Three-dimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field

The paper presents a numerical stability analysis of the flow driven by an alternating (ac) magnetic field in an electromagnetically levitated liquid metal droplet. The basic axisymmetric flow is found to become unstable at Reynolds numbers in the order of 100. The critical Reynolds number Re_c and the corresponding most unstable azimuthal wave number m are found for several configurations of the magnetic field depending on the skin-depth δ. For a uniform external' ac magnetic field the azimuthal wave number of the most unstable mode is m = 3. An additional steady (dc) magnetic field imposed along the axis of symmetry increases the stability of the flow.