What is divergence and curl?

Question

I have learned how to compute the two for a given vector field, but I don’t understand what the divergence and curl actually tells us.

In: 2

Answer 1

These visuals may help: https://books.physics.oregonstate.edu/GSF/visdivcurl.html

Divergence: how much more vectors point away from a point as they get farther from the point.
Curl: how much more vectors point in circles around a point as they get farther form the point.

Also see the bottom examples, where the “more” bit is missing and therefore thetres no divergence or curl.

Disclaimer: I’ve never learned calculus.

Edit: as for practical examples, an exploding firework has divergence, and a whirlpool in water has curl.