Vorticity

Vorticity, labelledis the tendency of fluid to spin. It may vary from point to point in a fluid, and with time. It arises because different parts of the fluid are in relative motion, so any fluid element between these two parts exhibits a tendency to spin.

In the bottom diagrams, even though the fluid is moving to the right, the fluid still has vorticity.

More formally, vorticity can be related to the amount of rotation in a fluid. The average vorticity in a small region of fluid flow is equal to the circulation Γ around the boundary of the small region, divided by the areaof the small region

By letting the areatend to zero, we can define the vorticity at a point as

Vorticity is a vector field and is can also be defined as the curl of the velocity field:

is perpendicular to the velocity of the fluid at each point in the fluid because it is equal to

Example: Find the vorticity of the vector field