Axial velocity - Knowlpedia

Relative to the $z$ -axis, the axial velocity is the scalar $u_z=u\cdot e_z$ ; its vector contribution is $u_z e_z$ . Along a particle trajectory, $dz/dt=u_z(t,X(t))$ .

Axial flow

A purely axial flow has $u=u_z e_z$ , while a general flow can have axial motion together with radial motion and swirl. “Axial outflow” describes motion away from a specified central region along the axis; its sign can differ on the two sides of that region.

For a purely axial differentiable flow, incompressibility requires $\partial_z u_z=0$ . Radial components can balance a nonzero axial derivative in a general incompressible flow.