Vorticity Equation when nu is not a constant

Sam

Folks:

I am interested in deriving the Vorticity equation in Cylindrical Coordinates (r,theta,z) with Theta symmetry and u_theta = 0.

The main problem is the viscosity cannot be treated as a constant but varies spatially. For a constant viscosity we get the simple equation,

dw/dt + u.Del(w) = nu Del^2(w)

where u = {u_r,0,u_z} and w = vorticity = {0,w,0}, where w = du_r/dz - du_z/dr.

I am interested in a similar vector equation when nu is not a constant. Could some one please help me or let me know where I can find it. Thanks.

Sam