Thermal convection below a conducting lid of variable extent: Heat flow scalings and two-dimensional, infinite Prandtl number numerical simulations

Theoretical heat flow scalings are presented for free thermal convection occurring below a conducting lid. Cases in which the lid covers the full extent of the convecting fluid and in which the lid has a variable lateral extent are treated. The scaling predictions are tested against a suite of two-dimensional numerical simulations that solve the full mathematical equations describing infinite Prandtl number thermal convection occurring below a conducting lid. The scaling predictions and simulation results show reasonably good agreement for Rayleigh numbers greater than 10⁷. The scaling predictions are also tested against previous numerical simulations of finite Prandtl number thermal convection below a laterally uniform lid. Scaling predictions and simulations results again show reasonable agreement.