💨 Rayleigh-Bénard Convection

A fluid layer heated from below. When the Rayleigh number Ra = gβΔTH³/(νκ) exceeds the critical value (~1708), the conductive state becomes unstable and convection rolls form spontaneously.

Fluid Parameters

Buoyancy (Ra scale) 1.0 Viscosity ν 0.5 Diffusivity κ 0.3

Display

Velocity arrows Streamlines (ψ)

Statistics

Max |v|–

Max |ω|–

Time steps0

Temperature

Cold (Top)Hot (Bottom)

What It Demonstrates

Rayleigh-Bénard convection occurs when a fluid is heated from below. Below the critical Rayleigh number Ra_c ≈ 1708, heat flows by conduction only. Above Ra_c, the buoyant instability drives the formation of counter-rotating convection rolls (Bénard cells). This simulation solves the 2D incompressible Navier-Stokes equations with the Boussinesq approximation using the stream function–vorticity (ψ-ω) formulation.

How to Use

Increase Buoyancy to drive stronger convection — more and faster rolls will form
Increase Viscosity to damp the flow — cells become sluggish and may disappear
Toggle velocity arrows to see the circulation direction
Click Perturb to add random temperature noise and trigger new cell formation

Did You Know?

Henri Bénard first observed these convection cells in 1900 using spermaceti wax. Lord Rayleigh derived the stability criterion in 1916. Today, Rayleigh-Bénard convection underlies solar granulation, ocean thermohaline circulation, and Earth's mantle convection — all driven by the same instability.