Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete de...Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics： Eulerian and La- grangian descriptions of three dimensional （3D） MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clar- ifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global con- straint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-fl limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results field notwithstanding the small resistivity. Strong Faraday in sheet dissipation, resistive heating and topological changes in the induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun＇s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.展开更多
We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the exi...We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.展开更多
基金The National Center for Atmospheric Researchis sponsored by the US National Science Foundation
文摘Magnetic field topology frozen in ideal magnetohydrodynamics （MHD） and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics： Eulerian and La- grangian descriptions of three dimensional （3D） MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clar- ifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global con- straint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-fl limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results field notwithstanding the small resistivity. Strong Faraday in sheet dissipation, resistive heating and topological changes in the induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun＇s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.
基金supported by National Natural Science Foundation of China(Grant No.11331005)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT13066)+1 种基金the Special Fund for Basic Scientific Research of Central Colleges(Grant No.CCNU12C01001)Excellent Doctorial Dissertation Cultivation Grant from Central Normal University
文摘We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.
