THE STREAM FUNCTION

The first animation is for the velocity field, here represented in term of the stream function.

On the left picture, with zero circulation, the velocity field is symmetric with respect to the x axis and the stagnation points lie on the intersections between the cylinder and the x axis.

The animation on the right shows the stream function as the circulation increases to a maximum and then decreases to zero. The uniform flow is from right to left and the circulation is counterclockwise. You can see the stagnation points moving towards the lower face of the cylinder as circulation increases.

The stream lines become closer on the upper face and more distant on the lower face, indicating an acceleration on the upper face and a deceleration on the lower face. In fact the mass flux (and then the discharge) in the stream tube defined by two adjacent stream lines is constant. When stream lines become closer the flow is accelerating and viceversa.