It is important to note the difference between the vorticity formed from the momentum and the corresponding quantity
in terms of the velocity. They differ because of the entrainment, and one can show that while the former is
conserved along the flow, the latter is not. To avoid confusion we refer to
as the “twist”. This makes some
sense because when we use it in Equation (288) we have not yet associated the four-velocity with the fluid
flow.