Zur Elektrodynamik turbulent bewegter leitender Medien

Abstract

This paper deals with the behaviour of electromagnetic fields in electrically conducting media carrying out turbulent motions. The basis is formed by Maxwell’s and the corresponding constitutive equations inclusive Ohm’s law, all with the neglections usual in magnetohydrodynamics. Attention is directed to certain mean fields defined by statistical averaging. From the equations mentioned above, except Ohm’s law, one gets equations of the same kind for the mean fields. In Ohm’s law, however, the transition to the mean fields leads to an additional term , the averaged vector product of the fluctuations in the velocity of the medium and the magnetic flux density. The investigation of this term makes up the centre in the elaboration of an electrodynamics of mean fields. As a very simple example a homogeneous isotropic turbulence showing reflexion symmetry is considered. In this case makes allowance for the introduction of a modified electrical conductivity. If the reflexion symmetry is violated, describes an effect allowing a dynamo action. Furthermore, a general method for calculation of for arbitrary turbulent motions is developed, and a survey is given of the results which can be expected for some special kinds of turbulence.