  When gas accretes onto a black hole, at a rate either much less than or much
greater than the Eddington rate, it is likely to do so in an "adiabatic" or
radiatively inefficient manner. Under fluid (as opposed to MHD) conditions, the
disk should become convective and evolve toward a state of marginal
instability. The resulting disk structure is "gyrentropic," with convection
proceeding along common surfaces of constant angular momentum, Bernoulli
function and entropy, called "gyrentropes." We present a family of
two-dimensional, self-similar models which describes the time-averaged disk
structure. We then suppose that there is a self-similar, Newtonian torque and
that the Prandtl number is large. This torque drives inflow and meridional
circulation and the resulting flow is computed. Convective transport will
become ineffectual near the disk surface. It is conjectured that this will lead
to a large increase of entropy across a "thermal front" which we identify as
the effective disk surface and the base of an outflow. The conservation of
mass, momentum and energy across this thermal front permits a matching of the
disk models to self-similar outflow solutions. We then demonstrate that
self-similar disk solutions can be matched smoothly onto relativistic flows at
small radius and thin disks at large radius. This model of adiabatic accretion
is contrasted with some alternative models that have been discussed recently.
The disk models developed in this paper should be useful for interpreting
numerical, fluid dynamical simulations. Related principles to those described
here may govern the behaviour of astrophysically relevant, magnetohydrodynamic
disk models.
