  (abridged) MHD turbulence is known to exist in shearing boxes with either
zero or nonzero net magnetic flux. However, the way turbulence survives in the
zero-net-flux case is not explained by linear theory and appears as a purely
numerical result. Aims: We look for a nonlinear mechanism able to explain the
persistence of MHD turbulence in shearing boxes with zero net magnetic flux,
and potentially leading to large-scale dynamo action. Method: Spectral
nonlinear simulations of the magnetorotational instability are shown to exhibit
a large-scale axisymmetric magnetic field, maintained for a few orbits. The
generation process of this field is investigated using the results of the
simulations and an inhomogeneous linear approach. Results: The mechanism by
which turbulence is sustained in zero-net-flux shearing boxes is shown to be
related to the existence of a large-scale azimuthal field, surviving for
several orbits. In particular, it is shown that MHD turbulence in shearing
boxes can be seen as a dynamo process coupled to a magnetorotational-type
instability.
