Penetrative turbulent Rayleigh-Benard convection in two and three dimensions

Penetrative turbulent Rayleigh-Bénard convection which depends on the density maximum of water near is studied using two-dimensional and three-dimensional direct numerical simulations. The working fluid is water near with Prandtl number. The considered Rayleigh numbers range from to. The density inversion parameter varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thicknesses increases with increasing, and the relationship between and seems to be independent of. The centre temperature is enhanced compared to that of Oberbeck-Boussinesq cases, as is related to with, is also found to have a universal relationship with which is independent of. Both the Nusselt number and the Reynolds number decrease with increasing, the normalized Nusselt number and Reynolds number also have universal relationships with which seem to be independent of both and the aspect ratio. The scaling exponents of and are found to be insensitive to despite of the remarkable change of the flow organizations. © 2019 Cambridge University Press.