I am looking for example applications of Green's theorem (in $2D$) that appeal to physicists or engineers. It's to come up with example for the divergence theorem in fluid dynamics, but finding a very accessible one for the rotation operator seems much more of a challenge.
Do you know a good example from physics that illustrates the physical meaning (one of them...) of the curl operator in $2D$?
My favorite way of looking at it is: if I fix a rotor at at flow field, then the curl will tell me the orientation and the speed of that rotor when subject to the flow field.