scholarly journals Shear flow instabilities in shallow-water magnetohydrodynamics

2016 ◽  
Vol 788 ◽  
pp. 767-796 ◽  
Author(s):  
J. Mak ◽  
S. D. Griffiths ◽  
D. W. Hughes
Keyword(s):  
Magnetic Field ◽  
Shear Layer ◽  
Shallow Water ◽  
Froude Number ◽  
Water System ◽  
Shear Layers ◽  
Linear Instability ◽  
Horizontal Shear ◽  
Shallow Water Magnetohydrodynamics ◽  
The Magnetic Field

Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as Høiland’s growth-rate bound and Howard’s semi-circle theorem, are extended to this shallow-water system for quite general flow and field profiles. In the limit of long-wavelength disturbances, a generalisation of the asymptotic analysis of Drazin & Howard (J. Fluid Mech., vol. 14, 1962, pp. 257–283) is performed, establishing that flows can be distinguished as either shear layers or jets. These possess contrasting instabilities, which are shown to be analogous to those of certain piecewise-constant velocity profiles (the vortex sheet and the rectangular jet). In both cases it is found that the magnetic field and stratification (as measured by the Froude number) are generally each stabilising, but weak instabilities can be found at arbitrarily large Froude number. With this distinction between shear layers and jets in mind, the results are extended numerically to finite wavenumber for two particular flows: the hyperbolic-tangent shear layer and the Bickley jet. For the shear layer, the instability mechanism is interpreted in terms of counter-propagating Rossby waves, thereby allowing an explication of the stabilising effects of the magnetic field and stratification. For the jet, the competition between even and odd modes is discussed, together with the existence at large Froude number of multiple modes of instability.

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.

Linear and nonlinear barotropic instability of geostrophic shear layers

1991 ◽  
Vol 224 ◽  
pp. 49-76 ◽  
Author(s):  
L. J. Pratt ◽  
J. Pedlosky
Keyword(s):  
Shear Layer ◽  
Nonlinear Evolution ◽  
Shear Layers ◽  
Linear Instability ◽  
Barotropic Instability ◽  
Reasonable Estimate ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Geostrophic Shear

The linear, weakly nonlinear and strongly nonlinear evolution of unstable waves in a geostrophic shear layer is examined. In all cases, the growth of initially small-amplitude waves in the periodic domain causes the shear layer to break up into a series of eddies or pools. Pooling tends to be associated with waves having a significant varicose structure. Although the linear instability sets the scale for the pooling, the wave growth and evolution at moderate and large amplitudes is due entirely to nonlinear dynamics. Weakly nonlinear theory provides a catastrophic time ts at which the wave amplitude is predicted to become infinite. This time gives a reasonable estimate of the time observed for pools to detach in numerical experiments with marginally unstable and rapidly growing waves.

Magnetosensitive Polymer Composites and Effect of Magnetic Field Directivity on their Properties

2016 ◽  
Vol 251 ◽  
pp. 3-7 ◽  
Author(s):  
Egidijus Dragašius ◽  
Evguenia Korobko ◽  
Zoya Novikava ◽  
Elena Sermyazhko
Keyword(s):  
Magnetic Field ◽  
Mechanical Properties ◽  
Magnetic Properties ◽  
Polymer Composites ◽  
Matrix Material ◽  
Vertical Shear ◽  
Horizontal Shear ◽  
Dispersed Particles ◽  
The Magnetic Field ◽  
Ferromagnetic Particles

Mechanical properties of polymer composite materials, containing ferromagnetic small dispersed particles of carbonyl iron that create structures along force lines of the magnetic field have been investigated. In paper the influence of the polymer matrix material and the orientation of ferromagnetic particles inside it on the properties of polymer composites are considered in the regimes of horizontal shear, vertical shear and periodical (sinusoidal) deformation of the samples. Magnetic properties at the change of magnetic field induction B in the range of 0 to 1 T are determined.

