RayleighBénardinstabiliteit

Rayleigh–Bénard convection is a type of natural convection that occurs in a horizontal layer of fluid heated from below and cooled from above. When the temperature difference ΔT between the plates is large enough, buoyancy drives fluid motion, organizing into patterns such as convection cells rather than remaining conductive.

The phenomenon is analyzed using the Boussinesq approximation, with key dimensionless numbers: the Rayleigh number Ra and the Prandtl number Pr. Ra = g α ΔT H^3 / (ν κ), where g is gravity, α thermal expansion coefficient, H layer thickness, ν kinematic viscosity, κ thermal diffusivity. Pr = ν/κ. If Ra is below a critical value, heat is transferred by conduction; above the threshold, convection begins. For a fluid between rigid plates, the onset occurs at Ra_crit ≈ 1708 for an infinitely wide layer.

Upon onset, the fluid forms regular convection cells, often roll-like patterns aligned with boundaries; as Ra increases, the flow can become time-dependent, develop wavy or chaotic motions, and ultimately turbulence. Pattern selection depends on boundary conditions, Pr, and geometric factors.

Rayleigh–Bénard convection is a canonical model for studying pattern formation, nonlinear dynamics, and heat transfer. It has analogues in geophysics and astrophysics, including mantle convection and stellar convection, and serves as a laboratory system for exploring transitions to turbulence.

Historically, the phenomenon was studied experimentally by Henri Bénard in the early 20th century, while Lord Rayleigh provided the theoretical framework in 1916 that established the stability criterion and dimensionless analysis.