What is the relationship between angular speed and curl in different systems?

[Gonzolo]

Hi, I'm looking for a clear descripion of what a curl is. From what I understand, the curl of a point in flowing water can conceptually be measured by placing the center of a paddle-wheel at the point. The vector direction is then given by the rotation axis when it spins the fastest and orientation by the right-hand rule. Is the value given by the angular speed of the wheel or twice the angular speed or neither, and why?

In the three following systems, which seem to me to be 3 possibilities of a similar case, which has the greatest curl? :

-Water flow in a bowl when I make circles with my finger at the edge of the bowl. (angular speed greater with greater radius)

-A rotating LP (angular speed constant with radius)

-Water flow in a bowl when I make circles with a rod at the center (angular speed smaller with geater radius).

Thanks.

 

[fresh_42]

Curl is a rotation of a vector field, which is again a vector field, so it is curl at a certain point not of a point and the neighborhood of this point cannot be neglected. I think there can be not much added to what Wikipedia says:

The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation.

So curl is a rotation of a fluid mathematically described.