Both the net linear momentum and the net angular momentum of a developing swirling flow can play important parts in determining its ultimate form. To illustrate this the turbulent wake with both axial and swirl components of mean velocity is discussed, in particular for the two limiting cases of domination by linear momentum and domination by angular momentum. The dual conservation of axial and angular momentum implies that in general the mean swirl component decreases more rapidly downstream than does the defect in the mean axial velocity. Hence wakes with non-zero momentum flux ultimately have the familiar length scale $\sim Z^{\frac{1}{3}$ and velocity defect scale $\sim Z^{-\frac{2}{3}$. But in the wake of a self-propelled body the net drag is negligible and a swirl-dominated development can persist with length scale $\sim Z^{\frac{1}{4}$ and swirl velocity scale $\sim Z^{-\frac{3}{4}$.