The evolution of magnetic flux ropes in sheared plasma flows

2000 ◽  
Vol 64 (1) ◽  
pp. 41-55 ◽  
Author(s):  
J. M. SCHMIDT ◽  
P. J. CARGILL
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Shear Layer ◽  
Cross Section ◽  
Circular Cross Section ◽  
Flux Rope ◽  
Plasma Pressure ◽  
Magnetic Flux Ropes ◽  
Flux Ropes ◽  
The Magnetic Field

The evolution of magnetic flux ropes in a sheared plasma flow is investigated. When the magnetic field outside the flux rope lies parallel to the axis of the flux rope, a flux rope of circular cross-section, whose centre is located at the midpoint of the shear layer, has its shape distorted, but remains in the shear layer. Small displacements of the flux-rope centre above or below the midpoint of the shear layer lead to the flux-rope being expelled from the shear layer. This motion arises because small asymmetries in the plasma pressure around the flux-rope boundary leads to a force that forces the flux rope into a region of uniform flow. When the magnetic field outside the flux rope lies in a plane perpendicular to the flux-rope axis, the flux rope and external magnetic field reconnect with each other, leading to the destruction of the flux rope.

scholarly journals EFFECT OF A MAGNETIC FIELD ON RHEOLOGICAL PROPERTIES OF GELATIN - WATER SYSTEM

2020 ◽  
pp. 155-162
Author(s):  
Сергей Анатольевич Вшивков ◽  
Елена Витальевна Русинова ◽  
Ахмад Сафуан Абу Салех
Keyword(s):  
Magnetic Field ◽  
Rheological Properties ◽  
Isoelectric Point ◽  
Water System ◽  
Solvent System ◽  
First Time ◽  
The Magnetic Field

Изучено влияние магнитного поля на вязкость системы желатин - вода при разных рН среды. Впервые для системы полиэлектролит - вода показано, что магнитное поле приводит к увеличению вязкости системы в 1.5 раза при рН=7.2, но к уменьшению вязкости системы в 2.5 раза в изоэлектрической точке при рН=4.7. The effect of a magnetic field on the viscosity of the gelatin-water system at different pH of the medium is studied. For the first time it is shown for a polyelectrolyte - solvent system that the magnetic field increases the viscosity of the system by 1.5 times at pH = 7.2, but decreases the viscosity of the system by 2.5 times at the isoelectric point at pH = 4.7.

Thermodynamic Model for Vapor-Liquid Phase Equilibrium in an Exerted Magnetic Field

2012 ◽  
Vol 550-553 ◽  
pp. 2704-2711
Author(s):  
Hong Bo Tang ◽  
Min Qing Zhang
Keyword(s):  
Magnetic Field ◽  
Phase Equilibrium ◽  
Liquid Phase ◽  
Magnetic Fields ◽  
Thermodynamic Model ◽  
Water System ◽  
Liquid Equilibrium ◽  
Vapor Liquid Equilibrium ◽  
The Magnetic Field ◽  
Vapor Liquid

Many researchers have shown a great deal of interest in the effects that magnetic fields have when applied in chemical reactions, crystallization, magnetic separation of materials, magnetic levitation, materials processing, and wastewater treatment. However, surprisingly little research has been done on the effects of magnetic fields on the vapor-liquid equilibrium and the thermodynamic model for vapor-liquid phase equilibrium. The influence of magnetic fields on vapor-liquid equilibrium of binary heterogeneous azeotrope was investigated with ethanol-water in this paper. It was found that the vapor-liquid equilibrium of an ethanol-water system is influenced by the external magnetic field, but that the azeotropic point of the ethanol-water system is not changed by the magnetic field when the magnetic intensity reaches 0.8 T. Rather, the exerted magnetic field reduces the equilibrium temperature and shortens the distance between T-x curve and T-y curve in T-x-y diagram of the vapor-liquid equilibrium of the ethanol-water system. A thermodynamic model for vapor-liquid phase equilibrium in the exerted magnetic field was derived theoretically, based on the fundamental thermodynamic theory. The results show that the logarithm value of the ratio of the composition of the certain component in a magnetic field to that without the magnetic field is proportional to the magnetic susceptibility of the solution, and to the square of magnetic field intensity. This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

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.

