High Rayleigh number flows in a cubical enclosure

High Rayleigh number (Ra) natural convective flows in cubical enclosures were investigated using Direct Numerical Simulation (DNS). Here the bottom of the cavity was heated while the top was cooled, each maintained at a different constant temperature, with the sidewalls insulated. The Prandtl number was maintained at 2.5 and the Ra varied between 106 and 10(8). In order to observe the transition to turbulence with increasing Ra, power spectrum slopes were compared with Kolmogorov's -5/3 rule for turbulent flows. At the higher Ra studied, the flows showed characteristics typically attributed to "chaotic" flows. However, the transition to full turbulence was not observed, which is expected around Ra similar to 10(9) and may not be predicted using DNS with the state-of-the-art computing technology.