圆盘内稳态磁流体动力学（MHD）流动的普朗特-巴彻勒（Prandtl--Batchelor）与通量驱逐选择
Prandtl--Batchelor and flux-expulsion selection for steady MHD flows in a disk
浏览论文内容
中文总结 AI 辅助
该研究针对圆盘内稳态不可压缩MHD流动，在特定条件下构造收敛解，实现了普朗特-巴彻勒选择与通量驱逐的完全耦合，还通过论证解释了单涡族的核心结构。
中文摘要 AI 辅助
我们研究圆盘内稳态不可压缩磁流体动力学（MHD）流动的同时 vanishing-viscosity（ vanishing 译为“消失”）与 vanishing-resistivity（消失）极限。边界速度是平均角速度为α的刚性旋转的小非轴对称扰动，而规定的切向磁迹的平均值为β。假设α≠0且非阿尔文条件|α|≠|β|，我们构造了在紧致内部子圆盘上收敛到刚性旋转理想MHD核心的解，该核心具有恒定涡量和垂直于平面的电流密度。一种新的MHD-伍德（MHD--Wood）定律从边界数据确定两个核心旋转：速度核心由耦合的动理学-磁平衡选择，而磁核心由规定的平均环量确定。因此，零环量给出完全的内部磁通量驱逐，而非零环量在非轴对称模式被限制在薄边界层后留下均匀的磁旋转。这提供了普朗特-巴彻勒选择和通量驱逐的完全耦合实现；与经典运动学模型不同，磁场主动改变流动且不必是弱场。证明结合了周期MHD边界层的非阿尔文 coercive（ coercive 译为“ coercive”，此处保留）理论、两个场的全局匹配以及适配磁边界条件的耦合稳定性估计。单独的条件刚性论证使用精确的粘性恒等式和局部收敛，但无内部渐近展开，解释了更广泛的单涡族的相同核心结构。
英文摘要
We study the simultaneous vanishing-viscosity and vanishing-resistivity limit of steady incompressible MHD flows in a disk. The boundary velocity is a small nonaxisymmetric perturbation of a rigid rotation with mean angular speed \(α\), while the prescribed tangential magnetic trace has mean \(β\). Assuming \(α\neq0\) and the non-Alfvénic condition \(|α|\neq|β|\), we construct solutions converging on compact interior subdisks to a rigidly rotating ideal MHD core with constant vorticity and out-of-plane current density. A new MHD--Wood law determines the two core rotations from the boundary data: the velocity core is selected by a coupled kinetic--magnetic balance, whereas the magnetic core is fixed by the imposed mean circulation. Consequently, zero circulation gives complete interior magnetic expulsion, while nonzero circulation leaves a uniform magnetic rotation after the nonaxisymmetric modes are confined to a thin boundary layer. This provides a fully coupled realization of Prandtl--Batchelor selection and flux expulsion; unlike classical kinematic models, the magnetic field actively changes the flow and need not be weak. The proof combines a non-Alfvénic coercive theory for a periodic MHD boundary layer, global matching of the two fields, and a coupled stability estimate adapted to the magnetic boundary condition. A separate conditional rigidity argument, using exact viscous identities and local convergence but no interior asymptotic expansion, explains the same core structure for a broader single-eddy family.
