Recently, I dipped my spoon into my tea. I saw that as I dipped my spoon into my tea, two vortices formed at both edges of the spoon. I guess this is similar to vortices forming at the end of aeroplane wings. Here I assume both vortices have equal strength and according to Kelvins circulation theorem, the sum of circulation must equal zero in my system (my cup of tea).
However, I noticed that if I stirred my tea first and then dipped my spoon into my tea (whilst the fluid was rotating), two vortices would still form (for a very short period of time) and then they would combine together (since the fluid was still rotating from when I stirred my tea). They would form one vortex. However, I would like to ask why the two vortices don't cancel out? Are they not of equal strength?
Best Answer
Your fluid was rotating, so you could, in a sense, see it as a vortex, to begin with. So, you can see the spoon-induced vortices as canceling out, and what's left is just the original vortex (probably more visible with vortex stretching). Another way is to think of the underlying vorticity weakening one vortex while strengthening the other.