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Vorticity in polar coordinates
Referring to Section 2.4.3 where polar coordinates were introduced, the corresponding definition of vorticity in polar coordinates is
g, dq, 1 dqn
^ r dr r ffl
Note that consistent with its physical interpretation as rate of rotation, the units of vorticity are radians per second.
Fig. 2.26
2.7.3 Rotational and irrotational flow
It will be made clear in Section 2.8 that the generation of shear strain in a fluid element, as it travels through the flow field, is closely linked with the effects of viscosity. It is also plain from its definition (Eqn (2.76)) that vortidty is related to rate of shear strain. Thus, in aerodynamics, the existence of vortidty is associated with the effects of viscosity.* Accordingly, when the effects of viscosity can be neglected, the vortidty is usually equivalently zero. This means that the individual fluid elements do not rotate, or distort, as they move through the flow field. For incompressible flow, then, this corresponds to the state of pure translation that is illustrated in Fig. 2.26. Such a flow is termed irrotational flow. Mathematically, it is characterized by the existence of a velodty potential and is, therefore, also called potential flow. It is the subject of Chapter 3. The converse of irrotational flow is rotational flow.
