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Abstract

Penetrative turbulent Rayleigh-Bénard convection which depends on the density maximum of water near 4 • C is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is water near 4 • C with Prandtl number P r = 11.57. The considered Rayleigh numbers Ra range from 10 7 to 10 10 . The density inversion parameter θ m varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thickness (F λ = λ θ t /λ θ b ) increases with increasing θ m , and the relationship between F λ and θ m seems to be independent of Ra. The centre temperature θ c is enhanced compared to that of Oberbeck-Boussinesq (OB) cases, as θ c is related to F λ with 1/θ c = 1/F λ + 1, θ c is also found to have a universal relationship with θ m which is independent of Ra. Both the Nusselt number N u and the Reynolds number Re decrease with increasing θ m , the normalized Nusselt number N u(θ m )/N u(0) and Reynolds number Re(θ m )/Re(0) also have universal relationships with θ m which seem to be independent of both Ra and the aspect ratio Γ . The scaling exponents of N u ∼ Ra α and Re ∼ Ra β are found to be insensitive to θ m despite of the remarkable change of the flow organizations.