Determination of the instantaneous geostrophic flow within the three-dimensional magnetostrophic regime.
Determination of the instantaneous geostrophic flow within the three-dimensional magnetostrophic regime.
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三维磁转区域内瞬时地转流的测定。
DOI：
10.1098/rspa.2018.0412
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Hardy CM
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文献类型：
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作者：
Hardy CM
泰勒（Taylor，1963年）在他的开创性著作中指出，外核内发电机作用的磁动力学相关极限是磁流体动力学方程中可以忽略的小惯性和粘性。在这个极限内，他证明了一个必要条件的存在，现在被称为泰勒约束，它要求圆柱平均洛伦兹力矩必须处处为零;满足这个条件的磁场被称为泰勒态。泰勒进一步指出，这个约束条件在时间上连续满足的要求，规定了地转流的演变，即圆柱平均的方位流。我们表明，泰勒原来的处方的地转流，满足给定的二阶常微分方程，是只适用于一个小的泰勒状态的子集。边界条件的不完全处理使他的方程一般是不正确的。在这里，通过适当考虑的边界，我们描述了一个概括的泰勒的方法，使正确的评价的瞬时地转流的任何三维泰勒状态。我们提出了第一个完整的球的例子，地转流驱动的非轴对称泰勒状态。虽然在轴对称的地转流承认一个温和的对数奇异的旋转轴上，在完全三维的情况下，我们表明，这是不存在的，事实上，地转流似乎无处不在的规则。
In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically-averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically-averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalisation of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any 3D Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully 3D case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.