Inferring flows from magnetic field constraints

Examplified by three case studies, we address the problem on how flow structures can be inferred from various magnetic field constraints. At first, we present the contactless inductive flow tomography in which we reconstruct the three-dimensional velocity field from externally measured induced magnetic fields. At second, we reconsider the optimization problem for the sodium flow in the Riga dynamo experiment. The third example concerns the special inverse spectral dynamo problem on how a spherically symmetric alpha^2 dynamo can become oscillatory.