Velocity reconstruction in electrically conducting fluids from external electromagnetic measurements

A possibility for the determination of velocity fields in electrically conducting fluids is presented. Applying an external magnetic field, electric and magnetic fields are induced by the fluid motion. The electric potential can be measured at the walls and the magnetic field outside the fluid volume. The inverse problem of reconstructing the velocity from the measured quantities is solved using Tikhonov regularization. Several examples will be given to illustrate the potential of such type of velocity reconstruction. The problem of uniqueness is treated in detail for the spherical geometry. Our ultimate aim is to develop a fully contactless velocity measurement technique whereby measuring the electric potential at the wall can be avoided.