Numerical simulation of two-dimensional buoyancy-driven turbulence in a tall rectangular cavity

A computational study of natural convection of air in a tall rectangular cavity with 4:1 aspect ratio is conducted. In an effort to investigate the applicability of the Boussinesq approximation to turbulent flow simulation, the cavity is differentially heated from the sides and is insulated at the ends at a Rayleigh number of 10(9). Starting from quiescent and isothermal flow conditions, the flow is driven to turbulence without any artificial perturbations. The computer programme developed integrates the two-dimensional, time-dependent Navier-Stokes equations with the Boussinesq approximation and the energy equation by a time-accurate method on a stretched, staggered grid. The simulation proceeds to a statistically steady solution in which large-scale structures are found in the mean. Both mean and fluctuating quantities provide good agreement with experimental results.