FLOW INTO A BLACK-HOLE

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.