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

摘要

In order to understand the onset of convective instability and multiple stable convection patterns of buoyancydrivennconvection of cold water near its density maximum in a vertical cylindrical container heated from below,na series of three-dimensional numerical simulations were performed. The aspect ratio of the container was 2 andnPrandtl number of cold water was 11.57. The sidewall was considered to be perfectly adiabatic, and the densityninversion parameter was fixed at 0.3. The result shows that the density inversion phenomenon in cold water hasnan important effect on the critical Rayleigh number for the onset of convection and the pattern formation at highernRayleigh numbers. When the Rayleigh number varies from 3×103 to 1.2×105, eight stable, steady convectionnpatterns are obtained under different initial conditions. The coexistence of multiple stable steady flow patterns isnalso observed within some specific ranges of the Rayleigh number.