Synergetics pp 85-93 | Cite as

Velocity Field in the Rayleigh-Benard Instability: Transitions to Turbulence

  • M. Dubois
  • P. Bergé
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 3)


When an horizontal layer of pure fluid, depth of which is d, is submitted to a temperature gradient ΔT, as shown on Fig.1, motion sets in, when ΔT exceeds a critical value ΔTc. The properties of this motion are related to the Rayleigh number
$${R_{a}} = \frac{{\partial g.\Delta T{d^{3}}}}{{vk}} ]$$
where α, ν and κ are respectively the volumic expansion coefficient, the cinematic viscosity and the thermal diffusivity of the fluid: the Rayleigh number takes into account the different mechanisms involved in the convective motion: buoyancy forces, viscous damping, and thermal relaxation, according to the fact that, here, we are dealing only with fluid layers under rigid-rigid horizontal boundaries. (In this case, Rac = 1707).


Rayleigh Number Fluid Layer Convective Motion Hexagonal Pattern Asymmetric Roll 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • M. Dubois
  • P. Bergé

There are no affiliations available

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