circulation

How much a vector field pushes along a closed curve, totaled all the way around — the paddle-wheel reading summed over an entire loop.

For $C$ parametrized by $\mathbf{r}(t)$ with unit tangent $\mathbf{T}=\mathbf{r}'/|\mathbf{r}'|$ , circulation is $\oint_C \mathbf{F}\cdot \mathbf{T}\,ds = \oint_C \mathbf{F}\cdot d\mathbf{r} = \oint_C P\,dx+Q\,dy$ — the line integral of $\mathbf{F}$ dotted against the tangential direction around a closed loop.

Examples

A hose spraying water outward in all directions has zero circulation around any circle centered at it, since nothing spins.
For $\mathbf{F}=(x,y)$ around the unit circle: circulation $=0$ (pure radial flow has no spin).