Visualization of Three Vector Fields with Different Divergence and Curl

The two demonstrations collectively illustrate the geometric meaning of the divergence and curl operators. The initial static visualization clearly differentiated vector fields: the position vector ( $x$ ) displayed a pure outward flow, confirming its non-zero divergence (source-like behavior) and zero curl (no rotation). Conversely, the fields $v_1$ and $v_2$ exhibited circulation, visually confirming their zero divergence (solenoidal flow) and non-zero curl. The second, dynamic animation reinforced this by showing particles actively following the flow lines of $v_2$, dynamically proving that a non-zero curl value directly corresponds to the fluid's constant local rotation or "vorticity" in the plane.

🎬Narrated Video

https://youtu.be/1pKdyYC8dyk

🏗️Structural clarification of Poof and Derivation

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🗒️Downloadable Files - Recursive updates (Feb 10,2026)

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