A new approach to the nonlinear stability of viscous flow in a coplanar magnetic field

2016 ◽  
Vol 40 (10) ◽  
pp. 3415-3423 ◽  
Author(s):  
Lanxi Xu ◽  
Wanli Lan
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Nonlinear Stability ◽  
New Approach

scholarly journals New approach to describe two coupled spins in a variable magnetic field

2021 ◽  
Author(s):  
Yury Belousov ◽  
Roberto Grimaudo ◽  
Antonino Messina ◽  
Agostino Migliore ◽  
Alessandro Sergi
Keyword(s):  
Magnetic Field ◽  
Variable Magnetic Field ◽  
New Approach

On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Broad Class ◽  
Mhd Flow ◽  
Two Dimensional ◽  
Energy Principle ◽  
Inviscid Flows ◽  
Virtual Displacement ◽  
Euler Flows ◽  
Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

An application of high-temperature superconductors YBCO to magnetic separation

2017 ◽  
Vol 31 (25) ◽  
pp. 1745001 ◽  
Author(s):  
Qiudong Guo ◽  
Peng Zhang ◽  
Lin Bo ◽  
Guibin Zeng ◽  
Dengqian Li ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Magnetic Separation ◽  
High Magnetic Field ◽  
Low Cost ◽  
Rapid Development ◽  
High Temperature Superconductors ◽  
New Approach ◽  
Industrial Areas ◽  
Ybco Tape

With the rapid development of manufacturing technology of high temperature superconductive YB[Formula: see text]Cu3O[Formula: see text] YBCO materials and decreasing in cost of production, YBCO is marching into industrial areas with its good performances as source of high-magnetic field and rather low cost in reaching superconductivity. Based on analysis of the performance of high temperature superconductors YBCO and development of technology in superconductive magnetic separation both home and abroad, we propose a new approach of taking YBCO tape to make a solenoid as the source of a high magnetic field of magnetic separatior of ores. The paper also looks into the future of the YBCO high temperature superconductive magnetic separation from the perspective of technology and cost, as well as its applications in other industries.

scholarly journals Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January, 1993

2000 ◽  
Vol 18 (10) ◽  
pp. 1257-1262 ◽  
Author(s):  
A. V. Pavlov ◽  
T. Abe ◽  
K.-I. Oyama
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electron Temperature ◽  
Field Line ◽  
Electron Density ◽  
Magnetic Field Line ◽  
New Approach ◽  
Additional Heating ◽  
Vibrational Levels ◽  
The Magnetic Field

Abstract. We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20–30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N2(v > 0) and O2(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v > 0) and O2(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.Key words: Ionosphere (ionospheric disturbances; ionosphere-magnetosphere interactions; plasma temperature and density)  

scholarly journals Trajectory control of PbSe–γ-Fe2O3nanoplatforms under viscous flow and an external magnetic field

2010 ◽  
Vol 21 (17) ◽  
pp. 175702 ◽  
Author(s):  
Lioz Etgar ◽  
Arie Nakhmani ◽  
Allen Tannenbaum ◽  
Efrat Lifshitz ◽  
Rina Tannenbaum
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Viscous Flow ◽  
Trajectory Control

IMPACT OF ALIGN MAGNETIC FIELD ON VISCOUS FLOW WITH COMBINED CONVECTIVE TRANSPORT

2021 ◽  
Vol 23 (1) ◽  
pp. 127-137
Author(s):  
Siti Farah Haryatie Mohd Kanafiah ◽  
Hussein Ali Mohammed Al-Sharifi
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Convective Transport

The stability of viscous flow between rotating cylinders in the presence of a magnetic field. II

1961 ◽  
Vol 262 (1311) ◽  
pp. 443-454 ◽  
Keyword(s):  
Magnetic Field ◽  
Viscous Flow ◽  
Rotating Cylinders ◽  
Counter Rotation ◽  
Angular Velocities ◽  
The Stability

The theory developed in an earlier paper (Chandrasekhar 1953) is extended to allow for counter-rotation of the two cylinders. Explicit results are given for the case when the two cylinders rotate in opposite directions with equal angular velocities.

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.

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