  
Constant Rate ◽  
The Magnetic Field

In this paper the invariant theory of isotropic turbulence in magneto-hydrodynamics is developed on the basis of the equations of motion recently derived by Batchelor to describe the hydrodynamics of an incompressible fluid which is also a good electrical conductor. The theory allows for the interaction between the electromagnetic field and the turbulent motion when there is no externally imposed electric or magnetic field. Various double and triple correlation tensors involving the components of the velocity and the magnetic field intensity are defined, and three equations governing the scalars defining these tensors are derived; these latter equations admit integrals of Loitsiansky’s type. The equations governing the dissipation of energy by viscosity and conductivity are also derived; they exhibit the manner in which energy is exchanged between the velocity and the magnetic fields. Finally, the equations appropriate for the case, when an external agency supplies kinetic energy to the system at a constant rate and a stationary condition prevails, are obtained; they suggest that the energy in the magnetic field is contained, principally, in the eddies with large wave numbers.

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.  

Thermal Instability in Rivlin-Ericksen Elastico-Viscous Fluids in Hydromagnetics

1997 ◽  
Vol 52 (4) ◽  
pp. 369-371 ◽  
Author(s):  
R. C. Sharma ◽  
P. Kumar
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Newtonian Fluid ◽  
Thermal Instability ◽  
Viscous Fluids ◽  
Sufficient Condition ◽  
Vertical Magnetic Field ◽  
Stationary Convection ◽  
Stabilizing Effect ◽  
The Magnetic Field

Abstract The thermal instability of a layer of Rivlin-Ericksen elastico-viscous fluid acted on by a uniform vertical magnetic field is considered. For stationary convection, a Rivlin-Ericksen elastico-viscous fluid behaves like a Newtonian fluid. The magnetic field has a stabilizing effect. It is found that the presence of a magnetic field introduces oscillatory modes which were non-existent in its absence. The sufficient condition for the non-existence of overstability is also obtained.

scholarly journals The magnetic nature of umbra–penumbra boundary in sunspots

2018 ◽  
Vol 611 ◽  
pp. L4 ◽  
Author(s):  
J. Jurčák ◽  
R. Rezaei ◽  
N. Bello González ◽  
R. Schlichenmaier ◽  
J. Vomlel
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Field Component ◽  
Vertical Component ◽  
Vertical Magnetic Field ◽  
Intensity Threshold ◽  
The Magnetic Field ◽  
Magnetic Nature

Context. Sunspots are the longest-known manifestation of solar activity, and their magnetic nature has been known for more than a century. Despite this, the boundary between umbrae and penumbrae, the two fundamental sunspot regions, has hitherto been solely defined by an intensity threshold. Aim. Here, we aim at studying the magnetic nature of umbra–penumbra boundaries in sunspots of different sizes, morphologies, evolutionary stages, and phases of the solar cycle. Methods. We used a sample of 88 scans of the Hinode/SOT spectropolarimeter to infer the magnetic field properties in at the umbral boundaries. We defined these umbra–penumbra boundaries by an intensity threshold and performed a statistical analysis of the magnetic field properties on these boundaries. Results. We statistically prove that the umbra–penumbra boundary in stable sunspots is characterised by an invariant value of the vertical magnetic field component: the vertical component of the magnetic field strength does not depend on the umbra size, its morphology, and phase of the solar cycle. With the statistical Bayesian inference, we find that the strength of the vertical magnetic field component is, with a likelihood of 99%, in the range of 1849–1885 G with the most probable value of 1867 G. In contrast, the magnetic field strength and inclination averaged along individual boundaries are found to be dependent on the umbral size: the larger the umbra, the stronger and more horizontal the magnetic field at its boundary. Conclusions. The umbra and penumbra of sunspots are separated by a boundary that has hitherto been defined by an intensity threshold. We now unveil the empirical law of the magnetic nature of the umbra–penumbra boundary in stable sunspots: it is an invariant vertical component of the magnetic field.

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