Okay, here's the question:

Why is the pictured (bitmap file attached) vector field not continuous?

I think I understand the general idea, because I know that there's some point in the middle of the vector field where the vectors rotating around each point are going in the same direction. By this logic, there must be a vector normal to the outer curve.

What I don't understand is how I'm supposed to prove this using technical terms and/or formulas.

Thanks in advance to anyone who can help me out!