Three-dimensional numerical simulation of rotating spoke pattern in an oxide melt under a magnetic field

On the surface of various oxide melts under a vertical magnetic field, the rotating spoke pattern appears. In order to provide a first basic view of this phenomenon, a series of three-dimensional numerical simulations of LiNbO 3 melt flow in a crucible (47 mm φ × 46 mm H) under a uniform vertical magnetic field were performed. In this model, the oxide melt was assumed to be a dielectric fluid with a uniform electric charge density c e 0. The Marangoni effect was also taken into account. The simulations indicated that the spoke pattern is caused by the Marangoni instability and the rotating motion is driven by the Lorentz force caused by the interaction between the vertical magnetic field and the radial motion of charged fluid which is driven by the Rayleigh–Marangoni convection in the crucible. A charge density of 0.1 C/m 3 is sufficient to express the experimentally observed rotating spoke patterns on the LiNbO 3 melt which were reported by Miyazawa et al. (1996).