Stability of melt flow due to traveling magnetic field in a closed ampoule

The linear three-dimensional instability of the flow due to a low frequency traveling magnetic field in a regular cylinder is studied numerically for height-to-diameter ratios in the range [0.5:2.5]. The first instability has the form of a non-rotating azimuthal wave with wave numbers between 1 and 6 depending on the aspect ratio. It is shown that the flow is stable if the Reynolds number is below 290. Even stronger stationary flows may be obtained in a flattened cylinder.