Kelvin-Helmholtz instabilities of supersonic, magnetized shear layers

1986 ◽  
Vol 35 (3) ◽  
pp. 375-392 ◽  
Author(s):  
S. Roy Choudhury
Keyword(s):  
Magnetic Field ◽  
Finite Thickness ◽  
Vortex Sheet ◽  
Shear Layers ◽  
Step Function ◽  
Pressure Gradients ◽  
Contour Plots ◽  
Perturbation Frequency ◽  
Ideal Magnetohydrodynamic ◽  
The Magnetic Field

The linear stability of finite-thickness, compressible, ideal magnetohydrodynamic sheared flows along the z direction, with a magnetic field in the (y, z) plane is studied. This paper extends earlier work with the magnetic field parallel to the flow. The present formulation also includes the effects of density and pressure gradients in the equilibrium shear layer. Analytical solutions are obtained for strongly and weakly magnetized shear layers having a vortex sheet profile (where the velocity is a step function). For an equilibrium layer having a linear velocity profile, and uniform pressure and density, contour plots of the real and imaginary parts of the perturbation frequency (corresponding to unstable waves) are numerically generated in (wavenumber, Mach number) plane using a shooting technique. The structure of two distinct regimes of instability (unstable standing modes and unstable travelling modes) is mapped out for various values of the inverse plasma beta, and various angles of propagation of the mode to the flow and the magnetic field.

The Research of Permanent Magnetic Field Treatment on the Iron & Steel Industry Circulating Water Impacts of Stability Index

2012 ◽  
Vol 236-237 ◽  
pp. 265-272
Author(s):  
Dong Kui Li ◽  
Li Li Jiang ◽  
Hai Bin Zuo ◽  
Zan Lin Tan
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Magnetic Field Intensity ◽  
Water System ◽  
Stability Index ◽  
Water Velocity ◽  
Circulating Water ◽  
Circulating Water System ◽  
The Magnetic Field

Iron & steel industrial circulating water system there is a scaling and corrosion problems, the system fouling or corrosion may be judged by monitoring the water quality Stability index. In this paper, we use the magnetic treatment equipment developed by us in the laboratory to simulate the physical treatment process of magnetic field on the industrial circulating water system, and the experimental data is analysis by two-way ANOVA. We have found that: when the circulating water is tap water: (1) if water velocity is 0.6m/s, the magnetic field intensity, magnetic treatment time has a significant influence on the PSI, PSI decline with the magnetic field processing time to increase , and the PSI as well as the time have a good linear relationship; (2) if water velocity is 1.2m/s, the magnetic field strength has a significant influence on the PSI; (3) if water velocity is 2.3m/s, the magnetic field intensity and time has a significant effect for the PSI; when the magnetic field strength is 3.4T, and reaction time is 5 h, PSI is close to 6, water quality is stable; (4) speed and the magnetic field there is an interaction for PSI, that the magnetic field strength and speed of circulating water changes in the PSI also. When the circulating water is CaCl2 and Na2CO3 aqueous solution configuration: as water velocity is 1.2m/s and well as 2.3m/s, the magnetic field strength and time has a significant effect on the PSI .The results show that: iron & steel industrial circulating water system be deal with by proper the magnetic field treatment can control the PSI. The appropriate range PSI of the circulating water can reduce the fouling and corrosion damage, it is significant to develop circulating water system quality control model.

Effects of Heating on Two-Dimensional Mixing Layers

1997 ◽  
Vol 119 (3) ◽  
pp. 180-183
Author(s):  
N. Butuk ◽  
S. R. Gollahalli
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Room Temperature ◽  
Shear Layers ◽  
Mixing Layers ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Streamwise Direction ◽  
The Mean

Transverse profiles of temperature and the mean velocities in the streamwise direction in a horizontal shear layer are presented. The variation of vorticity thickness along the streamwise coordinate is examined for the cases when both streams were at room temperature and when the top stream was heated to 360 K. The similarity of the velocity field is observed only near the plane of the interface of the two streams in both cases. The vorticity thickness-velocity ration correlation agrees well with the data available for the isothermal shear layers. The heating of one stream was not found to significantly influence the vorticity thickness, which is explained by the counteracting influences of viscosity and density changes.

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