Inverse problems in magnetohydrodynamics: theoretical and experimental aspects

Abstract

We consider inverse problems related to velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to homogeneous dynamos in finite domains, which can be cast into a linear inverse problem in case that the magnetic Reynolds number of the flow is not too large. Some mathematical problems of the inversion, including the uniqueness problem in the sphere and a paradigmatic isospectrality problem for mean-field dynamos, are touched upon. For practical purposes, the inversion is carried out with the help of Tikhonov regularization using a quadratic functional of the velocity as penalty function. We present results of an experiment in which the three-dimensional (3D) velocity field of a propeller driven flow in a liquid metal is reconstructed by a contactless inductive measuring technique.

Keywords:

• Magnetohydrodynamics
• Flow measurement
• Tikhonov regularization

Acknowledgments

Financial support from German “Deutsche Forschungsgemeinschaft” under Grants No GE 682/10-1,2, GE 682/12-2, and in frame of the Collaborative Research Center SFB 609 is gratefully acknowledged.