differentiation - Curl of a vector field

What is the physical interpretation of curl of a vector field? Just as divergence implies flux through a surface.

I mean if $\vec A$ is a vector field, what does $\left(\nabla \times \vec A \right)$ indicate?

Any mathematical help is welcome.

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Answer

Curl is a measure of the rate at which a(n infinitesimally small) region of fluid rotates about its own centre. You might measure it by inserting a (very) small paddlewheel in the fluid - the speed at which it rotates is the curl. For example, on a fairground Ferris wheel, the big wheel rotates (non-zero curl) the gondolas gyrate (zero curl). Swirl some beer in a glass; the beer rotates (non-zero curl), the glass gyrates (zero curl).

BTW, 'divergence' is flux over a closed curve/surface. If the curve/surface doesn't enclose a source or sink, and the fluid is incompressible, the divergence is zero. Essentially 'what goes in, comes out'