A contactless method for velocity reconstruction in electrically conducting fluids

A contactless method for three-dimensional velocity reconstruction in electrically conducting fluids is presented. The method is based on the fact that an additional magnetic field is induced if the moving fluid is exposed to a primary magnetic field. By applying the primary magnetic field successively in two different directions and measuring the corresponding induced magnetic fields, the fluid velocity can be reconstructed if some kind of regularization of the velocity field is used. For a conducting fluid in a sphere, analytical expressions for the connection between spherical harmonics expansion coefficients of the induced magnetic fields on one side and of the defining scalars of the velocity on the other side are derived. For other geometries a general method for numerical inversion is proposed.