Incompressible Viscous Flows

Intrinsic Coordinates

 It is sometimes simpler to work with a coordinate system, which is attached to the surface of revolution. For the body of revolution shown Figure 5, consider the unit vectors

Thus

The stream function for axisymmetric flows may now be introduced as

That is

Figure 5. Schematics of intrinsic coordinate systems.

The vorticity is now given as

where

Note that in terms of