Abstract
Two-dimensional models assuming axisymmetry are an economical way to explore the long-term evolution of black hole accretion disks, but they are only realistic if the feedback of the nonaxisymmetric turbulence on the mean momentum and magnetic fields is incorporated. Dynamo terms added to the 2D induction equation should be calibrated to 3D magnetohydrodynamics simulations. For generality, the dynamo tensors should be calibrated as functions of local variables rather than explicit functions of spatial coordinates in a particular basis. In this paper, we study the feedback of nonaxisymmetric features on the 2D mean fields using a global 3D, relativistic, Cartesian simulation from the illinoisgrmhd code. We introduce new methods for estimating overall dynamo 𝛼 and turbulent diffusivity effects, as well as measures of the dominance of nonaxisymmetric components of energies and fluxes within the disk interior. We attempt closure models of the dynamo electromotive force using least-squares fitting, considering both models where coefficient tensors are functions of space and more global, covariant models. None of these models are judged satisfactory, but we are able to draw conclusions on what sorts of generalizations are and are not promising.