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 ϖμν as the “twist”. This makes some sense because when we use it in Equation (288View Equation) we have not yet associated the four-velocity with the fluid flow.