The equation of change for vorticity

(a) By taking the curl of the Navier-Stokes equation of motion (in either the D/Dt form or the ?/?t form), obtain an equation for the vorticity, w = [? x v] of the fluid; this equation may be written in two ways in which ? is a third-order tensor whose components are the permutation symbol ?ijk (see SA.2) and v = ?/p is the kinematic viscosity.

(b) How do the equations in (a) simplify for two-dimensional flows?

Dw = vw + [w [v] D Dt W vVw+le: (Vv). (Vv)|