A simple model is proposed to describe the flow into a black hole from
the turbulent flow of matter in initially circular orbits about the b
lack hole. Magnetic effects are not considered. The shear between flui
d elements at slightly different orbital radii causes turbulent eddies
to be formed. These eddies determine the dissipation rate of kinetic
energy into thermal energy. For approximately circular orbits, the mag
nitude of the gravitational potential energy is always equal to twice
the kinetic energy; the destruction of the latter resulting in a reduc
tion in the orbital radius and hence the potential energy. In this mod
el, the turbulent eddy rotation period is presumed to be determined by
the gradient in the gravity acceleration, leading to an eddy period p
roportional to the orbital period. If the flow speeds are supersonic b
ut not relativistic, then the turbulent eddy size is set by the produc
t of the eddy rotation period and the speed of sound. At a certain sma
ller radius, the orbital speeds and hence the dissipation rate are so
great that the speeds become relativistic and the molecular speed tend
s toward its limit c/root 3. Then the effective eddy size is controlle
d by the product of the eddy rotation period and the speed of light. U
sing these estimates for the important eddy size, the dissipation rate
, temperature, density and sinking speed as a function of the orbital
radius and the rate of mass flow into the black hole are derived.