Page 414 - Introduction to Continuum Mechanics

398 Vorticrty Transport Equation for Incompressible Viscous Fluid with a Constant Density

Reduce, from Eq. (6.23.5) the vorticity transport equation for the case of two-dimensional
flow.
Solutions. Let the velocity field be:

Then

becomes

That is, the angular velocity vector( £ / 2) is perpendicular to the plane of flow as expected.
Now,

Thus, Eq. (6.23.5) reduces to the scalar equation

where