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Magnetorotational instability (MRI)-driven turbulence and dynamo phenomenaare analyzed using direct statistical simulations. Our approach begins bydeveloping a unified mean-field model that combines the traditionally decoupledproblems of the large-scale dynamo and angular-momentum transport in accretiondisks. The model consists of a hierarchical set of equations, capturing up tothe second-order cumulants, while a statistical closure approximation isemployed to model the three-point correlators. We highlight the web ofinteractions that connect different components of stress tensors -- Maxwell,Reynolds, and Faraday -- through shear, rotation, correlators associated withmean fields, and nonlinear terms. We determine the dominant interactionscrucial for the development and sustenance of MRI turbulence. Our general meanfield model for the MRI-driven system allows for a self-consistent constructionof the electromotive force, inclusive of inhomogeneities and anisotropies.Within the realm of large-scale magnetic field dynamo, we identify two keymechanisms -- the rotation-shear-current effect and therotation-shear-vorticity effect -- that are responsible for generating theradial and vertical magnetic fields, respectively. We provide the explicit(nonperturbative) form of the transport coefficients associated with each ofthese dynamo effects. Notably, both of these mechanisms rely on the intrinsicpresence of large-scale vorticity dynamo within MRI turbulence.

Unified treatment of mean-field dynamo and angular-momentum transport in magnetorotational instability-driven turbulence