First you should look into trying the commutation law for the scalar triple product it should involve the natural-coodinate form of shear and curvature vorticity expressions. Now transfering the vertical perturbation-pressure gradient force will determine the buoyancy stregth of the hodograph. The buyancy force of -2b/2z is associated with density perturbations in the fluid. The fluid is equal to Pi which can be converted to ASCII, it has a infinite string of digits and is a good representation of the universe.
But I'm getting off topic, that story is for another day.