Calculus
Divergence
Divergence measures the net flow out of an infinitesimal region. Drop a tiny material patch into the flow: positive divergence makes it swell, negative divergence squeezes it, and zero divergence keeps its area fixed even as the flow stretches and shears it.
∇ · F at probe+2.00
Flux ÷ area+2.00
Patch area1.00×
Local behaviorexpanding
Drag the ring to move the probe. The teal blob is a small material patch carried along by the flow, not a bundle of field arrows. Its area change is the divergence.
What to observe
- At a source more flow leaves the patch than enters, so its area grows and ∇ · F > 0. Flip the strength negative and the very same field becomes a sink that swallows the patch.
- Pick Saddle. The patch stretches one way and squeezes the other, yet its area stays constant: violent deformation can still have zero divergence (incompressible flow).
- In the Variable field, drag the probe around. Divergence islocal: the tinted background shows teal source regions and amber sink regions in the same field. Watch the patch swell or shrink as you drag between them.
Shortcuts: space run/pause · s step · r reset · f fullscreen