On the uniqueness of velocity reconstruction in conducting fluids from measurements of induced electromagnetic fields

The problem of velocity reconstruction in conducting fluids from measurements of induced magnetic fields and electric potentials is discussed in spherical geometry. Under the special case that the externally applied magnetic field is uniform and homogeneous throughout the fluid, the non-uniqueness problem is treated in detail. Assuming kinetic energy minimization for the moving fluid, it is shown that the velocity field can be reconstructed completely.