Two interactive 3D visualizations are designed to contrast key principles in fluid dynamics, offering distinct operational modes to highlight the difference between flow circulation and local spin. The simulation demonstrates that a complex appearance of rotation does not always equate to fluid vorticity: the Rigid-Body Rotation is fundamentally rotational ( $\omega \neq 0$ ), possessing constant, uniform vorticity, whereas the Irrotational Vortex is defined by zero vorticity ( $\omega=0$ ), where particles orbit but do not spin internally. Functionally, the tool offers modes that contrast volume conservation, such as Divergence-Free (swirling, constant volume) versus Divergent (spreading, volume increasing), all while enabling analytical evaluation through Real-Time Momentum Tracking of $x, y$, and $z$ components. User control is streamlined via a Toggle Mode Button and Reset Simulation Button, complemented by Dynamic Descriptions that instantly explain the physics of the current flow state.
This fluid model (two demos) illustrates the fascinating distinction between local kinematics and global dynamics: while the first demo reveals a state of "Rigid-Body Rotation"-where every fluid parcel spins with an identical, constant vertical vorticity-the second demo demonstrates how spatial orientation dictates "Orbital Momentum." Because the cubic volume is positioned off-center relative to the rotation axis, its angular momentum is not merely a reflection of internal spin ( $L_3$ ), but also a result of the massive lever arms that create "tilting" components ( $L_1, L_2$ ) as the fluid translates upward. Together, these demos prove that even a uniform, divergence-free flow can exhibit complex, asymmetric global properties simply based on where in space the observation "cube" is placed.
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