In cartesian coordinates, a particle position is denoted by (x,y,z) and velocity field is denoted by (u,v,w). Similarly a particle position is denoted by (r,phi,z) in cylindrical coordinates. But how to represent the velocity field?
The velocity field in the cylindrical coordinates is presented by the three following components: the radial, the tangential (circumferential) and the axial i.e. along the z direction. See the textbook of Dixon for turbomachine classification.