RayleighZahl

Rayleighzahl, or Rayleigh number, is a dimensionless quantity in fluid dynamics that characterizes buoyancy-driven flow in a vertical fluid layer heated from below and cooled from above, as in Rayleigh–Bénard convection. It measures the balance between buoyancy forces that drive convection and the dissipative effects of viscosity and thermal diffusion. The Rayleigh number is defined as Ra = g α ΔT d^3 / (ν κ) = Gr × Pr, where g is gravitational acceleration, α the thermal expansion coefficient, ΔT the temperature difference between the plates, d the distance between plates, ν the kinematic viscosity, κ the thermal diffusivity, Gr the Grashof number, and Pr the Prandtl number.

Conduction remains stable when Ra is below a critical value; above this threshold, convective motion emerges. For a layer with rigid, no-slip boundaries, the onset occurs at Ra_crit ≈ 1708; with free-slip boundaries, Ra_crit ≈ 657.5. In higher Rayleigh number regimes, the flow can transition from laminar to cellular and then to turbulent, depending on geometry, boundary conditions, and the Prandtl number.

The Rayleigh number is used across geophysics, meteorology, astrophysics, and engineering to predict and analyze convection in contexts such as planetary mantles, stellar interiors, oceans, and industrial processes. It is named after Lord Rayleigh, who studied buoyancy-driven stability in fluid layers.