Physical Motivation for Curl and Divergence

[ninevolt]

So I know what they are and I've been given some really vague and weak interpretations, but I want to build up my intuition and know more about the specifics of curl and divergence. To my understanding now I know that

curl is similar to a paddle wheel spinning in a direction dependent on the vector field, if the vector field lines are water currents.

Divergence is the amount of stuff leaving directed along the normal


So as you can see my understanding of these fundamental operators is crap, and I need a lot of help. Tips on how you interpret curl and rigorous definitions welcome (everything welcome)

 

[fresh_42]

I find the explanations on Wikipedia not so bad. You can also look at the pages in other languages and let Google translate them for you, so you will find a variety of different wordings.

Roughly speaking is the curl the rotation of a vector field and divergence measures attractors and repellers or the absence of them.