Nonlocal dynamo waves in a turbulent shear flow

Abstract. The turbulent dynamo action in a shear flow is considered by making use of a quasilinear approximation and neglecting the back-reaction of a generated magnetic field on turbulence. The shear can stretch turbulent magnetic field lines in such a way that turbulent motions may become suitable for the generation of a large-scale magnetic field even in the absence of any stratification. There is no α-effect present in our computations. The nonlocal integral representation for the mean electromotive force is derived, which is valid even if the turbulent length scale is comparable to that of the mean field. The basic result is that the presence of shear changes the type of the equation governing the mean magnetic field so that the latter indeed can be generated even in the absence of rotation or large-scale stratification of turbulence. To this end, however, if the turbulence field has a monotonously falling (“turbulence-type”) spectrum, a rather strong shear is needed. For Kepler disks the instability condition reads τcorr > 2τrot/π, which might be fulfilled in the transition layers between star and disk. A system, on the other hand, consisting of random waves, large-scale magnetic fields and mean-field shear flow can never be stable.