Gellert Marcus, Rüdiger Günther
Astrophysikalisches Institut Potsdam, Potsdam, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046314. doi: 10.1103/PhysRevE.80.046314. Epub 2009 Oct 22.
The stability problem of hydromagnetic Taylor-Couette flows with toroidal magnetic fields is considered for various magnetic Prandtl numbers. Only the most uniform (but not current-free) field has been treated. For high enough Hartmann numbers, the toroidal field is always unstable due to the magnetic kink-type instability, which is stabilized by rigid basic rotation. The axial electric current, which drives the instability, is reduced by the electromotive force induced by the instability itself. Numerical simulations show that this electromotive force only depends on the molecular magnetic diffusivity rather than the viscosity. The resulting eddy diffusivity should be on the order of the molecular diffusivity for all the considered magnetic Prandtl numbers. If this is true also for very small magnetic Prandtl numbers (not possible to simulate) then one can use this effect to measure the eddy diffusivity eta(T) in a laboratory. In a sodium experiment (without rotation), a detectable potential difference of approximately 16 mV between top and bottom will result for a container of 1 m length and a gap width of 10 cm.
针对不同的磁普朗特数，研究了具有环形磁场的磁流体泰勒 - 库埃特流的稳定性问题。仅考虑了最均匀（但非无电流）的场。对于足够高的哈特曼数，由于磁扭结型不稳定性，环形场总是不稳定的，而刚性基本旋转可使其稳定。驱动不稳定性的轴向电流会因不稳定性本身感应出的电动势而减小。数值模拟表明，该电动势仅取决于分子磁扩散率而非粘度。对于所有考虑的磁普朗特数，由此产生的涡扩散率应与分子扩散率量级相同。如果对于非常小的磁普朗特数（无法模拟）也是如此，那么就可以利用这种效应在实验室中测量涡扩散率η(T)。在一个钠实验（无旋转）中，对于一个长度为1 m、间隙宽度为10 cm的容器，顶部和底部之间将产生约16 mV的可检测电位差。
