Formation of a rotational accretion column

We consider the problem of the flow produced by the accretion of gas from a rotating cloud onto a point gravitational source. It is shown that, for a cloud initially in uniform rotation, the effect of accretion is to produce a Taylor column in the cloud parallel to the rotation axis. Only gas within the column is accreted; the gas outside the column undergoes oscillatory flow, which is probably subject to shear instability. The column forms in approximately one-half rotation period from the time at which accretion begins. Its initial radius is determined by the accretion rate and the angular velocity of the cloud. Application of the results to the formation of Jupiter by accretion is discussed.