Pattern formation of Rayleigh-Benard convection of cold water near its density maximum in a vertical cylindrical container

In order to understand the onset of convective instability and multiple stable convection patterns of buoyancy-driven convection of cold water near its density maximum in a vertical cylindrical container heated from below, a series of three-dimensional numerical simulations were performed. The aspect ratio of the container was 2 and Prandtl number of cold water was 11.57. The sidewall was considered to be perfectly adiabatic, and the density inversion parameter was fixed at 0.3. The result shows that the density inversion phenomenon in cold water has an important effect on the critical Rayleigh number for the onset of convection and the pattern formation at higher Rayleigh numbers. When the Rayleigh number varies from 3 x 10(3) to 1.2 x 10(5), eight stable, steady convection patterns are obtained under different initial conditions. The coexistence of multiple stable steady flow patterns is also observed within some specific ranges of the Rayleigh number.