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首页> 外文期刊>Journal of Experimental and Theoretical Physics >Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field
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Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field

机译：在强势场中旋转的粘性球形层的磁流体动力学

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An analytic solution is given for classical magnetohydrodynamic (MHD) problem of almost rigid-body rotation of a viscous, conducting spherical layer of liquid in an axisymmetric potential magnetic field. Large-scale flows bounded by rigid spheres are described for the first time in a new approximation. Two problems are solved: (1) in which both spheres are insulators and (2) in which the outer sphere is an insulator and the inner sphere a conductor. Axially symmetric flows and azimuthal magnetic fields are maintained by a slightly faster rotation of the inner sphere. The primary regeneration takes place in the boundary and shear MHD layers. The shear layers, described here for the first time, smooth out the large gradients at the boundaries of the MHD structures encompassed by them. There is essentially no azimuthal magnetic field inside these original structures, which are bounded by potential contours tangent to the spheres. An applied constant magnetic field creates a rigid MHD structure outside an axial cylinder tangent to the inner sphere. Inside the cylinder the rotation is faster and the meridional flux depends on height. A magnetic dipole forms a structure tangent to the outer equator. Outside the structure, the rotation is also rigid-body when both spheres are insulators. When a conducting sphere is present, the liquid rotates differentially everywhere, while near the axis and inside the MHD structure, it rotates even faster than the inner sphere. The last example of a general solution is a quadrupole magnetic field. In this case, two equatorially symmetric MHD structures are formed which rotate together with the inner sphere. Outside the structures, as in the most general case, the rotation is differential, the azimuthal magnetic field falls off as the first power of the applied field, and the meridional flux falls off as the square of the field in the first problem, and as the cube in the second.
机译：针对经典的磁流体动力学（MHD）问题，给出了一种解析解决方案，该问题涉及在轴对称势场中的液体的球形导电层的几乎刚体旋转。首次以新的近似值描述了由刚性球体界定的大规模流动。解决了两个问题：（1）两个球都是绝缘体，（2）外球是绝缘体，内球是导体。内球的旋转稍快，可以保持轴对称的流动和方位磁场。主要再生发生在边界层和剪切MHD层中。剪切层，这里首次描述，消除了它们所包围的MHD结构边界处的大梯度。在这些原始结构内部基本上没有方位角磁场，该磁场由与球体相切的潜在轮廓所限制。施加的恒定磁场会在与内球面相切的轴向圆柱体外部创建刚性MHD结构。在圆柱体内旋转更快，子午通量取决于高度。磁偶极子形成与外赤道相切的结构。在结构外部，当两个球都是绝缘体时，旋转也是刚体。当存在导电球体时，液体在各处均以不同的方式旋转，而在轴附近和MHD结构内部，它的旋转速度甚至比内球体还要快。通用解决方案的最后一个例子是四极磁场。在这种情况下，形成了两个赤道对称的MHD结构，它们与内球一起旋转。在结构外部，如最一般的情况一样，旋转是微分的，方位磁场随着所施加场的第一幂而下降，子午磁通随磁场在第一问题中的平方而下降。第二个立方体。

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