Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity

A two-dimensional direct numerical simulation of the natural convection flow of air in a differentially heated square cavity was performed for a Rayleigh number of 10 10 . The simulation was commenced from isothermal and quiescent conditions and was allowed to proceed to a statistical steady state. Two-dimensional turbulence resulted without the introduction of random forcing. Good agreement of mean quantities of the statistically steady flow is obtained with available experimental results. In addition, the previously proposed (George & Capp 1979) − $\frac{1}{3}$ and $+\frac{1}{3}$ temperature and velocity variations in the buoyant sublayer are confirmed. Other statistics of the flow are consistent with available experimental data. Selected frames from a movie generated from the computational results show very clearly turbulence production via the sequence from initial instability, proceeding through transition, and eventually reaching statistical steady state. Prominent large-scale structures are seen to persist at steady state.