We now have the field equations for the vorticity in a fluid with constant \(\rho\). We can see that \(\nu\nabla^2u\) will represent the rate of change of the \(\omega\) caused by diffusion of vorticity and \(\left(\omega\cdot\nabla\right)u\) representing the rate of vorticity caused by the stretching and tilting of vortex lines. We can also see that the central body forces for gravity and pressure are not found in this equation as they cause no torques. To relate this equation to the equation we will use to numerically solve our system we will relate the vorticity and velocity functions by the stream function such that,