6-2. Transport of Vorticity The vorticity vector obeys differential equations that resemble conservation equations, with convective, diffusive, and (sometimes) source terms. The following pertains to an incompressible, Newtonian fluid. (a) By taking the curl of each term in the Navier-Stokes equation, show that, in general DtDw=wv+2w Thus, (=/) is the diffusivity for vorticity as well as momentum. (b) For any planar flow, where wz is the only nonzero component of w, show that the result in part (a) reduces to DtDwz=2wz The absence of a homogeneous source term indicates that vorticity in planar flows originates only at surfaces. (c) Show that the result in part (b) can be derived also from Eq. (6.8-6) and the stream function equations in Table 6-12. Consider both types of planar flow