Meet the forces inside a swirl. Move through time and watch what changes.
Paused · drag to exploreFixed camera · actual relative scale
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Starting shape
Scale locked · 1×
One particle. An entire journey.
A schematic path through the vortex. Move the tracer to see where it travels.
What makes a swirl slow down?
Experiment 1 of 3 · Make a prediction
Same moment. Different friction.
Later
00.250.500.750.995
More friction, faster slowing.
Speed proxy1.00 ×
Core radius100 %
Energy proxy100 %
Viscosity smooths differences in motion. Turn it up, then press play.
Schematic paths and toy decay. Not a fluid solver.
This first view uses speed = exp(−2νt) to illustrate friction, not an exact fluid solution. The paper views use the source’s leading-core scaling laws.
All numbers are relative to the start of the illustration. Colours distinguish regions, not calibrated speeds. The paper timeline begins at a developed core and stops before t = 1.
Speed rises. Energy falls.
The fast-moving region loses volume faster than its speed squared grows. Trace the curves to move through time.
Speed Core energy
Normalized time t · vertical scale is logarithmic · both start at 1×
Behind the flow.
THE IDEA IN EVERYDAY LANGUAGE
A tiny whirlpool. A very big question.
The Navier–Stokes equations balance motion, pressure, friction and outside forces. The puzzle is whether that balance always stays smooth.
↻01 / THE SPIN
Think of a skater.
Pulling the arms inward can increase rotation. In a fluid, inward transport can also strengthen a vortex, while viscosity redistributes momentum.
≋02 / THE FRICTION
Think of honey.
Viscosity is internal friction. It smooths differences in motion between neighbouring fluid layers. The question is whether this smoothing always wins.
∞03 / THE LIMIT
Think of a shrinking dot.
The paper claims a specially forced flow whose speed becomes unbounded in a shrinking region. “Blowup” is a mathematical singularity, not an explosion.
NO MATHS DEGREE REQUIRED
One equation. Four moving parts.
Tap a term to translate it.
=++
Motion changing motion. The acceleration of a fluid parcel includes both change over time and movement into a region with a different velocity.
Also: ∇·u = 0. Fluid does not pile up as it flows inward; it must flow out elsewhere.
HONEST ABOUT THE MODEL
An illustration of an idea. Not a proof in your browser.
This experience is based on Section 2 of Finite Time Blowup for Navier–Stokes, attributed to OpenAI in the supplied paper. It explains the claimed construction without validating its proof.
The paper views use normalized scaling laws with τ = 1 − t and h = 0.005: radius ∝ τ⁰·⁵; axial length ∝ τ⁰·⁴⁹⁵; speed ∝ τ⁻⁰·⁵⁰⁵; core volume ∝ τ¹·⁴⁹⁵; core energy ∝ τ⁰·⁴⁸⁵. Constants are set to one for illustration. These are leading-core scales, not exact whole-flow measurements.
Does this simulate the complete paper?
No. The three-dimensional paths and edge pulses are schematic. We do not solve the Navier–Stokes equations, reproduce the force or residual corrections, or model the full exterior. The timeline begins with a developed core; it omits the paper’s startup from rest. The display stops at t = 0.995, before the singular time t = 1.
Why is viscosity locked in the paper views?
The paper constructs different flows for each positive viscosity. Changing viscosity while holding this scene fixed would not reproduce those constructions. The first view instead uses a separate toy decay law, speed = exp(−2νt), to illustrate friction. It is not an exact Navier–Stokes solution.
Can a real fluid reach infinite speed?
The mathematical model treats fluid as a continuous medium. A singularity concerns that idealized model; it does not show that real water reaches infinite speed. Molecular effects and other physics matter outside the model’s range.
