Transition to oscillatory natural convection of water near its density maximum in a tall enclosure: Assessment of three-dimensional effects

Numerical simulations have been performed for three-dimensional natural convection of water near its maximum-density (cold water) inside rectangular enclosures with differential heating at the vertical (left and right) walls. The horizontal (top and bottom) walls and the lateral (front and rear) walls are taken as insulated. Computations are performed for the buoyancy-driven convection of cold water with density inversion parameter θ_m = 0.5 in the enclosures with aspect ratio (height/width) A_y = 8 and depth ratios (depth/width) A_z = 0.5, 1, and 2. The influence of the depth ratio on the onset of oscillatory convection in a cold-water-filled enclosure is investigated. The presence of the lateral walls tends to suppress the onset of unsteadiness in the convective flow. The main features of the oscillatory convection flow and temperature fields as well as the instability mechanism in the three-dimensional enclosure were similar to those found in the two-dimensional model. However, there exists a strong three-dimensionality in the spatial distribution of the fluctuation amplitude. With the decrease of the depth ratio, the damping effect of the lateral walls becomes increasingly pronounced, leading to a reduced heat transfer rate.