Magnetized turbulent systems such as accretion disks can be numerically evolved for long times much more cheaply if axisymmetry is assumed. However, the field in such 2D simulations unphysically decays unless dynamo terms, representing the underlying nonaxisymmetry, are explicitly added to the induction equation. Thus far, such simulations have commonly assumed an isotropic, diagonal forms of the dynamo coefficient tensors. While this does yield magnetic fields that do not die off, it is unclear that it is necessarily correct. We test this assumption by azimuthally averaging data from a 3D black hole accretion simulation carried out by the IllinoisGRMHD code. Multiple local models, in which the dynamo electromotive force is a linear function of the local azimuthally averaged magnetic field and current, are tested, but no statistically reliable model could be attained. However, we do find that most of the turbulent kinetic and magnetic energy in the disk is not in the azimuthal mean, but in the RMS deviation, although the jet is mostly axisymmetric. As such, we conclude by discussing more general models that incorporate turbulent energy, dynamo electromotive force and momentum transport.

"Mean-field theories have become indispensable for studying astrophysical hydromagnetic flows which are otherwise hard to solve exactly. The proper modeling of turbulent velocity and magnetic fields, the validity of mean-field theories in astrophysical flows, and its accuracy and precision when compared to astronomical observations are the main focus of this thesis. In particular, the following studies on astrophysical dynamos and accretion disks are presented: (1) We construct a new model of galactic dynamos in which the turbulent kinetic energy and correlation time are coupled to the galactic differential rotation. We find that a strong differential rotation, while contributing to field amplification by line stretching, can ultimately reduce the overall saturated magnetic field strength compared to conventional models because it decreases the turbulent correlation time when its effect on turbulence is included. (2) We present an efficient, concise, physically grounded way of calculating turbulent transport coefficients through averaging the motion of a single fluid blob. The demonstrated configuration-space calculation gives the same result as much lengthier previously used Fourier-space methods. (3) We generalize dynamo quenching theory to anisotropic flows. Understanding how strong magnetic fields can become in astrophysical objects via dynamos is an active area of research, but quenching theories with predictive power so far have almost exclusively been restricted to systems in which turbulence is isotropic and homogenous. We generalize the isotropic dynamical quenching formulae to anisotropic a2 dynamos, where a new 'selective-damping-t' closure is proposed that conserves magnetic helicity as required, reduces to previous results when the turbulence is isotropic, and includes the full Lorentz force back reaction of the magnetic field for anisotropic flows. (4) We study the consequences of finite scale separation on validity and precision of mean-field dynamo theories. The governing equations for mean field dynamos are newly derived to properly include terms in higher order of the scale ratio between mean and fluctuating fields, and the intrinsic and filtering errors as two types of precision are identified. The formalism is then applied to a galactic dynamo model and its Faraday rotation measure, in order to quantify the precision of theoretical predictions. (5) We generalize the technique and approach for mean field precision calculation that we first worked out for dynamos and apply it to a hydrodynamic accretion disk model. The fluctuations in the local black-body emission are carefully averaged to obtain a predicted 1s error bar in the observed spectrum. This produces a precision error of the theory that must be included when assessing agreement or disagreement between theories and observations"--Pages ix-x.

A companion to earlier volumes (497, 536, 596, 617 and 631) of the Annals, this entry in the nonlinear astronomy series has contributions by most of the acknowledged experts in the field. They write on many topics, all of current interest. As several hold strong opposing views, this is a lively, important and timely publication.

Turbulence is believed to be of importance in molecular cloud formation as well as the star formation processes within them, such as accretion of matter onto young stars from the surrounding accretion disk. The kinetic viscosity associated with differentially rotating accretion disks is not believed to be strong enough to account for observed accretion rates. Turbulent motion, driven by the magnetorotational instability (MRI), may provide an anomalous viscosity well in excess of the kinetic viscosity alone leading to enhanced transport of angular momentum, resulting in a higher rate of accretion onto the forming star. We perform large-scale 3D multifluid simulations of a weakly ionised accretion disk and examine the development and saturation of the turbulence driven by the MRI. This numerical study is carried out using the multifluid MHD code HYDRA. An important effect of multifluid MHD is diffusion of the magnetic field. Simulations which isolate ambipolar and Hall diffusion are studied individually and comparisons between these and ideal MHD and full multifluid simulations are presented. The stresses (magnetic and kinetic) and an estimation of the anomalous viscosity are calculated for all models. From this information we can determine how accretion is affected by the multifluid physics in the presence of the MRI.

Large-scale magnetic fields have been observed in widely different types of astrophysical objects. These magnetic fields are believed to be caused by the so-called dynamo effect. Could a large-scale magnetic field grow out of turbulence (i.e. the alpha dynamo effect)? How could the topological properties and the complexity of magnetic field as a global quantity, the so called magnetic helicity, be important in the dynamo effect? In addition to understanding the dynamo mechanism in astrophysical accretion disks, anomalous angular momentum transport has also been a longstanding problem in accretion disks and laboratory plasmas. To investigate both dynamo and momentum transport, we have performed both numerical modeling of laboratory experiments that are intended to simulate nature and modeling of configurations with direct relevance to astrophysical disks. Our simulations use fluid approximations (Magnetohydrodynamics - MHD model), where plasma is treated as a single fluid, or two fluids, in the presence of electromagnetic forces. Our major physics objective is to study the possibility of magnetic field generation (so called MRI small-scale and large-scale dynamos) and its role in Magneto-rotational Instability (MRI) saturation through nonlinear simulations in both MHD and Hall regimes.

The increasing power of computer resources along with great improvements in observational data in recent years have led to some remarkable and rapid advances in astrophysical fluid dynamics. The subject spans three distinct but overlapping communities whose interests focus on (1) accretion discs and high-energy astrophysics; (2) solar, stellar, and galactic magnetic fields; and (3) the geodynamo, planetary magnetic fields, and associated experiments. This book grew out of a special conference sponsored by the London Mathematical Society with the support of EPSRC that brought together leading researchers in all of these areas to exchange ideas and review the status of the field. The many interesting problems addressed in this volume concern: