Confinement of rotating convection by a laterally varying magnetic field
Confinement of rotating convection by a laterally varying magnetic field
复制标题
横向变化磁场对旋转对流的限制
DOI：
10.1017/jfm.2017.286
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
V. Gopinath
中科院分区：
文献类型：
--
作者：
B. Sreenivasan;V. Gopinath
基于旋转对流的球壳发电机模型表明，切线圆柱体内的流动以离轴羽流为主，该羽流从内核边界延伸到高纬度并向西漂移。早期的研究解释了这种羽流的形成是由于均匀轴向磁场的影响，该磁场显着增加了旋转平面层中对流的长度尺度。然而，快速旋转的发电机模拟表明，切线圆柱体内的磁场具有严重的横向不均匀性，可能会影响孤立羽流的出现。在我们的发电机模拟中增加旋转速率（通过减少艾克曼数 $E$ ）会产生逐渐变细的羽流，这些羽流似乎正在寻找磁场最强的位置。受此结果的启发，我们研究了受到横向变化的轴向磁场影响的快速旋转流体层中对流的线性起始。选择笛卡尔几何，其中有限维度 $(x,z)$ 模拟柱坐标中的 $(\unicode[STIX]{x1D719},z)$。场的横向不均匀性产生了一种独特的不稳定模式，其中对流完全局限于峰值场区域。即使场强（由 Elsasser 数 $\unicode[STIX]{x1D6EC}$ 测量）很小并且粘度控制对流的最小长度尺度，磁场也会导致流动的局域化。球壳发电机模拟中切线圆柱内出现孤立羽流的最低瑞利数与平面层线性磁对流模型中的粘性模式瑞利数非常一致。模拟中羽流形成的最低 Elsasser 数明显高于线性磁对流的起始值，这表明具有空间变化场的粘性-磁模式转变点被移动到更高的 Elsasser 数。横向变化的磁场对粘性模式对流的局部激发提供了在地球切线圆柱体内形成孤立羽流的机制。因此，地核中的极地涡旋可能是非轴对称的。更一般地说，这项研究表明，空间变化的磁场强烈控制旋转对流的结构，其瑞利数与其非磁性值相差无几。
Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the length scale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Increasing the rotation rate in our dynamo simulations (by decreasing the Ekman number $E$ ) produces progressively thinner plumes that appear to seek out the location where the field is strongest. Motivated by this result, we examine the linear onset of convection in a rapidly rotating fluid layer subject to a laterally varying axial magnetic field. A Cartesian geometry is chosen where the finite dimensions $(x,z)$ mimic $(\unicode[STIX]{x1D719},z)$ in cylindrical coordinates. The lateral inhomogeneity of the field gives rise to a unique mode of instability where convection is entirely confined to the peak-field region. The localization of the flow by the magnetic field occurs even when the field strength (measured by the Elsasser number $\unicode[STIX]{x1D6EC}$ ) is small and viscosity controls the smallest length scale of convection. The lowest Rayleigh number at which an isolated plume appears within the tangent cylinder in spherical shell dynamo simulations agrees closely with the viscous-mode Rayleigh number in the plane layer linear magnetoconvection model. The lowest Elsasser number for plume formation in the simulations is significantly higher than the onset values in linear magnetoconvection, which indicates that the viscous–magnetic mode transition point with spatially varying fields is displaced to much higher Elsasser numbers. The localized excitation of viscous-mode convection by a laterally varying magnetic field provides a mechanism for the formation of isolated plumes within the Earth’s tangent cylinder. The polar vortices in the Earth’s core can therefore be non-axisymmetric. More generally, this study shows that a spatially varying magnetic field strongly controls the structure of rotating convection at a Rayleigh number not much different from its non-magnetic value.