Laminar-turbulent transition in an electromagnetically levitated droplet

During experiments on the MSL-1 (first microgravity science laboratory) mission of the space shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the nondeforming droplet, the resultant magnetohydrodynamic (MHD) flow inside the drop can be inferred from motion of impurity particulates on the surface. In the experiments, subsequent to melting, Joule heating produces a continuous reduction of viscosity of the fluid resulting in an acceleration of the flow with time. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal drop that undergo flow instabilities. As the fluid temperature rises, the amplitude of the secondary flow increases, and beyond a point, the tracers exhibit noncoherent chaotic motion signifying emergence of turbulence inside the drop. Assuming that the observed laminar-turbulent transition is shear-layer type, the internal structure of the toroidal loops is used to develop a semiempirical correlation for the onset of turbulence. Our calculations indicate that the suggested correlation is in modest agreement with the experimental data, with the transition occurring at a Reynolds number of 600.