Bénard convection
A 2D cross-section of fluid heated from below and cooled from above. As the temperature difference grows, the fluid transitions from still conduction to organized convection rolls, and eventually to chaotic turbulence. Thousands of particles trace the flow, colored by their temperature.
Ra = g α ΔT L³ / (ν κ) — the Rayleigh number governs the onset of convection
About this lab
Rayleigh-Bénard convection is one of the most studied phenomena in fluid dynamics. When a thin layer of fluid is heated from below, the hot fluid at the bottom becomes less dense and wants to rise, while the cooler fluid above is denser and wants to sink. At low temperature differences, heat transfers through conduction alone — the fluid stays still.
Once the temperature difference exceeds a critical threshold (the critical Rayleigh number, Ra ≈ 1708), buoyancy overcomes viscous resistance and the fluid spontaneously organizes into counter-rotating convection rolls. These are the Bénard cells — elegant structures where hot fluid rises on one side and cool fluid descends on the other.
As the Rayleigh number increases further, the orderly rolls become unstable. Secondary instabilities introduce oscillations, and eventually the flow becomes fully turbulent. This transition from order to chaos through a sequence of bifurcations was one of the early successes of chaos theory, studied extensively by Edward Lorenz (whose famous "butterfly" attractor was derived from a simplified model of convection).
This simulation uses a velocity field derived from a stream function with sinusoidal convection rolls, perturbed by noise at high Rayleigh numbers. The particles are advected through this field and their temperatures evolve based on their vertical position, creating the characteristic warm-rising, cool-sinking pattern visible in the colors.