The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean-field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-type dynamo. In view of this application the second-order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$ effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.

Coherent structures in the distribution of the Faraday rotation measure (RM) of extragalactic radio sources are isolated using wavelet transformation

We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from nonhelical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand, the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law $k^{-5/3}$ for a nonhelical turbulence, to a non-Kolmogorov scaling law $k^{-7/3}$ for a maximally helical turbulence. In the latter case we find that the characteristic time of the turbulence is not the turnover time but a time based on the helicity injection rate. We also analyze the results in terms of helical modes decomposition. For a maximally helical turbulence one type of helical mode is found to be much more energetic than the other one, by several orders of magnitude. The energy cascade of the most energetic type of helical mode results from the sum of two fluxes. One flux is negative and can be understood in terms of a decimated model. This negative flux, however, is not sufficient to lead an inverse energy cascade. Indeed, the other flux involving the least energetic type of helical mode is positive and the largest. The least energetic type of helical mode is then essential and cannot be neglected.

Context.The origin of the spiral pattern of magnetic fields in disc galaxies is an open question.Aims.Comparison of the regular magnetic field orientation with the gaseous spiral arm pitch angles can tell us whether spiral shock compression is responsible for the magnetic spirals. We also wish to see whether the ridges of different components of the ISM show the large-scale, systematic shifts expected from density wave theory.Methods.We have developed a technique of isolating elongated structures in galactic images, such as spiral arms, using anisotropic wavelets and apply this to maps of the CO, infrared and radio continuum emission of the grand-design spiral galaxy M 51. Results.Systematic shifts between the ridges of CO, infrared and radio continuum emission that are several long are identified, as well as large variations in pitch angle along spiral arms, of a few tens of degrees. We find two types of arms of polarized radio emission: one has a ridge close to the ridge of CO, with similar pitch angles for the CO and polarization spirals and the regular magnetic field; the other does not always coincide with the CO arm and its pitch angle differs from the orientation of its regular magnetic field.Conclusions.The offsets between ridges of regular magnetic field, dense gas and warm dust are compatible with the sequence expected from spiral density wave triggered star formation, with a delay of a few tens of millions of years between gas entering the shock and the formation of giant molecular clouds and a similar interval between the formation of the clouds and the emergence of young star clusters. At the position of the CO arms the orientation of the regular magnetic field is the same as the pitch angle of the spiral arm, but away from the gaseous arms the orientation of the regular field varies significantly. Spiral shock compression can explain the generation of one type of arm of strong polarized radio emission but a different mechanism is probably responsible for a second type of polarization arm.