  The formation and evolution of a wide class of astrophysical objects is
governed by turbulent, magnetized accretion disks. Understanding their secular
dynamics is of primary importance. Apart from enabling mass accretion via the
transport of angular momentum, the turbulence affects the long-term evolution
of the embedded magnetic flux, which in turn regulates the efficiency of the
transport. In this paper, we take a comprehensive next step towards an
effective mean-field model for turbulent astrophysical disks by systematically
studying the key properties of magnetorotational turbulence in
vertically-stratified, isothermal shearing boxes. This allows us to infer
emergent properties of the ensuing chaotic flow as a function of the shear
parameter as well as the amount of net-vertical flux. Using the test-field
method, we furthermore characterize the mean-field dynamo coefficients that
describe the long-term evolution of large-scale fields. We simultaneously infer
the vertical shape and the spectral scale dependence of these closure
coefficients, with the latter describing non-local contributions to the
turbulent electromotive force. Based on this, we infer a scale-separation ratio
of about ten for the large-scale dynamo. We finally determine scaling
properties of the mean-field dynamo coefficients. The relevant component of the
dynamo {\alpha} effect is found to scale linearly with the shear rate, as is
the corresponding turbulent diffusion, {\eta}. Together, these scalings allow
us to predict, in a quantitative manner, the cycle period of the well-known
butterfly diagram. This lends new support to the importance of the
{\alpha}{\Omega} mechanism in determining the evolution of large-scale magnetic
fields in turbulent accretion disks.
