It is kinematic property of the flow, and at each point it gives the angular velocity of the fluid particle. Now, once omega bar is this, this is a vector and it is the angular velocity of the fluid particle provides. Then with this we can go to what is vortex free motion rather we will call it vortex free motion, in case of a vortex free motion; that means, if omega bar is equal to 0; that means, fluid particle will not rotate and we call this as. So, if omega bar is 0 then we call this a vortex free motion, sometimes we call this as a irrotational motion same we call it as irrotational motion.