Spiraling vortex
Particles spiral inward through vortex velocity fields, tracing the invisible structure of rotational flow. Click to place vortex centers — left-click for counterclockwise, right-click for clockwise. Multiple vortices interact, creating complex swirling patterns from simple superposition of irrotational flow fields.
vθ = Γ / (2πr) | vr = −α / r | Γ = circulation, α = inward drift
The vortex velocity field
A point vortex in 2D fluid dynamics generates a velocity field where fluid elements circle the center with tangential velocity inversely proportional to distance: vθ = Γ / (2πr), where Γ is the circulation strength. This is an irrotational flow everywhere except the singular center — the curl of the velocity field is zero, yet everything rotates.
Superposition and interaction
Because the governing equations (for inviscid, irrotational flow) are linear, multiple vortex fields simply add together. Two co-rotating vortices orbit each other; a vortex-antivortex pair translates as a unit. The complex patterns you see here are nothing but vector addition of simple 1/r velocity fields.
The inward spiral
Real vortices (like bathtub drains or tornadoes) have an inward radial component in addition to the tangential circulation. The decay rate parameter controls this radial drift: how quickly particles spiral toward the center rather than orbiting indefinitely. When particles reach the core, they’re respawned at random positions to maintain a constant particle count.
In nature
Vortex dynamics appear everywhere: hurricanes, Jupiter’s Great Red Spot, the trailing vortices behind aircraft wings, and the von Kármán vortex streets that form behind obstacles in flowing fluid. The mathematics here is the same that Helmholtz formalized in 1858 and that Kelvin proved circulation is conserved.