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

Let’s start with a classic vector field: the velocity field of a fluid in 3D space.

Div at any point is positive if more of the local flow is away from the point than towards it. In other words div tells you if the fluid is expanding or being compressed at that point.

Curl tells you if there is overall rotation in the flow of the fluid at a point. Anywhere in a whirlpool you will see non-zero curl.