Eddy diffusivity from hydromagnetic Taylor-Couette flow experiments

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 η_T in a laboratory. In a sodium experiment (without rotation), a detectable potential difference of ∼16 mV between top and bottom will result for a container of 1 m length and a gap width of 10 cm.